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8013812

W a r d , J a m e s R e g in a l d

THE RELATIONSHIP BETWEEN CLIENT CHARACTERISTICS AND THOSE
NON-MEDICAL HOME CARE SERVICES AND COSTS ASSOCIATED WITH
THE LONG-TERM CARE OF THE IMPAIRED AGED IN MICHIGAN

PH.D.

Michigan Slate University

University
Microfilms
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1979

18 Bedford Row, London WC1R 4EJ, England

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THE RELATIONSHIP BETWEEN CLIENT CHARACTERISTICS AND
THOSE NON-MEDICAL HOME CARE SERVICES AND COSTS ASSOCIATED
WITH THE LONG-TERM CARE OP THE IMPAIRED AGED IN MICHIGAN

By

James Reginald Ward

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OP PHILOSOPHY

Department of Agricultural Economics

1979

ABSTRACT

THE RELATIONSHIP BETWEEN CLIENT CHARACTERISTICS AND
THOSE NON-MEDICAL HOME CARE SERVICES AND COSTS ASSOCIATED
WITH THE LONG-TERM CARE OP THE IMPAIRED AGED IN MICHIGAN
By
James Reginald Ward

A major problem in the provision of non-medical long­
term care services to the chronically ill or disabled patient
lies in making the assignment of appropriate types of ser­
vices to match the condition or needs of the patient.

A

second problem lies in identifying key predictors of service
costs to facilitate improved cost control.
Support services delivered in the client's home are
primarily non-medical and in this study include light clean­
ing, meal preparation, home maintenance and repair, shopping,
transportation, non-nursing personal services, and others.
In 1975-76 these services were supplied to over 10,000 low
income Michigan residents by the Adult Chore Service Program
of the Michigan Department of Social Services.

The services

were proportedly assigned to clients on the basis of attributes
such as the clients' functional status (e.g., mobility, dexteri­
ty, sensory perception, comprehension and ability to manage

James Reginald Ward
*

home); socio-economic status (e.g., age, sex, location, in­
come, relationship to provider and living arrangement); and
medical status.
In part, this study was addressed to determining if
patterned relationships could be detected between client at­
tributes and the services assigned to compensate for client
impairments.

If such relationships were detected, it should

be possible to infer that for any client profile, a range of
services is appropriate.

Knowing that range, it should then

be possible, by analyzing costs, to identify the appropriate
service or service mix of lowest cost.

A cost analysis was

conducted to determine which attributes significantly explained
variation in cost.
The sample of 628 cases was randomly divided into two
groups, a 'training set* of 428 cases and a

'test set.'

An

information theory based algorithm called entropy minimax
was used in an attempt to detect patterned relationships be­
tween a client's attributes and the services assigned to them.
For example, given a specific client profile, it Was antici­
pated the probability of services assigned to that profile
could be determined.

No such relationships were discovered.

These results could be explained by;

1) the failure of social

workers to assign systematically services to clients on the
basis of the client profile; or 2) no such relationship im­
plies the lack of a systematic relationship between needed,
and therefore, assigned services; or 3) inappropriate specifi­
cation of the attributes and services may have obscured the
the real relationship.

James Reginald Ward
The results of a regression analysis using three
models in which the endogenous variables were, cost per month
of service, hours of service provided per month, and cost
per hour respectively, tended to confirm the pattern detec­
tion results.

Detailed functional status variables explained

very little of the variation in costs and hours.

More aggre­

gated functional status indicators such as comprehension and
ability to manage the home, explained more monthly cost
variation than mobility, dexterity or sensory perception.
The form of the functional status variable explaining over
40 percent of the variation in monthly costs was specified
according to services.

The most significant explanatory

service categories were light cleaning, meal service and non­
nursing personal service.

Location was the most significant

socio-economic status category explaining monthly cost.
Categories of variables best explaining hours of service per
month and service costs per hour were relationship of the
provider to the client and the living management between
them.

Medical status was not a significant variable in any

of the models.
The results of this research indicate further work
is necessary on relating client attributes to services received.
A shortcut to achieving this goal might be to classify patients
according to service needs.

The other attributes could be

used as an accountability check on the program and its workers.

DEDICATION

To my wife Sheila, for her patience and encourage­
ment ,
and
my children Kerry and Laura, whose joyous young
presence opportunely dovetailed with the discre­
tionary times afforded by academic studies,
and
my mother, who despite her own judgement of what
her son should be doing, has always been supportive
of, if at a loss to explain, what he actually does.

ii

ACKNOWLEDGMENT

A diverse group of people contributed to this work.
Lois Libby induced me to become involved in the local
health planning systems and the thorny issue of long-term
care.

Jackie Argyle and Diane Emling of the Michigan

Department of Social Services were helpful in describing
the Chore Service Program and providing data.
The initial conceptualization of the thesis was
assisted by Dr. Paul Ginsburg.

The assistance of Mr. Bill

Schonbein and his associate, Dave Gift, were of enormous
value in understanding the intricacies of the entropy mini­
max procedures and their applications.

Bob Stevens has

always been supportive of my activities, both academic and
otherwise, in the health care system.
Alan Schmid has had a pervasive influence on this
research stemming from his insightful course on public
policy and his active search for deeper insights into vari­
ous schools of economic theory from an institutional per­
spective.
When the inevitable obstacles thwarted progress on
this study, or methods and results were unclear, the thesis
committee chairman, Lester Manderscheid, unfailingly and
carefully came to my assistance.
iii

For such help and for his

fairness, integrity, and flexibility as my program advisor,
I will always be in his debt.
Thanks are also due to Alyne Tennis and Sue Smith
for the typing of this dissertation.

TABLE OF CONTENTS
Page
LIST OF T A B L E S .......................................... viii
LIST OF F I G U R E S ....................................
CHAPTER 1

1

Problem Statement ......................
Project Justification ..................
Project Goals and Methodology .........
Description of Chapters ...............

1
4
6
9

P R O B L E M .............

11

Principal Dilemmas
....................
Research Priorities ....................
Investigative Boundaries
..............
Problems Associated with the Study
. .
V a r i a b l e s ..............................

11
18
22
23
25

LITERATURE REVIEW .. '......................

27

I.
II.
III.
IV.

NATURE AND SCOPE OF
I.
II.
III.
IV.
V.

CHAPTER 3

I.
II.
III.
IV.
V.
VI.
CHAPTER 4

x

..............

PROJECT ORIENTATION

CHAPTER 2

.

I n t r o d u c t i o n ..........................
An Overview of Approaches to Cost
A n a l y s e s ...................
A Model for the Analysis of LongTerm C a r e ............................
The Detection of Patterned Relation­
ships Between Patient Profiles
and S e r v i c e s .......................
Empirical Findings
....................
C o n c l u s i o n ............................

DESCRIPTION OF ADULT CHORESERVICE
P R O G R A M ..................................
I.
II.

Overview of Chore Service Program . . .
Data B a s e ..............................

v

27
27
30
37
39
40
41
41
48

Page
CHAPTER 5

TECHNICAL DESIGN AND SUBSTANCE OF COST
A N A L Y S I S ................................
I.
II.

I n t r o d u c t i o n ..........................
Technical Design ......................

50
51

A.

Endogenous Variables
.............
1. Total Cost Per Month (TCM)
. .
2. Cost Per Hour (CH)
...........
3. Total Hours per Month of
Service Received (THM)
...

53
53
54

Exogenous Variables ...............
1. Functional Status Categories
.
a.
"Cardinal11 and binary
forms of the functional
status variable .........
b. Functional status classi­
fied according to
services received . . . .
2. The Socio-Economic Status
V a r i a b l e ...................
3. The Medical Status Variable . .

55
55

B.

C.
D.
III.
CHAPTER 6

III.
IV.
V.
VI.

55

56
62
68
74

Economic M o d e l ...................
Econometric Specification and
A s s u m p t i o n s .....................

76

C o n c l u s i o n ............................

87

THEORY UNDERLYING THE ENTROPY MINIMAX
PATTERN DETECTION ALGORITHM AND ITS
UTILITY IN DETERMINING THE RELATIONSHIPS
BETWEEN CLIENT ATTRIBUTES AND SERVICES
.
I.
II.

50

85

88

I n t r o d u c t i o n ..........................
88
Choice of Methodology to Detect
Relationships Between Sets of
Multiple Outcomes and Sets of
Characteristic Attributes ...........
88
Background on the Entropy Minimax
A l g o r i t h m ............................
91
The Entropy Minimax Procedure .........
95
The Mathematics of Entropy Minimax
. . 105
The Application of the Entropy
Minimax Algorithm in Pattern
D e t e c t i o n .............................. 112
A. Selection of Outcome Classes
. . . 112
B. Choice of A t t r i b u t e s .............120

vi

Page
CHAPTER 7

RESULTS FROM THE APPLICATION OF THE ENTROPY
MINIMAX A L G O R I T H M ...................... 124

I.
II.
III.
IV.
V.
VI.
CHAPTER 8

I n t r o d u c t i o n ..................... 124
Attributes and Outcome C l a s s ....124
A Priori Probability of Attributes
and Outcome C l a s s e s ............126
E n t r o p y ........................... 131
Probability of Outcome Classes
. . . .
Discussion
...............

138
142

REGRESSION M O D E L S ............................ 146
I.
II.

I n t r o d u c t i o n ..................... 146
The Effects of Variables on the Varia­
tion in Total Cost Per Month, Total
Hours Per Month and Cost Per Hour . .
A.
B.
C.
D.

III.

IV.
V.
CHAPTER 9

147

Functional Status .................
159
Socio-Economic Status .............
161
Medical S t a t u s .................. 165
The Search for an Optimal Model . .
165

Effects of Variable Categories on the
Variation in Total Cost Per Month,
Total Hours Per Month and Cost
Per H o u r ...................... 168
An Examination of Coefficients
. . . .
Results From the "Test" Sample
. . . .

169
176

C O N C L U S I O N .................................. 187
I.
II.

Introduction
...........................187
The Relationship Between Client
Attributes and Assigned Services . .
189
III. The Determination of Categories
Influencing Costs ...................
195
IV. Other Conclusions and Implications
for R e s e a r c h .................. 198
V. Policy Implications
.............. 203
APPENDIX A

DSS FORM 3492

APPENDIX B

SAMPLE COUNTY R A T E ...................... 209

BIBLIOGRAPHY ...........................................

207

212

LIST OF TABLES
Table
3.1
6.1
6.2

Page
Appropriate care settings for different
p a t i e n t s ......................................

33

Data format for individual client attributes
and the outcome s t a t e .......................

97

Conditional probabilities of specific outcomes
given characteristic attributes of profiles
.

101

6.3

Frequency of services received by clients
according to total number of services
p r o v i d e d ......................................... 116

6.4

The number of clients at different impairment
levels and the service categories employed
by t h e m ......................................... 122

7.1

Forms of outcomes (service mixes) and client
attributes employed in Entropy Minimax
computer r u n s .................................. 125

7.2

Array of outcome classifications, attributes
and probability and other results from
run number 2 .....................................135

7.3

Summary of results from nine computer runs of
the pattern detection algorithm .............

7.4

137

Array of outcome classifications, attributes
and results from run number 1 .................140

8.1

Results of

Model A, total costs per month

(TCM). 149

8.2

Results of

Model B, total hours per month

(THM). 153

8.3

Results of

8.4
8.5

Model C, costs per hour (CH)
. . . .
156
2
A comparison of R for all m o d e l s ................170
Test results - Models A, B, C

viii

.............. 177

Page

Table
8.6
8.7

8.8

8.9

Means and standard deviations of endogenous
variables
..................................

.

180

A comparison of selected categories and sub­
categories between "training" and "test"
samples from two equations in Model A
. . . .

182

A comparison of selected categories and sub­
categories between "training" and "test"
samples from two equations in Model B . . . .

184

A comparison of selected categories and sub­
categories between "training" and "test"
samples from two equations in Model C . . . .

185

ix

LIST OP FIGURES
Figure
2.1

Page
Decision processes as to the disposition and
assignment of long-term care patients
. . . .

19

Cost of patient care according to change in
impairment. Alternative relationships . . . .

32

Costs of different kinds of care at differing
levels of i m p a i r m e n t ..........................

32

Hypothetical costs of care for different
levels of impairment for patients in nursing
h o m e ...........................................

34

Variation in costs of client care according
to the extent of family assistance for a
specified impairment level ...................

36

Cost of care according to the length of time
the client receives assistance from family
members or f r i e n d s ............................

36

4.1

Rate of provider p a y m e n t .......................

45

4.2

Percentage distribution of hourly rate of pay
by provider t y p e ..............................

45

Percentage distribution of hours of service
provided by primary provider .................

46

Screening of a three dimensional space into
two o u t c o m e s ..................................

99

3.1
3.2
3.3

3.4

3.5

4.3
6.1
6.2

Screening of a three dimensional space into
four o u t c o m e s .................................. 102

7.1

Part 1 of computer printout from run number 2

. . 127

7.2

Part 2 of computer printout from run number 2

. . 128

7.3

Part 3 of computer printout from run number 2

. . 129

7.4

Part 4 of computer printout from run number 2

. . 130

CHAPTER 1
PROJECT ORIENTATION

I.

Problem Statement
During the last 5 to 10 years there has been in­

creasing debate over the question of what constitutes appro­
priate long-term care services for the chronically ill and
disabled.

This debate stemmed/ in part, from an intensifying

concern about the increasing institutionalization of the aged
and a concomitant rise in the costs of medical care.

A great

deal of uncertainty prevails about what constitutes the appro­
priate care for populations of long-term care patients with
varying functional abilities and in varying socio-economic
circumstances.
The general aim of this research is to shed light on
the inter-relationships among characteristics of long-term
care patients, the services they receive and the costs of
those services.

Specifically, it focuses on the long-term

non-medical services delivered in the home.

Since long-term

care patients are relatively stable medically, particular in­
terest is focused on specific patient attributes such as func­
tional levels of impairment, socio-economic status and the
non-medical types of services assigned to compensate for im­
pairment.

The study is conducted on a sample of chronically

ill and disabled, predominantly aged people who are benefi­
ciaries of a Michigan chore service program.
The problems associated with identifying appropriate
long-term care services became apparent to the writer while
serving on the project review committee of the Capital Area
Comprehensive Health Planning Agency in Lansing, Michigan
between 1973 and 1975.

The committee received several re­

quests from nursing home operators to approve the construc­
tion of new nursing homes.

It was claimed by the applicants

that all nursing homes in the area had an occupancy rate in
excess of 99 percent of capacity and that there was a waiting
list for future vacancies.

A major question (of nationwide

significance) surfaced in the hearings:

how appropriate

were nursing home and other long-term care services for
those disabled and chronically ill persons using them?

It

became apparent the answer to the question was fraught with
controversy.

Third party reimbursement of long-term care

services overwhelmingly favored institutionalized long-term
care patients.

It seemed placement decisions were being

influenced by what was available (KNOX ET AL 1973).

Since

few substitute services were available that usually meant
institutionalization.

Little attention was being paid by

either public or private financing agencies, such as govern­
ment social service departments or private insurance compan­
ies, to financing the care of the chronically ill outside
of institutions.

3
The problem for the project review committee was
accentuated by the lack of agreed upon concepts and variables
by which the various kinds of long-term care, and thus costs,
could be assessed.

Consequently, there were no means by

which to adequately compare the various types of long-term
care services with each other.

Attempts to compare the costs

of different types of long-term care programs proved futile
because it was not possible to relate the attributes employed
in classifying patients to the type of services assigned to
them; a major objective of this research.
In general, a patient's profile of attributes can be
broken down into 3 distinct types:

medical status, socio­

economic status, and functional status.

The latter index

either measures the patient's ability to perform various
everyday tasks such as walking, bathing, cleaning, etc., or
uses measurable

proxies for impairments such as degree of

mobility or degree of mental capacity and extent of sensory
faculties.

The two approaches may be combined.

Without a

common understanding and agreement on the form of patient
profile to be used for assessing the needs of long-term care
patients, it was not possible to examine the appropriateness
of the various services nor compare their costs.

This kind

of information is required to learn how decisions are made
with respect to the assignment of long-term care services to
the chronically impaired.

At issue, is not only whether

appropriate attribute profiles exist, but also whether they
would be used consistently by workers who assign long-term
care services to the impaired.

4
II.

Project Justification
The aged constitute a large proportion of the chronic­

ally ill and disabled population.

Between 1960 and 1970, the

population increase among persons aged 65 years and over
amounted to 21.1%; among those 75 years and over the increase
totalled 37.1%.

These increases occurred during an overall

population growth of 12.1%.
As people age, the likelihood of them suffering from
one or more chronic diseases increases.

Diabetes, heart pro­

blems, cancer, arthritic and mental disorders are often
accompanied by disablement.

Forty two percent of those aged

65 and over have long-term activity limitation due to chronic
illness (NATIONAL CENTER FOR HEALTH STATISTICS 1973).

It is

estimated that three million of the nations 20 million aged
are so seriously disabled that they need some form of personal
care (CARO 1972).
Modern medical practice, particularly chemotherapy,
has enabled the chronically ill to maintain reduced but rela­
tively stable physical and mental capacities.
living longer in various states of dependency.

They are thus
The multipli­

cation of therapies employed to stabilize the chronically
disabled patient serves to increase the cost of both medical
services and non-medical support services such as cleaning,
personal care or meal preparation.

The latter derive from

the need to physically, psychologically and socially care
for the patient.

Among the aged, the number of disability

days now averages 34 per person annually.

5
Thefinancial burden
chronically

of medical care falling on the

illrose to such levels that indemnity insurance

and outright government subsidization have become the chief
sources of payment for medical services and for support ser­
vices, principally in institutions.

These developments

slowly emerged from the awareness that, "Economic life in
the health care sector is less subject to the influence of
exchange as a means of organization."

"Instead, the grant

is rapidly becoming the instrument of political and economic
organization"

(BOULDING AND PFAFF 1972).

Additional services

required by the patient to compensate for his/her disability
outside the institutional setting, e.g., cleaning, meal pre­
paration etc., are often not covered in benefits received
by the chronically ill.

Exceptions to this generalization

>

are increasing as in Michigan where patients in certain in­
come categories
assistance.

can, through grants, secure non-medical

It is important to note that reimbursement for

institutional care in nursing homes and hospitals covers
room and board in addition to professional medical services.
The financial strains imposed on third party payors
have thus increased due to a larger population at risk, in­
creasing medical intervention, and rapidly rising costs.
Realizing this, third party payors have sought to gain in­
formation on appropriate types of medical and non-medical
care for given patient characteristics.

With this knowledge,

they could then identify the lowest cost appropriate care
and reimburse for it.

In practice, patient characteristic

profiles are not uniform, rendering comparisons difficult.

6
Institutions tend to emphasize the medical status of
the patient and rarely supply sufficient detail on the func­
tional status of the patient.

Non-institutionalized patients

are also predominantly characterized by their medical status.
A population of the chronically ill and disabled in which
this is not the case is to be found in Michigan, in the Adult
Chore Service Program of the Michigan Department of Social
Services.

Patient functional status, socio-economic status

and to a lesser extent, medical status have all been recorded.

III.

Project Goals and Methodology
The allocation of funds by state and federal legisla­

tors among various long-term care programs is arbitrary to
the extent it proceeds without significant insights into the
relative merits and unit costs of those programs.

This re­

search is intended to examine one particular government pro­
gram in Michigan and to develop a method whereby various long­
term care programs can be compared with each other with
respect to appropriateness of care and associated costs.
In comparing long-term care programs, it is important
to have common indicators of patient status.

Given common

indicators we could then determine how they relate to the
assignment of both medical and non-medical services to the
patient.

It is assumed there would be overlap between one

type of service, e.g., home care, and another service such
as nursing home care for some common patient profiles.

In

these instances, an incentive may be introduced or a cost

ceiling imposed to induce the patient, or those assigning
services, to choose the service of lowest cost.
This research has two primary objectives and an asso­
ciated third objective.

The first objective is to detail

and test a methodology for determining whether a relationship
can be detected between patient attributes and the long-term
non-medical services assigned to them.

If such relationships

can be detected, the knowledge should be useful in determin­
ing the range of services deemed appropriate for patients
with given attribute profiles.

A knowledge of the alterna­

tive mixes of services appropriate for any given patient
attribute profile when linked to associated costs should
enable us to identify the appropriate service mix of lowest
cost.
The hypothesis underlying the above objective is
that given a specific patient attribute profile, a person
assigning long-term care services will systematically base
the choice of services on that profile.

At a more mundane

level, the question is whether or not Michigan Chore Service
workers utilize the particular profile developed by the
Michigan Department of Social Services to assign services
to patients benefitting from the Chore Service Program.
The second major objective of this research is to
determine to what extent the various attributes of the patient
profiles are related to long-term care service costs.

Here

we are seeking to learn which particular attributes of the
profile are the most useful predictors of service costs.

8
An associated third objective is to determine which
long-term care services, as distinct from patient characteris­
tics, are the most useful indicators of Chore Service Program
costs.
To meet the first objective, a pattern detection
algorithm called Entropy Minimax will be employed to deter­
mine if any systematic relationship exists between patient
attributes and assigned services.

If such a relationship

is found to exist, regression analysis will be employed on
a separate set of data to confirm the results.

There are

sufficient cases to randomly split the total sample of clients
into 2 parts; the larger "training set" of at least 400 cases
will be used to evaluate the effect of various specifications
of the model; the smaller "test set" of approximately 200
cases will be employed to test the best results of the en­
tropy minimax analysis.
In pursuing the second and third objectives, regres­
sion analysis will be used to estimate the costs of care
and the hours of services provided.

Since specification of

the cost functions will involve many adjustments in the
equations, the training set described above will be used to
isolate the "best" specified equations.

The test set will

be used to test these models and ensure results from the
"training data" are not contrived.

It is anticipated this

research will result in information and predictions that
bear on policy-making in the Michigan Chore Service Program.

9
Of a more general nature, further research will be
suggested that will enable comparisons of services among
groups of patients receiving various types of long-term care
services (e.g., nursing home care, home nursing, home chore
services, and others).
Theoretical advances will include explicating proce­
dures for identifying key variables within the context of a
decision-making model and making them applicable to analysis
of long-term care patients in general, and chore service
beneficiaries in particular.

Implicit in this procedure

will be the identification of the specific key variables
that influence assignment of services and costs.

IV.

Description of Chapters
A more detailed analysis of the problems of long-term

care are discussed in Chapter 2.

There, assumptions and

general hypotheses, about decision-making are explained to­
gether with a reference to the investigative boundaries of
the research.
In Chapter 3, a brief survey of theoretical work is
presented in the review of literature.

A discussion of

various approaches to conducting research on long-term care
is also presented.

In Chapter 4, a description of the

Michigan Adult Chore Services Program is offered together
with a description of the data.
Chapter 5 outlines the technical design underlying
the research, detailing the models employed in the regression

10
analysis of costs and hours of service.

All variables are

specified in Chapter 5 and entered into econometrically
specified models.

In Chapter 6, the variables are trans­

formed for adaption to the pattern detection algorithm.
This algorithm, entropy minimax, is of relatively recent
origin and was developed from information theory; a rela­
tively full explanation of the methodology and reasons for
its use are provided.

Its adaptation to the problem of

estimating probabilistic relationships between sets of out­
comes, e.g., services assigned, and sets of attributes is
also described.

In Chapter 7, further explanation of the

entropy minimax procedure is supplied along with empirical
results from its application.
Chapter 8 is devoted to the display and discussion
of the regression results and analysis in which costs per
month, costs per hour and hours per month constitute the
endogenous variables.

Each is estimated using various

combinations of functional status characteristics, socio-v
economic status indicators, medical status and long-term
care non-medical types of service.
Finally, the conclusions pertaining to the study are
offered in Chapter 9.

Further research is also suggested

along with implications for policy making in non-medical
long-term care services.

CHAPTER 2
NATURE AND SCOPE OF THE PROBLEM

I.

Principal Dilemmas
The United States is one of the few countries in the

world where the nursing home is viewed as a practical means
of caring for the severely handicapped (TRACY 1974).

Be­

tween 1966 and 1974 national expenditures on nursing homes
increased from $1.41 billion to $7.45 billion (WORTHINGTON
1975) .

In 1974 the Michigan Medicaid program spent $250

million of state funds on nursing home services but less
than $1 million on services delivered in the patient's home.
Among Michigan residents the likelihood of a person entering
a nursing home in his/her lifetime is now 1 in 4 (KASTENBAUM
1972).
Gerontologists are of the opinion that institutionali­
zation of chronically ill and disabled patients often leads to
traumatic effects among the aged and that home care would be
more appropriate for purposes of maintaining a higher quality
of life for many (BLENKNER 1974).

Estimates of the proportion

of people in nursing homes who could be better cared for out­
side of the institutional setting range between 20% and 50%
(CARO 1972, BARNEY 1973, GENESEE

1970, KISTIN and MORRIS

1972, WAGER 1972, WHITE and TENBRUNSEL 1971, FLORIDA 1971,
11

12
WILLIAMS ET AL 1973, MICHIGAN 1975, DAVIS and GIBBON 1971,
HUNDERT 1974, ROBINSON ET AL 1974).
Clearly there Is considerable disagreement on what
constitutes appropriate long term care for the physically
and mentally disabled and the chronically ill.

The disagree­

ment on appropriateness of care is, in part, derived from
disagreement on the issue of how to classify the long-term
care patient.

Indexes now used to classify patients can be

broken down into three distinct areas; indexes describing
the patient's medical status, socio-economic status, and
functional status.

Specifying medical status and socio­

economic status, though somewhat problematic, is relatively
straightforward compared to the confusion over how to define
functional status.
Medical status is conventionally classified accord­
ing to the International Classification of Disease Adapted
(ICDA).

However, physicians vary considerably in their

assessment of pathology in an older person (SHANAS 1968).
A possible problem here is that grouping of cases by diagno­
sis takes no account of their severity or complexity (EVANS
1971) .
The ICDA index has had considerable importance in
the designation of appropriate services, including non-medical
services for the chronically ill.

Since the patient requir­

ing long-term care services is usually medically stable, the
acute care intervention of a physician is often unnecessary.
Monitoring and treatments by nurses or friends often

13
constitute adequate care.
question is raised:

This being the case, an important

how important is the patient's medical

status in designating long-term care services for him/her?
The socio-economic status of the patient is relatively clear­
ly defined and the concepts involved generally agreed upon.
A consensus on the indexing of functional status
has been difficult to achieve.

It does not appear that one

standard means of classifying functional status has been
applied across the full range of long-term care patients.
Several indexes have been used in various settings.

Among

them are the Activities of Daily Living (ADL) index (KATZ
ET A L r 1963, 1970), Index of Functional Impairment (SHANAS
1971), the Townsend Scale (TOWNSEND 1963), the Minnesota
State Periodic Medical Review (ANDERSON 1974) and the func­
tional and socio-economic status assessment (Form DSS-3492)
employed by the Michigan Adult Chore Service Program.

The

latter index is examined in this thesis.
The importance of a patient profile for this analysis
lies not so much in the accuracy with which it describes the
patient per se but in its utility in predicting appropriate ser­
vices (and associated costs) required by the patient.

We are

concerned about finding those key attributes of the profile which
account for the assignment of various types of services desig­
nated to be appropriate for the patient.

Without some under­

standing of the impact of the various patient attributes on
service determination, it is questionable whether the esti­
mates of costs for the various patient profiles can be of

14
value to policy makers in predicting future costs.

The esti­

mation of relationships between patient attributes and
services provided would facilitate the use of administrative
rule-making such as choice of patient eligibility criteria
and the designation of fitting services.

There is agreement

within States, if not among them, as to what constitutes a
patient profile that justifies institutionalization in a
nursing home or hospital.

Justification implies some go/no-

go index which enables institutional administrators to
determine whether or not their services will be reimbursed
by third-party payors.

It should be noted that justification

for the provision of care does not necessarily imply provi­
sion of one specific type of appropriate care.

Alternative

forms of care might also be appropriate for the nursing
home resident as was noted above.
Since no clearly established deterministic relation­
ship between patient attributes and appropriateness of care
has yet been discovered, the latter tends to be prescribed
on an adhoc basis by the interplay of the concerned "publics"
as they engage in transactions, rule-making and legislation.
In order to gain insights into the consequences of the inter­
play of these four "publics" on the determination of appro­
priate care, it is useful to make some assumptions about
their objective functions and assess their implications for
the selection of appropriate care.
A)

Patients.

We might presume the objective func­

tions of patients to be characterized by:

15
maximum independence and freedom of choice in
the long-term care setting; home based care (BUSSE
and PFIEPPER 1969, MICHIGAN 1975, WAGER 1972);
and minimum out-of-pocket cost of service.

Such

an objective function would place institutional­
ized care low in priority for many.

Appropriate

care from the patient's point of view would be
best provided in their own residence or that of
relatives by family or friends and health pro­
fessionals.

The patient might thus push for

those rules which provided for a wide choice
of optional services for any given patient pro­
file, the emphasis being on home care services.
B)

Patient's Family.

In addition to empathizing

with the patient and approving of his/her
objective function, the family might also be
concerned about minimizing family members'
opportunity costs.

The cost of looking after a

patient might be foregone employment.

This might

be offset by hiring outside help if the cost of
doing so is less than benefits enjoyed in a job.
The family might also favor institutionalization
if it results in not only removing the inconveni­
ence of looking after the patient in the family
home, but also results in reimbursement for the
patient's room and board while in the institution.
Families thus might favor rules that resulted in

reimbursement to themselves in order to offset
the opportunity costs (at least in part) of fore­
gone employment.

Barring such rules they might

then favor those alternatives that liberally
allow for reimbursement of nursing home service
charges by third party payors.

This would have

the effect of freeing them from the necessity of
providing care and would also result in lower
household costs since the family would no longer
have to bear room and board expenses of the
patient.
Service Administrators Including Owners.

Since

many long-term care services are provided by
proprietary firms whose major objective is
assumed to be profit maximization, it follows
that such providers would seek to keep costs
low, maintain high occupancy rates and produce
as wide a range of reimbursable long-term care
services as possible.

Providers with institu­

tions to maintain have fixed costs of a higher
magnitude than those providers of in-home services.
It follows that they would have strong incentives
to increase the size of their firms e.g. supply
more beds or, assuming current high occupancy levels,
at least maintain the status quo.

Small rule

changes that would liberalize reimbursement cri­
teria of non-institutionalized long-term care

services could result in substantial losses to
nursing home owners, at least in the short-run.
They thus have a large vested interest in the
nature of the rules as they apply to the rela­
tionship between patient attributes and the
appropriateness of services provided.
D)

Third Party Payors.

Let us presume the objective

function of third party payors is to minimize
costs and avoid expenditures in excess of the
amounts budgeted.

Here the interest lies in

determining the appropriate care at lowest cost.
It might even extend to mandating the shift of
costs to others (e.g. the family, if the family
feels obligated to live with or near the patient).
To facilitate this a rule might be promulgated
to the effect that no patient below a given
level of disability is eligible for reimburse­
ment services if they live with their family.
Or, as in many cases, it could ensure that only
those patients who are institutionalized would
have services reimbursed.
It is perhaps of interest that historically few nurs­
ing homes have existed.
nursing home

It is possible that the increase in

services in the last decade has been nurtured

by the growth of third party reimbursement for long-term care
in institutionalized settings.

18
II.

Research Priorities
Prom the foregoing overview of the problem, it fol­

lows that a major research priority lies in identifying and
utilizing a methodology for detecting patterned relationships
between a patient's profile of attributes and services
designated appropriate.

Then, given the range of what is

customarily identified as appropriate services for given
profiles, it is important to determine from among appropriate
services those services of lowest cost.

Figure 2.1 illus­

trates the components involved in the decision making pro­
cess by which services are designated for long-term care
patients.
When patients are recognized to be in potential need
of long-term care services, the nature and degree of needs
have largely been assessed according to the patient's medical
status by a health professional.

Rarely is the health pro­

fessional left out of the decision making process.

The

patient's socio-economic status is appraised usually by
agents (e.g., social workers) of the third-party^payor.

The

assessment and categorizing of a patient's functional status
is not consistently detailed according to a common index
across long-term care programs, but may be consistent within
a specific program.
Each index is generated and related to the constraints
that are peculiar to that index.

In addition, constraints

with respect to permissable services, and the time period of
such services, may be proposed together with possible ceilings

PATIENT
PROFILE

CONSTRAINT

DECISION
MAKERS

SERVICES
PROVIDED
CHORE
SERVICES

HEALTH
PROFESSIONALS
MEDICAL
STATUS
FUNCTIONAL
STATUS

HOME SERVICES
THIRD
PARTY
PAYOR
RULES

\

MICHIGAN DEPARTMENT
OF SOCIAL SERVICES
WORKERS

PROFESSIONAL
MEDICAL
SERVICES

NURSING HOME
(MEDICAL SERVICES
ROOM
BOARD)

SOCIO-ECONOMIC
STATUS

NONE
PATIENT &
FAMILY

OTHER, e.g., DAY CARE HOSPITALIZA­
TION

FIGURE 2.1.— Decision processes as to the disposition and assignment of long-term care
patients.

20
on unit or total costs.

Taking into consideration the

patient's attributes and third-party constraints on patient
eligibility according to both attributes and services, a
package of appropriate long-term care services can be
assembled and made available to the patient.

In some cases,

services are offered in one undifferentiated lump such as
in hospitals and nursing homes which include room and board.
In the case of non-institutionalized services, benefits can
be disaggregated into discrete types and amounts.

The health

component of services rendered can be delivered (if necessary)
separately from personal care.

With respect to home delivered

long-term care services, cost centers can also be identified
and charges made only for those specific services received.
The primary thrust of this thesis is to analyze non-medical
services delivered in the home setting.

There is consider­

able justification for this thrust in so far as the demand
for such care becomes more intensely articulated.
It is considered axiomatic that people suffering
from chronic disabilities wish to maintain their independence
for as long as possible.

Surveys of the chronically ill

themselves attest to their desire to live in familiar sur­
roundings with familiar people.

Long-term care services

are valued to the extent they facilitate the patient's inde­
pendence (BUSSE and PFEIFFER 1969, BARNEY 1973 and 1975).

It

is generally acknowledged that institutionalization leads to
virtual denial of independent decision making and to unwanted
regimentation.

Gerontologists have observed the positive

21
differences in attitudes and outlook on life that favor
those who live in independent as opposed to institutional
settings.
It is postulated here that the major aim of describ­
ing a patient profile is to facilitate the matching of a
patient's attributes to services required to compensate for
the patient's disabilities.

It is further assumed that it

is desirable to keep the profile to a minimum, thus reducing
sources of error, facilitating the training of those con­
structing profiles, and cutting the costs of processing and
administering the profile.
An important assumption in this thesis is that dif­
ferent and mutually exclusive types of appropriate services
are available (not necessarily in one geographic location)
for groups of patients characterized by virtually identical
profiles.

There are probably extremes in this range of

service types which would not be considered alternatives by
a large proportion of patients or those making decisions on
appropriate services.

The full range of long-term care now

being delivered to patients can be statistically determined.
Statistical analysis can help define those services.

It is

the bulk of the services designated "appropriate” that we
wish to examine with respect to their costs.

It is antici­

pated that some patterns of patient attributes will yield a
wider range or variety of alternative acceptable services
than others.

For example, a person who is relatively immo­

bile may justify the provision of cleaning services, or meals,

22
or laundry services, or yardwork or non-nursing personal
care services or any combination of those services.

Whereas

a person who is mentally confused to some degree may only
justify the provision of financial management services.

III.

Investigative Boundaries
Theoretically, this thesis addresses the whole range

of long-term care services together with those patient attri­
butes deemed appropriate indicators of service needs.

In

part, this research also examines what may be loosely termed
the "production function" of long-term care where the patient
profile is viewed as a set of inputs and the services rendered
as outputs.

Services rendered are a proxy

for the output that

is viewed here as the maintenance of an independent lifestyle.
Empirical research here is limited to analyzing
statistically a government financed population of people
with low incomes.

Neither professional medical care nor

institutional care are empirically analyzed in this thesis.
Medical status has been neither sufficiently clearly speci­
fied in the data used here nor consistently recorded in the
patient profiles, therefore, little weight should be placed
on findings with respect to the significance of the patient's
medical status.

Since the thesis is concerned with persons

who are not necessarily receiving medical services, these
persons will from now on be referred to not as patients but
as clients.

23
The functional status indicator analyzed here was
specifically developed for the Michigan Department of Social
Services Adult Chore Service Program.

Generalization of the

results to other populations should, therefore, be viewed
with circumspection.

IV.

Problems Associated with the Study
The research conducted here was directed into two

major areas:

(i) the analysis of the relationship between

client profiles and the services provided to clients? and (ii)
the estimation of the relationships between client profile and
costs.

With the exception of a few studies cited in Chapter

3, there has been little attention devoted to providing theore
tical structure nor empirical work to suggest the nature of
specific relationships between client attributes and the kinds
of services received by clients with given attributes.
problem

The

of analysis is accentuated by the presence of a rela­

tively large number of endogenous binary variables (i.e. ser­
vices) which serve to render more common forms of econometric
analysis unsuitable in this case.
more detail in Chapter 6.

This issue is examined in

The employment of proxies for

aggregations of services such as service costs or hours of
service provided was considered but would not meet the speci­
fic objectives of determining the relationship between speci­
fic attributes and specific services.

A broad hypothesis

adopted here is that client attributes result in appropriate
assigned services.

If this is the case there should be some

24
detectable patterned relationship between client attributes
and services received.

A procedure, namely, entropy minimax,

was utilized to attempt the detection of patterned relationships.

This procedure is detailed in Chapter 6.

If such

relationships are observed, they would serve as more conven­
tional hypotheses for confirmation of the results utilizing
more common estimation procedures such as regression analysis.
Regression analysis is employed in meeting the second
objective of this thesis namely the estimation of relation­
ships between specific attributes and costs of specific ser­
vices.

Using regression analysis, it is possible to deter­

mine which attributes affect costs in a statistically signi­
ficant way.
The reader might be puzzled as to why, if cost esti­
mation is of ultimate concern, we do not forego the problem
of estimating the relationships between attributes and services
since cost estimates can be obtained directly from both attri­
butes and services.

The direct estimation of costs is not

of great value to the decision maker who is seeking, for any
given patient profile, the range of services appropriate and
that service-mix of lowest cost that meets the needs of a
specific client.

Direct estimation of costs does not indi­

cate which services are appropriate for which clients.

From

another perspective, the services assigned might be appropriate
when considering decision rules that award grants to the
clients who then choose and purchase their optimal mix of
services.

V.

Variables
The specific designation of the variables employed,

e.g. endogenous or exogenous, depends in part on the type of
analysis used.

The endogenous variables to be employed are:

services (where they are designated as outcomes in the
entropy minimize algorithim); costs of services per month;
hours of services provided to clients monthly? and costs
per hour.
In the regression analysis, services are treated as
an exogenous variable, the categories of which are:

laundry,

shopping, heavy cleaning, light cleaning, meal preparation,
non-nursing personal care, transportation, financial manage­
ment, attendant, home maintenance and repair, and yard work.
Medical services are considered in this study but are given
little credence because of the poor quality of the data used.
The other exogenous variables or patient profile attributes
are divided into the three major areas:

medical status,

socio-economic status, and functional status.
The medical status variable is indicated by the major
medical problem judged to characterize the patient.
attributes are:

Medical

MI (mental illness), MR (mental retardation),

heart problems, respiratory system problems, mobility, dia­
betes, cancer, recuperation, and other.
The socio-economic attributes are characterized by
categories of:

age, sex, location, income, living arrange­

ment, and the relationship between the provider of services
and the patient.

The living arrangement category is

26
subdivided into:

owns own home, rents own home, rents

apartment, rents room, rooms with parent, rooms with child,
rooms with non-relative, non-householder and other.

The

relationship of the primary provider to the patient is
broken down in the following way:
other relative, non-relative,

parent, daughter/son,

(each of the foregoing cate­

gories is subdivided according to whether the service is in
the home of that category or not), and other.

The living

arrangement and relationship variables were aggregated into
4 groups:

client lives in same home as provider who is

a relative; client lives separately from the relative pro­
viding services; client lives with non-relative service
provider; client lives separately from non-relative pro­
vider.
The functional status attributes are characterized
by:

mobility, dexterity, sensory perception and comprehen­

sion faculties

and home management abilities.

Each of

these designations is divided into five levels from zero to
high degrees of disability or impairment.
The treatment of these variables in the context of
long-term care services has been seriously attempted by few
other analysts as is evident in the next chapter which sur­
veys studies in long-term care services delivered in the
home.

The variables, models and data base are developed

in more detail in Chapters 4 and 5.

CHAPTER 3
LITERATURE REVIEW

I.

Introduction
This chapter contains a review of the various types

of cost analysis applicable to long-term care of the chronic­
ally ill and disabled.

In addition, an overview of a speci­

fic model is presented in which features of particular rele­
vance to this study are emphasized.

Clustering of services

and their relationship to patient attributes will also be
discussed together with references to various indexes of
patient attributes.

Finally, estimation procedures used in

a major relevant empirical study will be briefly considered
followed by a brief discussion of health industry related
cost functions.

II.

An Overview of Approaches to Cost Analyses
Assuming policy makers seek to learn which long-term

care programs are most appropriate in this society, one
basis for selection is to conduct a cost-benefit analysis
of the various alternative programs.

Such an approach im­

plies identification of all cost factors and all benefits
quantified in monetary units where possible.

To date, the

sole identified exercise in cost/benefit analysis in
27

28
long-term care, identified costs and benefits but failed to
monetarize the latter (WAGER 1972).

Patient satisfaction

was identified as the chief benefit in the sense that most
elderly people asserted they would prefer to maintain their
independence in familiar settings as opposed to being in­
stitutionalized.
Since quantifying benefits is problematic, a second
means of analyzing costs is to conduct a "cost effectiveness"
analysis.

Given certain goals, e.g. minimizing costs or

maximizing client satisfaction with respect to ameliorating
the effects of physical and mental impairments, we can com­
pare costs of meeting these goals for specific groups of
clients and attempt to identify the lowest cost approach
(ANDERSON 1974).

It is assumed under this approach that

patient profile formats are common across alternative pro­
grams being offered.

The lack of such uniformity of data

makes comparisons of appropriateness of care and cost of
care very difficult.
A third means of estimating costs of care and the
one most commonly used in the health research literature,
is to analyze the costs of service directly without taking
into consideration the purpose of the services.
No benefits are considered here, merely implicit costs of
components that explain variation in the cost of a specified
unit of service such as a patient day of care or an episode
of illness.

There have been a few attempts at estimating

costs on this basis in the area of long-term care, principally

29
with respect to institutions such as nursing homes (BERGER
1970, HURTADO ET AL 1972, SPROAT 1972, SAGER, 1977, BURTON
ET AL 1974, CONGRESSIONAL BUDGET 1977).

However, most of

the work using this approach has been conducted in the
analysis of hospital costs (LAVE, LAVE and SILVERMAN 1972,
EVANS 1971).
Less systematic studies of homemaker and home health
aide costs have been conducted but they tend to be anecdotal
and heterogeneous with respect to specification of client
attributes and services received.

"Single agencies and

some multiple-entity programs such as state agencies gener­
ate statistics on costs and benefits, however, such statis­
tics are so diverse that there is little or no basis for
comparison,"

(ROBINSON 1974, pp. 9).

There were seemingly

no systematic methodologies developed to enable comparisons
among various types of long-term care programs.
The only evident empirical cross-sectional analysis
of long-term home care was conducted by Greenberg who is
extending the project (ANDERSON 1974) .

This is discussed

more fully in the section on empirical findings in this
chapter.
Two major emphases have been identified.

One recom­

mends that studies of various long-term care programs take
into consideration all costs including opportunity costs of
providers such as close relatives who offer their services
for no remuneration (POLLACK 1973).
with this approach were noted above.

The problems associated
The second thrust

30
advocated by Greenberg goes a step further and recommends
emphasis be placed on estimation of the relationship between
costs and what he considers to be the most important aspect
of the patient profile, namely the functional status attri­
butes of the client (ANDERSON 1974).

III.

A Model for the Analysis of Long-Term Care
Pollack was concerned about ensuring that cost com­

parisons between various types of long-term care be based
on total social costs, the common denominator being costs
per client per unit of time.

Because this data is difficult

to collect and quantify, a 'second best' approach is adopted
which analyzes on some components of social cost such as
government expenditures on long-term care services.
Real social costs according to Pollack depend on:
(i) the client's functional status;

(ii) the family status

of the client; and (iii) the quality of care provided.
Quality of care is usually unspecified but is assumed appro­
priate for whatever type of service is provided.

This does

not imply that the quality of one type of care is equivalent
to another even though both types of care may be deemed
appropriate for a particular client.
In addition to considering the comprehensiveness of
cost categories and the completeness of costs within cate­
gories, Pollack stressed the importance of identifying and
measuring the cost of non-market or quasi-market inputs.
To assure comprehensiveness, he recommended measuring costs

31
of housing, nutrition, supervision, personal care, trans­
portation, recreation, medical care, environmental hygiene
and other relevant miscellaneous items.

Further complete­

ness of costs may be ascertained by detailing administrative
costs, and accounting for subsidies on such items as rent,
parking, etc.

Non-market and quasi-market inputs would

include such items as travel costs of providers, shadow
prices of opportunity costs of volunteers (including family
members) and foster families.

Pollack stressed this point

because future projections of eligible need may involve
expansion of services to such an extent that volunteers can­
not be relied upon to provide the additional services.
In Pollack's opinion, family status is a very signi­
ficant category of the socio-economic status variable.

He

hypothesizes that costs of the personal care of clients with
identical functional status attributes will differ substan­
tially depending on their family status.

For example, for

a given client, nursing home care may cost $22 per day,
in-home care with family $40 per day, and home care with a
retired spouse $4 per day.

He also hypothesizes ceteris

parabus that as functional status decreases, costs will rise
as illustrated in Figure 3.1.
When comparing two services, say home care and nurs­
ing home care, Pollack hypothesized the relationships would
be characterized by the graph in Figure 3.2.
Here it is clear an able spouse of family can delay
entry into an institution for greater degrees of client

32

Costs/
patient/
day

Level of Impairment
Source:

Pollack W. Costs of Alternative Care Settings for
the Elderly.
Working Paper 963-11 (Draft), Urban
Institute/ Washington, D.C., March 12, 1973.

FIGURE 3.1.— Cost of patient care according to change in im­
pairment.
Alternative relationships.

.Home care alone
Home care with spouse or
/ family
y Nursing home

Costs/
client/
day

Level of Impairment
Source:

Pollack W.
Costs of Alternative Care Settings for
the Elderly.
Working Paper 963-11 (Draft), Urban
Institute, Washington, D.C., March 12, 1973.

FIGURE 3.2.— Costs of different kinds of care at differing
levels of impairment.

33
impairment than is possible with a client living alone.
Clearly, over some impairment ranges costs are less for one
specific type of care than another but for other ranges the
relative costs may be reversed.

In the case of nursing home

care, costs may not inevitably rise with the degree of im­
pairment.

Persons immobile in their beds with little compre­

hension of their surroundings possibly require less care
than the partially mobile, alert patient (HUNDERT 1974).
From this viewpoint, a case could be made for the peaking of
the cost impairment curve as illustrated by this writer in
Figure 3.3.
Implicit in Figure 3.3 is the observation that for
any one individual more than one mode of long-term care may
be appropriate.

Table 3.1 illustrates an example provided

by Pollack.
TABLE 3.1.--Appropriate care settings for different patients.

Home
Care

Mrs. Mayer

X

Mr. O'Neill

X

M r s . Cooke

X

Mrs. Jones
Source:

Foster
Care

Nursing
Home

Hospital
Extended
Care

X

X
X

X

X

Pollack, W. Cost of Alternative Care Settings for
the Elderly. Working paper 963-11 (Draft), Urban
Institute, Washington, D.C., March 12, 1973.

34

Costs/
patient/
day

Level of Impairment

FIGURE 3.3.— Hypothetical costs of care for different levels
of impairment for patients in nursing home.
Given these ranges of appropriate types of care for
different individuals it is possible to identify those of
either lowest social cost, or lowest cost to third party
payors such as governments.
In his cost analysis of long-term care, Greenberg
examines not only patient attributes but also service pro­
vider characteristics including geographic and demographic
features.

He also takes into consideration the degree of

population dispersal and the degree of integration of
long-term services.

In his theoretical analysis of social characteris­
tics, Greenberg appears to ignore Pollack's concern for
family member opportunity costs, hypothesizing that cost
per client per unit time decreases to a constant level as
hours of assistance from family and friends increases.

This

is shown in Figure 3.4.
If we let the impairment level of the client case
illustrated in Figure 3.4 be z, then we can transform the
graph into a relationship between cost and level of im­
pairment as pictured in Figure 3.5.
As shown in Figure 3.5, third party costs of client
care decrease with increased time offered by family mem­
bers for any given level of impairment.
From the foregoing, it is clear the identification
of impairment level, i.e., functional status, is important
for policy makers in their quest to control costs.

To quote

Greenberg "...if the study does not control for disability
level at all, then there is no way to distinguish cost sav­
ings due to place of service from cost savings due to treat­
ing healthier people"

(ANDERSON 1974, p. 9).

The underlying

assumption behind this assertion is that there is a relation­
ship between the functional status of the client and the

36

Costs/
Client/
Unit-time

z

Impairment level

Hours of Family or Friends Assistance
Source:

Anderson, N.N.
"A Planning Study of Services to
Non-Institutionalized Older Persons in Minnesota,"
The Governor's Citizens Council on Aging, State
of Minnesota, 1974.

FIGURE 3.4.— Variation in costs of client care according to
the extent of family assistance for specified
impairment level.

No family help
h9urs of family help
Costs/
Client/
Unit-time

+ Y hours of
family help

Level of Impairment
Source:

Anderson, N.N.
"A Planning Study of Services to
Non-Institutionalized Older Persons in Minnesota,"
The Governor's Citizens Council on Aging, State
of Minnesota, 1974.

Figure 3.5.— Cost of care according to the length of time the
client receives assistance from family members
or friends.

37
services delivered to compensate for those impairments.

In

addition, is is assumed decisions as to services assigned to
clients are based at least in part on functional status.

A

small amount of research is available on these relationships
(MEDICUS 1975, KATZ ET AL 1966, KATZ ET AL 1972, STROUD 1978).
However, at present, little knowledge is available about these
relationships for most long-term care conditions.

IV.

The Detection of Patterned Relationships Between Patient
Profiles and Services
Among the literature reviewed by this author, a

statistical analysis of the relationship between client attri­
butes and services has not been attempted in the area under
discussion here.

The nearest approach to it has been con­

ducted with respect to assessing efficacy of medical tests
for acceptable X-ray diagnosis of complaints associated with
the head (SCHONBEIN ET AL 1974, 1978).

The researchers in

this instance were attempting to discover if a specific
test ordered by a physician made any difference to the
health outcome of the patient.

Using the information theory-

based entropy minimax pattern discovery algorithm, the study
took patient profiles and attempted to find if there were
any patterned relationships between patient attributes to­
gether with the use or non-use of the test by the physician
and the patient's health outcome.

Should there be no dif­

ference between the patient's health outcome when using or
when not using the test and should the profiles be comparable,

38
then it would be concluded the test was of no value.

But

should there be such a relationship determined, then the
study would enable the researchers to determine which
patients

(classified according to profile) were most likely

to benefit from the test, and, more importantly, which
patients with given profiles were unlikely to benefit from
the test.

If such profiles can be identified, it should be

possible to cut down on patient care costs by foregoing cer­
tain tests on patients manifesting those profiles.

For the

purposes of the pattern detection research involving effi­
cacy of tests, the result of the test itself can be con­
sidered a patient attribute.

If the result is positive,

the patient outcome should be different from the outcome
where the test is negative.

The range of outcomes with and

without the test may be greater than two, numbering up to
five or six.

Beyond this number of outcomes, the reliability

of the technique drops.

However, it is precisely because

there is a possibility of relating multiple outcomes to a
set of attributes that makes the entropy minimax procedure
appropriate for the purposes of research on the topic of
this thesis.

In our case, we are not seeking the efficacy

of a test but the relationship, if any, between a set of
service outcomes and client

attributes.

To the extent there is a relationship between ser­
vice outcome mixes and client attributes, we should be able to
"distinguish between cost savings due to place of service
and cost savings due to treating healthier people."

39
V.

Empirical Findings
In attempting to compare costs of home services with

institutional type services, indirect costs such as housing
costs, food costs, laundry costs, etc. must be accounted
for with the home-bound patient.

Since the population

examined by this thesis is receiving care exclusively in noninstitutional settings, such costs can be ignored as con­
stant for any client.
For our purposes, the salient components of the
empirical research conducted by Greenberg include functional
status, socio-economic status and medical status variables
together with a specification of services rendered to the
patient receiving strictly chore-type services.

Dependent

variables employed by Greenberg included hours of homemaker
aid per week, global rating of patient functional ability
and cost of homemaker/home-health aid per month.

Only a few

of Greenberg's categories of medical diagnosis or functional
status are compatible with those adopted in this thesis.
Functional status categories included:

ambulation, bathing,

transfer (moving from one room to another), eating, communi­
cation, toileting and mental status.

Greenberg analyzed

only 47 cases drawn from a sample of 139 persons 65 and over,
all of whom, for various reasons, no longer received services.
2
Using the Freedman/Tukey T statistic because of low cell
counts, he found through partial correlation analysis, no
association between hours of service and medical diagnosis.
Among the exogenous variables only three functional status

40
categories, ambulation, bathing and transfer were found to
be significantly correlated at the .05 level with the endo­
genous variable hours of homemaker/home-health aid services.
Employing regression analysis to estimate average cost as a
function of various independent variable categories for
nursing homes, Greenberg found the log specification of
endogenous and exogenous variables yielded a slightly larger
explanation of variance

than a linear specification.

The

only two variables to prove significant were the percentage
of fully ambulatory patients
nursing home.

VI.

The R

and type of ownership of

varied from .50 to

the

.54.

Conclusion
From this and previous chapters it is clear that re­

search has only just begun to focus on the subject of long­
term care, especially that provided in the home.

The theore­

tical groundwork has been laid by Pollack and Greenberg with
respect to identifying the pertinent variables.
Considerable work has been devoted to constructing
indexes of functional status but little effort made to
statistically relate the indexes to patterns of services re­
ceived.

Schonbein's efforts in assessing the efficacy of

specific diagnoses pointed the way to determining the utility
of functional status indexes

with respect to judgingappro­

priateness of long-term care

services.

The next chapter describes the specific services
analyzed in this thesis as well as the data base.

CHAPTER 4
DESCRIPTION OP ADULT CHORE SERVICE PROGRAM*

I.

Overview of Chore Service Program
Started by the Michigan Department of Social Services

in 1972, the Adult Chore Service program was designed to
meet the strictly non-medical needs of the chronically ill
and disabled, hereafter referred to as clients.

The princi­

pal purpose of the program was to enable clients to maintain
a relatively independent life-style in familiar surroundings.
"Community services must no longer be thought of simply as
replacing the services of the family or substituting for
them when they cannot exist - though this is one primary
role.

They must also increasingly be thought of as supple­

menting or complimenting the service of the family"
HEALTH COUNCIL 1965, p. 113).

(MICHIGAN

To the extent this purpose is

achieved, the necessity of institutionalization of the dis­
abled and chronically ill in nursing homes or homes for the
aged is forestalled or eliminated.

*Much of the information in this chapter is taken
from a Michigan Department of Social Services study, "Adult
Chore Services" authored by Diane Emling (EMLING 1976). The
data used by Emling were also employed in this thesis.
41

42
In January 1976, 10,280 clients were beneficiaries
of the Chore Service program at a cost of $1.7 million per
month, an average of roughly $165 per client per month.

By

September 1976, the number of clients had grown to 11,180,
costing $2 million per month or $179 per client.
The observations on each client were collected by
MDSS workers who also made the service assignments.

All the

raw information used in this dissertation was recorded for
each client on form DSS-3492 (Rev. 2-75) and reproduced in
Appendix A.

Details on the specifications of the variables

are provided together with the theoretical framework in
which the data is analyzed in Chapters 5 and 6.
Services offered to eligible clients included:

light

cleaning, heavy cleaning, minor household repair, meal
preparation, laundry, shopping and/or other errands, guide
dog, assistance in financial management, transportation,
an attendant, yardwork such as lawn care or snow removal,
non-nursing personal care, interpreter, and unspecified
miscellaneous services.

The services are provided to the

client by a provider who is usually chosen and hired by the
clients.

Sometimes the social worker helps the client lo­

cate and hire a provider.

The program is unusual in the

sense that the client is provided with the resources to hire
a provider rather than the government reimbursing the pro­
vider directly.

Since the state government is not the em­

ployer of the provider, it need not pay the statutory
minimum wage.

43
To enter the program, prospective clients

must be

eligible; that is, they must be recipient of or eligible to
receive Supplemental Security Income (SSI).

In 1975, the

maximum social assistance payments to SSI recipients was
$170 per month if they

were single and $275 per month for

couples.

Security Income is provided toper­

Supplemental

sons who meet specific federal criteria with respect to age,
blindness or other disabilities and who have savings of
less than $1500 in the case of single people and $2500 in
the case of couples.

Further eligibility criteria are men­

tioned in the Emling Study.
Referring more

directly to the findings of Emling,

92 percent of the clients in the study
than $250 per month.
from other sources.

had incomes ofless

This included SSI payments, and income
Eighteen percent had incomes of less

than $150 per month.
In order to assess a potential client's eligibility
the local county Social Services Department would send a
social worker to draw up a profile on the client according
to a predetermined format [form DSS-3492 (Rev. 2-75)]

(see

Appendix A ) .
The social worker determines the impairment levels
or functional status of the individual and records the
details of various indicators of socio-economic status.
The kinds of services required are then agreed upon and their
costs determined.

Payments for costs incurred by the client

are forwarded to the client or to his/her agent in cases

44
where the client is mentally incompetent.

The client then

seeks to employ the services of a provider for the hours,
tasks and wages agreed upon.

The average rate of pay in

1975 was $1.78 per hour, the mode being $2.00 per hour while
the statutory minimum wage was $2.25 per hour.

Further

details on wage rates are given in the County Rate Schedule
in Appendix B.
A ceiling of $270 was placed on the total monthly
payments a client may receive from the state government.
The percentage distribution of payments to providers is
illustrated in Figure 4.1 (EMLING 1976, p. 36).

It should

be noted that only 23 percent of those providers in the top
range of payments, namely $240 to $270 per month, have their
expenses paid entirely out of program dollars.
The monthly payment received by providers breaks
down into an hourly rate as shown in Figure 4.2.
The hours of services provided by providers
down as shown in Figure 4.3. The figure shows only

breaks
hours

of service of what Emling refers to as the Primary Provider.
In only 5 percent of cases did the client receive services
from providers in addition to the Primary Provider.
minimum age for an eligible client was 18 years old.

The
Two-

thirds of the sample were over 60 years old and 6 percent
over 90 years.

Males constituted 25 percent of the client

population.
Among the clients, 21 percent owned their own homes,
19 percent rented homes, and 21 percent rented apartments.

45

29%

29%

30

26%
20

17%

10

$90-$180

<$90

$180-$240

$240-$270

Payment Amount
Source:

FIGUPE 4.1.— Rate of provider payment.
Emling, Diane. Adult Chore Service. A Profile of In-Home
Assistance. Studies in Welfare Policy No. 10, Michigan Depart­
ment of Social Services, November 1976.

100
21%

33%

0-. 90/hr N=110

100%

35%

91-1.80/hr N=177

Percent
1.81-2.40/hr N=204
28%

30%

18%

12%

All
providers

2.40+/hr N-133

Continuous All providers
except concare
providers
tinuous care

FIGURE 4.2. — Percentage distribution of hourly rate of pay by provider
type.
Source: Emling, Diane. Adult Chore Service. A profile of In-Home
Assistance. Studies in Welfare Policy No. 10, Michigan Depart­
ment of Social Services, November 1976.

46

40H
36%

30

28%

Per­
cent
20

12%

12%

6

8-23

10

2

4

2 4/day

Average hours per day

Source:

Emling, Diane. Adult Chore Service. A profile of
In-Home Assistance.
Studies in Welfare Policy
No. 10, Michigan Department of Social Services,
November 1976.

FIGURE 4.3.— Percentage distribution of hours of service pro­
vided by primary providers.

47
Of the remaining clients, 11 percent lived with a child, 13
percent with a parent, and 14 percent in other households.
Broadly defined, medical problems were categorized
as follows:

mentally disabled (9 percent of clients),

heart problems (23 percent), mobility problems (27 percent),
diabetes

(8

percent), other problems (33 percent).

Post

hospital recuperation accounted for 4 percent of the clients.
On the "average,” clients received six of the above
mentioned services, the most common ones being laundry (re­
ceived by 91 percent of clients), shopping and errands (87
percent), heavy cleaning (82 percent), light cleaning (77
percent) and meal preparation (75) percent.
Providers of services were predominantly females
over the age of 40, at least 50 percent of whom were un­
related to the client.

Thirty-nine percent of all providers

lived with the client.
Whether or not the state should be paying the ex­
penses of relatives caring for clients has raised questions
about the property right obligations of one family member
to another.

The issue continues to be debated.

One suggested

approach has been to render clients ineligible if they live
in households where the collective income exceeds a prede­
termined limit.

A major problem appears to be that an adult

cannot be held legally responsible for another adult to whom
he/she is not married while a resident in Michigan.

II.

Data Base
The sample of 628 Michigan clients which constitutes

the data base in this thesis were randomly drawn from a total
state chore service population of between 10,100 and 10,500
clients.

The range in client population stems from the

extended period of selection from October 1975 to February
1976.
The cases were drawn from those 23 counties, each
harboring 50 or more chore service clients.

Due to some

clients moving subsequent to their selection, the actual
number of counties represented was 31.

Of these, 17 encom­

passed Standard Metropolitan Statistical Areas and were
designated as urban for the purposes of this study.

The

other 14 counties were designated as rural areas and served
81 of the 628 chore service clients.

All the data employed

in the study were extracted from form DSS-3492 (Rev. 2-75).
Though justified in Chapters 5 and

6,

it should be

pointed out that largely for purposes of testing the empiri­
cal results of the entropy minimax algorithm the data were
divided into 2 sets; one set being a "training set" of 428
cases on which manipulation of the various variables was
extensive, the other set being a "test set" of

200

cases on

which the hypotheses to be generated from the pattern detec­
tion algorithm (see Chapters

6

and 7) could be tested.

In

addition, the results of the regression analysis of costs
could also be tested.

49
The variables employed in this study, together with
classification and specification of their categories and
sub-categories are listed and detailed in Chapter 5.

CHAPTER 5
TECHNICAL DESIGN AND SUBSTANCE OF COST ANALYSIS

I.

Introduction
The principal purpose of this chapter is to clarify

and specify the major research problems and to construct
testable hypotheses.

Variables employed in the analysis

will be defined and hypotheses posited with respect to the
impact of the exogenous variables on the endogenous variables.
The division of chapters in this thesis is somewhat
unusual in that this chapter will describe the variables
employed in Chapters

6,

7 and

8.

It will also describe the

hypotheses, economic model and econometric specification
with respect to the empirical analysis of models estimated
in Chapter

8

only.

These models describe the behavioral

relationships between, on the one hand, costs of services
and hours of service and, on the other, patient attributes
such as functional status, socio-economic status and medical
status.
Chapters

6

and 7 will address, respectively, the

theory and empirical results associated with the pattern
detection algorithm.

Should distinct patterns of relations

between client attributes and services be observed and, upon
further testing, be confirmed, the outcomes may have an
50

51
effect on the forms of the models discussed in this chapter
as they are empirically analyzed in Chapter

8.

To determine

whether any significant patterns were detected, the reader
should advance to the last section of Chapter 7.

II.

Technical Design
The major emphasis of this research focuses on esti­

mating the relationships between total service costs per
unit of time per client and client attributes.
relationships to be examined are:

Two related

those between patient

total service hours per unit of time and patient attributes;
and those between service cost per hour and patient attri­
butes.

These are not technical cost functions featuring

factors of production.

They are behavioral cost functions

typical of cost prediction studies in health care (EVANS
1971).

The major aim is to identify variables which will

explain a significant proportion of the variation in costs.
This approach obviates the necessity of clearly specifying
the output.
With much economic analysis of the production of
health, definitions of output that lend themselves to eco­
nometric manipulation of cost functions are rare.

In the

case of chore services, there is no readily agreed upon
measure of output.

Qualitatively, chore service output

might be described as the maintenance of independent lives
for individuals who otherwise could not live independently.
There is both a wide variety of services and service mixes

available to chore service clients seeking to maintain their
independence in familiar settings.

Within each service cate­

gory, the quantity of service offered may vary.

The proxies

used in this analysis to represent both the service mix and
intensity of service are three measurable entities:

Service

Cost Per Client Per Month (Total Cost per Month abbreviated
TCM) ? Hours of Service Per Client Per Month (Total Hours per
Month abbreviated THM); and Service Cost Per Client Per Hour
(Cost per Hour abbreviated CH).

These proxies can be related

to a variety of client attributes which are listed and
described later in this chapter.

The crucial variable among

these attributes is functional status.

Together with the

variable socio-economic status, functional status brings in
a level of detail found in few other studies.
To further the understanding of client attributes
and their relationship to costs, we will posit three mathe­
matical models, Model A, Model B and Model C, that lend
themselves to simplification of the relationships and, in
addition, to the construction of hypotheses and statistical
analysis.

In general terms, it is hypothesized that the

dependent variable, e.g., Total Costs Per Client Per Month
(TCM), is a function of the client's Functional Status (FS),
Socio-Economic Status

(SES), and Medical Status (HS).

Cost/Month (TCM) = f (FS, SES, HS)

Model A

Similarly, the same type of relationships is pre­
sumed for the other two endogenous variables, Total Hours

53
Per Month worked by the provider(s)

(TCM) , and Cost Per Hour

(CH), the payment received by the provider.
Hours/Month (THM) = f (FS, SES, HS)

Model B

Cost/Hour (CH) - f (FS, SES, HS)

Model C

The variables employed in the analysis have been
selected from among classifications of data obtained from
the form DSS-3492

(revised Feb. 1975) which is reproduced

in Appendix A.
Following is a description of each variable and its
categories and why it was selected, and in the case of the
exogenous variables and their categories, the hypothesized
relationship between them and the three endogenous variables.
A.

Endogenous Variables.

All three endogenous

variables are continuous.
1.

Total Cost per Month (TCM).

Total cost

refers to the total cost of providing chore
services to a client over a period of one
month.

Since the clients under considera­

tion had long-term disabilities that were
not subject to rapid change, costs assessed
over periods of one month remained stable.
The cost of service paid for by the
Michigan Department of Social Services was
limited to a maximum of $270 per month, an
additional justification for the chosen time
unit.

An alternative means of measuring

cost for purposes of analyzing medical
services is to conduct it on a case basis.
This approach was not deemed practical be­
cause services for the disabled and chroni­
cally ill are often provided for the dura­
tion of the patient's lifetime.

Government

rules, regulations and modes of rationing
services inevitably undergo change, thus
rendering the clear interpretation of re­
sults difficult if not impossible.

Also,

price changes may result from inflation.
For this reason, the highly desirable
time-series analysis of long-term care
problems is likely to be fraught with dif­
ficulties in the interpretation of results.
In cross-sectional analysis it is hypothe­
sized the functional status of the patient
will be found to explain a relatively high
proportion of the variance of TCM, especially
when compared with medical status.
Total Cost per Hour of Service Received by
the Client (CH).

The hourly cost of provid­

ing services is presumed to be more depend­
ent on the relationship of the provider to
the client and on whether or not the client
lives with the provider, than was the case
with TCM.

It is hypothesized the SES

55
categories will explain a higher proportion
of the variance of TCH than was the case
with the endogenous variable TCM.
3.

Total Hours of Care Provided to the Client
Each Month (THM).

This variable measures

the total amount of service time employed
by the patient in any month of care.

It is

included in the analysis to confirm the
hypothesis that relatives are more likely to
work for longer hours than non-relatives for
a patient of given functional status.
B.

Exogenous Variables.

With few exceptions, the

exogenous variables and their categories described
here are either dichotomous or polytomous.

Non­

binary variables are transformed into dichotomous
variables.

The three exogenous variables, func­

tional status, socio-economic status and medical
status, are disaggregated into the categories
described below.
1.

Functional Status Categories.

Since chore

type services are provided to compensate
largely for functional disability, it is
anticipated that a relatively large propor­
tion of the variance in total cost per month
will be accounted for under this category
of variable.

56
Functional status variable categories
will be specified in three different ways.
Broadly these are:

first, an inputed

"cardinal" index of functional status, based
on the five functional status variables,
mobility, dexterity, sensory faculties, com­
prehension and home management; second, a
binary index where each of the above mentioned
functional status categories will be disaggre­
gated into five binary categories or levels
of disability; third the functional status
of the patient will be classified according
to the type of service they are receiving.
This is justified in the belief that it is
feasible to classify clients according to the
everyday tasks they cannot perform regard­
less of the specific impairments or circum­
stances involved.

Where appropriate, two

of these three types of variable specifica­
tions may be combined in some form,
a)

"Cardinal" and Binary Forms of the Func­
tional Status Variable.
As they appear in the form DSS-3492,
the functional status variables are re­
corded at three levels of incapacity,
'None,’ 'Some,' and 'Much.1 Yet in the
data provided, they were recorded at

57
five levels.

For example, the category

mobility in the data

is an average of

two indexes recorded

in the DSS form,

namely walking and climbing.

The number

scale used to code the range of three
levels of a category

in the DSS form was

from one to five; one being

the score

given to an individual with no impairment
in, say, walking, a score of three for
some impairment, and a score of five for
much impairment.

The five levels for

the constructed mobility category were
determined by averaging the scores for
walking and climbing.

Thus, if walking

received a score of three and climbing
received a score of five, then the score
for the constructed category mobility
would be four, the average of these.
This same procedure was used to
determine the other four constructed
categories, the nearest whole number
being recorded where fractions appeared.
Original categories appearing on form
DSS-3492 and making up the five func­
tional status categories are referred
to below in the course of discussing
the constructed categories.

58
(i)

Mobility (MOB or alternatively Ml,
M2, M3, M4, M5).
As mentioned above, mobility
represents the aggregation of levels
of categories, walking and climbing,
from the form DSS-3492.

Two

approaches were taken when incorpor­
ating this category into the mathe­
matical model presented above.

The

first way was to treat each level
hierarchically by assigning the
number designating the lowest level
of impairment to represent no im­
pairment (i.e., number

1)

and the

number 5 to represent the highest
level of impairment.

This approach

represents mobility by an index be­
tween 1 and 5 called MOB.

In this

implicitly "cardinal” representation
of functional status, the highest
level of impairment is viewed as five
times more disabling than no impair­
ment.

For this measure of mobility

(MOB) it is hypothesized that the
variable in the equation will be
significant, indicating that the vari
ation in total costs per month is

59
significantly influenced by this
category of the functional status
variable.
The alternative specification
of the category is to treat each of
the five levels of disability as a
dummy variable:

Ml, M2, M3, M4, M5.

Here there is no implicit constrained
relationship relating the magnitude
of one level of impairment to an­
other.

It is hypothesized that this

specification of the mobility cate­
gory will explain more of the vari­
ance in the total costs than that
explained by the mobility index
category (MOB) which constrains the
relationship between one level of
disability and another.

As impair­

ment in mobility increases from Ml
through M5, it is hypothesized that
the coefficients will increase re­
spectively across the sub-categories
M2 to M5.

If as a result of testing,

such hypotheses prove plausible,
then greater costs for higher levels
of impairment would be indicated.
It is also hypothesized that the

60
mobility category will be signifi­
cantly related to the endogenous
variable Total Hours per Month in
a positive manner.
(ii)

Dexterity (DEX or alternatively Dl,
D2, D3, D4, D5) .
The dexterity index category
(DEX) is constructed similarly to the
mobility index category (MOB) utiliz­
ing the clients degree of impairment
with respect to grasping, bending,
and lifting as taken from the form
DSS-3492.
As with the mobility category
this category also has the alternative
binary specification utilizing the
five levels of impairment as dummy
variables: Dl, D2, D3, D4 and D5).
The hypotheses stated with re­
spect to the alternative specifica­
tions of the mobility category also
apply to the dexterity category and
to the sensory, comprehension and
home management categories listed
below.

(iii)

Sensory (perception)
S2, S3, S 4 , S5).

(SEN and SI,

61
The alternative specification
of this category is constructed
from the client's sensory impair­
ments in hearing and seeing.
(iv)

Comprehension (COMP of Cl, C2, C3,
C4, C5).
The ability to manage finances
and understand instructions, in
other words the client's mental
capacities, are incorporated in
this category.

(v)

Home Management (HOM or Kl, K2, K3,
K 4 , K5).
The clients level of impair­
ment in light cleaning and heavy
cleaning are used to construct this
category.
There is some potential con­
fusion in the use of this category
since home management also appears
to bear a strong relationship to
mobility, dexterity and sensory im­
pairments.

It could basically be

employed as a proxy category for
those three categories enabling us
to propose the hypothesis that the
amount of TCM variance explained by

62
the four categories mobility/
dexterity, sensory and comprehen­
sion will not significantly differ
from that explained by comprehen­
sion and home management.

The

implications of these observations
will be further discussed in the
section describing the econometric
specification of the model.
It is important to note that
the component parts of the attri­
bute category home management (light
cleaning and heavy cleaning) are
identical designations for two of
the services offered to the client,
namely light cleaning and heavy
cleaning.

This raises an important

issue which is discussed in the
following section,
b)

Functional status classified according
to services received.
Since the major decision makers
with respect to the appropriate care of
the disabled and chronically ill are
usually physicians, the medical model
of diagnosis and treatment is the princi­
pal guide in determining the kinds of

I

63
services patients require.

In employing

this model the physician, prior to desig­
nating the appropriate services, will
seek to accurately categorize the problem.
Thus a client might be classified as to
the degree of such impairments as in­
ability to walk, inability to bend down
and tie shoe laces, inability to put a
spoon to the mouth, difficulty with
bathing, etc.

The problem is that this

process of deciding on patient classifi­
cation has not been readily agreed upon
by the various researchers or agencies
(KATZ ET AL 1963, TOWNSEND 1963,
MICHIGAN DEPARTMENT OP SOCIAL SERVICES,
etc.).
Without such an agreement, it is
not easy to communicate with others
about the type of client being classi­
fied nor about the type of services that
should be made available to the client.
Another problem faced by the person
designing categories is the degree to
which the classifications employed will
overlap.

For example, the category

"Difficulty with Washing" is presumed to
be related to the category "Difficulty

64
with Dressing" and the category "Meal
Preparation" will overlap or be corre­
lated to some extent with the category
"Light Cleaning."
Consideration of these issues leads
to another possible means of classifying
functional status; that is by means of
designating the services required by
clients as the proxy for functional
status.

Thus instead of classifying

clients according to their degree of
impairment in mobility or dexterity,
etc., the classification might be in
terms of the service needs of the patient.
Using this approach, a client might be
classified as needing services such as
light cleaning, meal preparation, trans­
portation and yardwork.

Clients with

different attributes according to the
previous definitions of functional status
might require identical or different
mixes of services.

A possible limita­

tion on the use of needed service mixes
as indicators of functional status lies
in their strictly qualitative form.

The

amount of a particular service required
is unquantified in the data though the

65
hours required to perform the total mix
of services has been recorded.
Theoretically, there is a relation­
ship between the functional status as
measured by mobility, dexterity, etc.,
and the types of service provided to a
client.

This relationship, taking into

consideration socio-economic status is
analyzed in detail utilizing the entropy
minimax pattern detection algorithm as
described in Chapters

6

and 7.

In that

analysis, functional and socio-economic
status are both specified as inputs or
attributes.

Services provided to the

client are specified as outputs.

In the

analysis of costs under consideration in
this chapter, levels of impairment and
service mixes are both considered as
alternative forms of specifying functional
status.

In some forms of the model,

equations will be presented that encom­
pass aspects of both forms of functional
status.
Services received by patients are
listed and described below:
(i)

Light Cleaning (LK).

This service

includes such tasks as washing

66
dishes, tidying rooms, making beds,
and other light tasks performed on
a routine basis.
(ii)

Heavy Cleaning (HK).

Under this

designation appears such one-time
tasks as washing and waxing floors,
polishing furniture, cleaning bath­
rooms, appliances and windows.
(iii)

Home Maintenance and Repair (HMR).
Services performed under this
heading include small paint jobs,
repairs to furniture, attendance to
storm windows and similar tasks.

(iv)

Meal Preparation (MP).

Most com­

monly this service involves the
daily preparation of
the client.

2

meals for

Both meals may be pre­

pared during the same visit, one of
them being stored for later use by
the client.
(v)

Laundry (L).

Regular washing of

clothes, bedsheets and linens as
required.
(vi)

Shopping and Errands (S) .

With

this service the client expects
food and other goods to be purchased
and then delivered to his/her home.

67
(vii)

Financial Management (FM) .

Attend­

ing to income and expenses is some­
times beyond the client's ability
especially if mental impairment is
apparent.

For this reason, these

services are offered and cover such
tasks as making out tax forms, appli­
cations for benefits, and attending
to other money related problems.
(viii)

Transportation (TT).
are:

Included here

transport of clients to

physicians, to recreational and
cultural activities, to stores,
churches and friends.
(ix)

Attendant (A).

This service involves

a person being able to accompany the
client when being transported to a
hospital or to a doctor's office.

(x)

Yardwork (Y).

Yardwork largely en­

tails cleaning of yard, lawn
maintenance and snow removal.
(xi)

Non-Nursing Personal Care (NNP).
Personal care involves assisting
the client with dressing, toileting,
transferring from bed to chair or
to another room, bathing and other
personal care tasks.

The above listed clients services
are entered into the cost models as
binary exogenous variables, a procedure
described later in this chapter under
the discussion on the economic model.
They are treated differently, in
Chapters 7 and

8 where

they are consi­

dered to be outcomes which are some­
what equivalent to endogenous variables.
The Socio-Economic Status Variable and its
Categories.
The socio-economic status variable is
divided into

6

categories:

age, sex, loca­

tion, income, client contribution and rela­
tionship/domicile.
a)

They are described below,

AGE (A^, A 21 A^ f ^ 4) *
The ranges in age corresponding to
the 4 part grouping are A^: <60 years of
age; A 2 : 60 through 69; A^: 70 through
79; and A4 : >80.
It is hypothesized that age is
positively related to endogenous vari­
ables TCM and TH.

The reason for this

is that among the aged chronic conditions
tend to be more numerous and are likely
to interact with the level of disability
resulting in higher costs and hours of

69
service.

We should find coefficients of

categories in the higher age ranges to
be relatively larger than those in the
lower age ranges.
b)

SEX <SF).
Traditionally men, compared with
women, have done few of the domestic
maintenance chores associated with run­
ning a household.

On the basis of this

it is hypothesized that all other things
being equal, men will require more
services than women.

Since the binary

nature of this category is such that
for women a unit figure is indicated
and for men a zero, a negative sign on
this coefficient is hypothesized with
respect to all 3 endogenous variables.
Females are represented by 1, males by 0.
c)

LOCATION (LOC).
Clients living in Standard
Metropolitan Areas (SMSA's) are classi­
fied as urban dwellers. Others are classi­
fied as rural.

The postulated hypothesis

is that monthly and hourly costs of care
will be higher for urban dwellers.

This

is expected because opportunity costs
are higher for providers who have both

70
more employment opportunities and higher
wages in urban areas.

An urban client

is represented by unity, the rural client
by
d)

0.

INCOME (INCl, INC2, INC3, INC4, INC5).
Clients income largely derives from
Supplemental Security Income (SSI), Re­
tirement Disability Survivors Insurance
(RDSI) or a combination of the two.

The

few clients receiving less than the
minimum SSI amount are probably in the
process of applying for it.

Income is

stratified into 5 binary categories:
INC1, >$250.01 per month; INC2, $200.01
to $250.00; INC3, $150.01 to $200.00
per month, INC4, $100.01 to $150.00;
and INC5, <$100.00.
e)

CLIENT CONTRIBUTION (CLTl, CLT2, CLT3,
CLT4).
When assessing a client's eligi­
bility for chore services, client income
is reviewed.

The cost of the service

required by the client is also determined.
If the client's income or assets lie
above the SSI standard, the full amount
by which it exceeds the SSI standard is
deducted from the cost of the services.

71
The chore service payments# in effect#
make up the difference between that
which a client can afford and the total
cost of the services.

At least 80% of

clients have neither sufficient incomes
nor sufficient assets to enable them
to pay part of the cost of chore services
required.
Client contribution is broken down
into 4 binary categories:

CLT1# >$50.01;

CLT2# $25.01 to $50.00? CLT3# $0.01 to
$25.00; and CLT4 = 0.
It is hypothesized that as client
contribution increases# the cost of
care increases.

The basis for this hypo­

thesis lies in the assumption that for
low cost chore services the client with
income in excess of the (SSI) standard
is likely to pay for his/her own services
and not apply for chore service subsidi­
zation.
f)

RELATIONSHIP/DOMICILE (RL1, RL2, RL3, RL4).
This category refers to the nature
of the relationship between the provider
and the client as well as the living
arrangements of the client vis-a-vis the
provider.

This category is subdivided

into 4 sub-categories.

72
(i)

The client's relative providing
services in the home which both
share (RL1).
This subcategory of the SES
variables is characterized by a
situation in which both the client
and the provider live under the
same roof. Care is provided to the
client by a sonf daughter, parent or
some other relative.

It is believed

that relatives will work for lower
incomes than non-relatives since part
of their income will be psychic to
the extent they feel an obligation,
or like, to care for their relative.
It is also believed they will put
in longer hours of service than the
non-relative in an equivalent situa­
tion.

For these reasons we hypothe­

size that the subcategory will be
negatively related to TCM and CH
but positively related to THM.
(ii)

The client's relative providing ser­
vices in the client's home but liv­
ing elsewhere (RL3).
The relatives providing care
for clients in other households are

73
presumed to require greater benefits
to compensate for the greater oppor­
tunity costs incurred in leaving
their own home and providing ser­
vices in that of the client.

With

this in mind it is hypothesized the
coefficient of this subcategory will
be relatively larger than that of
RL1 for TCM and CH but smaller for
THM.
(iii)

Non-relative providing services in
the home where both the provider
and the client are domiciled (RL3).
Since the non-relative is
assumed to enjoy less psychic in­
come from the provision of care
for a non-relative than would be
the case with care of a relative,
the hypothesis with respect to
this subcategory would lead us to
expect the coefficient of RL3 to
be larger in a positive direction
than that of RLl for TCM and CH
but smaller for THM.

(iv)

A non-relative providing services
in a household of a client who lives
separately from the provider (RL4).

Based on theorizing with re­
spect to RLl, KL2 and RL3 above, it
is hypothesized here that the coeffi
cient of RL4 will be greater in a
positive sense than all other coeffi
cients of the KL subcategories for
TCM and CH but small for THM.
g)

OMITTED CATEGORIES OF THE SERVICE
VARIABLE.
Variable categories omitted from
the equations in which categories of the
service variable appear were GUIDE DOG,
INTERPRETER and OTHER.

These were left

out because they were supplied to only
a small number of clients.
The Medical Status Variable.
Medical Status was included in the data
as transcribed from the form DSS-3492 and
subdivided into 9 diagnostic conditions:
Mental retardation (HS1), mental illness
(HS2), heart-related problems such as
cardiac condition, coronary problems, hyper­
tension and strokes (HS3), respiratory and
related diseases such as paralysis, arthri­
tis and paraplegic conditions

(HS5),

diabetes (HS6) , cancer (HS7), recuperation
disabilities resulting from a recent

75
operation, accident or bone fracture (HS8),
and other (HS9).
Medical status was also categorized
according to whether the medical condition
was the first (or primary) health problem,
second health problem, third or fourth
health related problem.

Since the response

rate on the client encounter data sheet
(DSS-3492) was incomplete, 20% of the forms
ommiting

any reference to health related

problems, only the first health related
problem was employed in this analysis.
In the Greenberg study (ANDERSON ET AL
1974) medical status was found to have no
significant influence on costs of services
provided in the home even where costs of
medical professionals were included.

Medi­

cal status is included in this research to
confirm or question those results.

Costs

of medical professionals have not been in­
cluded in this data so comparisons will re­
late only to the chore services.
The hypothesis with respect to the medi­
cal status variable is that its inclusion or
exclusion from the equations being estimated
will make no significant difference to the
variation in any of the 3 endogenous variables.

Economic Model.
Each of the mathematical models posited at
the beginning of this chapter has so far been
characterized by 3 exogenous variables, functional
status (FS), socio-economic status (SES), and
medical status (HS).

Model A is characterized

by the endogenous variable total cost of chore
services per month (TCM); Model B by total hours
of service per month (THM); and Model C by cost
per hour (CH).
In economic terms the models embody behav­
ioral relationships between the endogenous vari­
ables and the exogenous variables.

Each

exogenous variable is subclassified according
to specified categories which are in turn sub­
divided into between 2 and 5 subcategories.
These were all listed and described above.
Within the relevant range in each model,
the relationship between each category of the 3
exogenous variables and the endogenous variable
is assumed to be linear.
The structural equation established in each
model has a set of structural parameters:

&1

to

Y1

to ^m ^or

for categories of functional status

cate9or:*-es

status

of socio-economic

77

6i

to

6n

for categories of medical status

The parameters are identically designated
for each model.

Thus in Model A the full equa­

tion would appear as follows:
TCM = (3FS' + ySBS' + <5HS' + U 1
where

EQUATION

3 is a vector of functional status
parameters
Y is a vector of socio-economic status
parameters
6 is a vector of medical status para­
meters
FS is a vector of functional status
categories
SES is a vector of socio-economic cate­
gories
HS is a vector of medical status categories
U is an error term.
In each of the models, Functional Status

has 3 alternative forms.

Taking as our example

the Functional Status portion of Model A, the
alternative Functional Status categories would
appear as designated below:
1.

Functional Status Specification in "cardinal 1
1
form.

TCM = *MOB M0B + ^DEX DEX +
EQUATION
(5.2)

where MOB = mobility on rising impairment
scale from 1 to 5
DEX = dexterity 1 to 5
SEN = sensory perception 1 to 5
COMP = comprehension 1 to 5
HOM = home management 1 to 5
Functional Status Specification in Binary
Form

EQUATION
(5.3)

where (all are specified as

1

if present,

if not):
Ml = mobility with no impairment
M2 = is between Ml and M3
M3 = mobility with some impairment
M4 = is between M3 and M5
M5 = much impairment in mobility.
= dexterity with no impairment
D 2 = is between Dl and D3

0

D 3 = dexterity with some impairment
= is between D3 and D5
D 5 = much impairment in dexterity
= sensory with no impairment
S 2 - is between SI and S3
Sg = sensory with some impairment
S^ = is between S3 and S5
Sg = much impairment in sensory
= comprehension with no impairment
C 2 = is between Cl and

c3

C 3 = comprehension with some impairment
= is between C3 and C5
Cg = much impairment in comprehension
= home management with no impairment
K 2 = is between K1 and K3
Kg = home management with some impairment
= is between K3 and K5
Kg = much impairment in home management
Functional Status Specified in the Form of
Services Required:
TCM = eLKLK + 3hkHK + ShmrHMR +

Bmp'® +

bll

+ 8s s +

3f m p m + *t t t t + &a a +

E<
EQUATION
(5.4)

3yY + ®NNPNNP
where (all are specified as
and

0

if not):

1

if utilized

LK = light cleaning services
HK = heavy cleaning services
HUM = home maintenance and repair
MP = meal preparation
L = location
S = shopping and/or errands
FM = financial management
TT = transportation
A = attendant
Y = yardwork
NNP = non-nursing personal services
The full specification of the equation
of Model
that

A appears below with the

any of the alternative forms

provision
ofFunc­

tional Status could be signified by the
term BFS in the following equation.
TCM

= 0FS 1 + Y ^ ^

+ VA2A2 +

*A3A3 + *A4A4 + YSFSF +
+ ^INC1 INC1 +

1rINC21NC2

+ Y INC3INC3 +

^INC4 ^^'4 +

*

YCLT1 CLT1 + YCLT2 CLT2 +

EQUATION
<5 *5)

YCLT3 CLT3 + YCLT4 CLT4 +
^RLl 1^ 1 + YRL2RL2 + YKL3 RL3 +
Yjy^RI^ +

6-jHSl

63H S 3

+

64H S 4

6gH S 6

+ 6^HS7 +

+ 62HS2 +

+ S5HS5 +

6gHS8

+ 69HS9

81
where (all are specified as if
present,

0 indicates

1

indicates

not present);

FS = vector of functional status cate­
gories
A^ - age, <60 years old
A 2 = age, 60-69 years old
Aj = age, 70-79 years old
A 4 = age, >80 years old
SF = sex,when SF = 1 client is female
LOC = location, when LOC = 1location

is

urban
INC1 = income >$250.01 per month
INC2 = income $201.00 to $250.00

per month

INC3 = income $150.01 to $200.00

per month

INC4 = income $100.01 to $150.00

per month

INC5 = income <$100.00 per month
CLT1 = clients contribution >$50.01 per
month
CLT2 = clients contribution $25.01 to
$50.00 per month
CLT3 = clients contribution $0.01 to
$25.00 per month
CLT4 = clients contribution of zero
dollars per month
KL1 = client is related to the provider
and they are living together

82
RL2 = client is related to the provider
and they are living apart
RL3 = client is not related to the pro­
vider and living together
RL4 = client is not related to the pro­
vider and living apart
HS1 — mental retardation
HS2 = mental illness
HS3 — heart related problems
HS4 = respiratory related problems
HS5 = mobility related problems
HS 6 = diabetes related problems
HS7 = cancer related problems
HS 8 = recuperation related problems
HS9 = other problems
One result we seek is the proportion of
the inter-client variation in each of the 3
endogenous variables which can be explained
by each of the 3 exogenous variables.

It

should be realized that among the 3 exogenous
variables, functional status is a special
case since there are several alternative
forms and combinations of those forms by
which it may be entered into the equations.
With the proviso that multicollinearity will
be taken into consideration, we can by drop­
ping each variable in turn, but not

83
simultaneously/ from the full equation,
determine the amount of inter-client varia­
tion in the endogenous variables associated
with the variable in question.

In so doing

we should be able to determine the amount
of inter-client variation attributable to
each of the 3 exogenous variables in each
of the 3 models.
In the case of the socio-economic status
variable we can drop simultaneously all levels
of each category from each of the 3 equations
one category at a time to determine which
categories account for significant changes
in inter-client variation in the 3 endogen­
ous variables.
Finally, we can observe the signs and
significance of coefficients at each cate­
gory level and determine within categories,
the relationship between one level of a
category and another level.

Such levels

within categories are sometimes cardinal,
occasionally ordinal, but usually qualita­
tive.

Problems of interpretation of coeffi­

cients is anticipated in the event that the
coefficients are unstable, that is exhibiting
both positive and negative signs or manifest­
ing large standard errors.

Such problems

84
may be exacerbated by evidence of multicollinearity.
The client attributes included in the
models are hypothesized to be important
categories in explaining the variation in
cost or hours worked by the provider.
Client attributes such as those associated
with socio-economic status (e.g., location,
age, etc., as distinct from the variable
SES) are also included to correct (adjust)
for differences among clients who have the
same functional status and medical status
but different costs due to the SES attri­
butes; for example, urban-rural cost differ­
entials.

We will examine the significance

of these categories to determine which ones
to include in future studies.

Inclusion of

significant attributes reduces the disturb­
ance term "U" and increases the accuracy of
our estimates of other coefficients.

Also,

if attributes are correlated with included
variables, their exclusion leads to bias.
Though bias is incurred, we can also
get some indication of category influence
on variation in the endogenous variable by
deleting it from the equation and observing
_2
the extent to whxch R changes.

85
D.

Econometric Specifications and Assumptions.
Multiple regression will be used to analyze
statistically the models using the standard
ordinary least squares algorithm.

The estimated

coefficients are assumed to be unbiased, effici­
ent and consistent if the disturbance term "U,"
appended to the end of each equation, meets the
standard assumption that its distribution is
normal and its mean, zero.

There is no reason

to doubt the assumption.
The likelihood that the other standard
assumptions (KMENTA 1973) are met is also high.
Homoskedasticity can be assumed because the
state puts an upper limit on costs.

The assump­

tion of linearly independent exogenous categories
can also be assumed because the study is crosssectional.
In order to test the models, the equations
were run in a form different from that specified
in the Economic Model discussed in the previous
section.

As mentioned, several of the variable

categories were qualitative.

In these cases,

dummy (0-1) variables had to be employed.

Where

this was the case, one of the subcategories had
to be dropped to avoid the problem of attempting
the inversion of a singular matrix.

The effects

of dropping these subcategories was picked up in

86
a new constant term "a" which became appended
to the front of the right hand side of the
equation.

Employing the second alternative form

of the functional status variable, in Model A
{EQUATION 5.3) the modified equation appears
below.
TCM = a +

6m 2M 2

+ ... + 0m 5M 5 +

BD2D2 + *•* + &D5D5 +
eS2S2

+ *** + eS5S 5 +

0C2C2

+

* * * + 0C5C 5 + ^K2HOM2 + * * * +
R HOM + v A +
+
EQUATION
K5
+ YA2A 2
•**
(5.6)
*A4A 4 + ^SFSF + YLL0C + Y INC2 ™

C2

+ •*' + YINC5 INC5 + YCLT2 CLT2 +
•** + yCLT4 CLT4 + YRL2 RL2 +
... + YRL4RL4 + « H81 + 62HS2 +
64HS4 + ... + 6gHS9 + U
It can be seen that in each category, the
first subcategory was dropped.

The exception

to this was in the medical status variable where
the third category (heart problems) was dropped,
this being the most

mentioned physical mani­

festation of poor health.
As a check on the accuracy of the estimated
equations, approximately one third of the 628
cases were randomly assigned to a "Test set."
The models will be estimated and modified using

87
428 "training" cases and the final modified
models will then be re-estimated using the
"test" cases.
the

2

200

When comparing the results from

sets of data we will be looking for con­

sistency in:

(i) the magnitudes and signs of

coefficients;

(ii) the significance of F-tests

associated with each coefficient; and (iii) the

—2

magnitude of R .

The larger sample of data is

hereafter referred to as the 'training set' and
and the smaller as the 'test set.'

III.

Conclusion
Since the description of variables is more readily

understood in the context of a common form of analysis, such
as regression analysis, the emphasis in the chapter was
placed on the variables as they were entered into the cost
analyses.

A description of the economic models and the

econometric specification of those models was presented in
this chapter.

The empirical analysis of data based on the

models presented in this chapter is to be found in Chapter
Chapters

6

8.

and 7 draw on this chapter in so far as

it describes the variables to be employed in analyzing the
relationships between client attributes and services.
Chapter

6,

the following chapter, describes the theory asso­

ciated with the entropy minimax algorithm and presents a model
for estimating the relationships between attributes and ser­
vices.

CHAPTER 6
THEORY UNDERLYING THE ENTROPY MINIMAX PATTERN
DETECTION ALGORITHM AND ITS UTILITY IN DETERMINING
THE RELATIONSHIPS BETWEEN CLIENT ATTRIBUTES AND SERVICES

I.

Introduction
This chapter addresses itself to describing a method

of discovering relationships between a client's profile of
attributes and the services received by the client.

If such

relationships are detected and found to hold up under further
testing, on different data, then it should be possible to
determine the types of service received and estimate their
costs on the basis of a client's profile.

Since such rela­

tionships have not been statistically demonstrated and since
there is no established theoretical basis on which to posit
testable hypotheses, a method was sought that would detect
such relationships.

II .

Choice of Methodology to Detect Relationship Between
Sets of Multiple Outcomes and Sets of Characteristic
Attributes
The problem at hand is to find an algorithm which

will enable us to estimate relationships between multiple
outcomes and multiple attributes.
88

For example, given a client

89
with a known attribute profile# is it possible to determine
the likelihood or probability of him/her receiving specific
services?

Since there is usually more than one service

assigned to a client, the algorithm should determine the
probability of one or more services assigned to a client,
given that client's attribute profile.
Two regression techniques,

'Probit' and 'Logit'

analysis offered possible avenues to approach the problem
since, in both, the dependent variable can be dichotomous
(THEIL 1971).

In both, probability of an event or outcome

is related to a set of attributes or independent variables.
In the case of probit analysis, the probability of
an event P is related to the independent variables X as fol­
lows:
P = 1 - F (a + BX)
subject to the constraint
There are several

0 < P < 1.
major drawbacks to using this

approach:
1)

The normal integral

F (a + BX) implies a normal

distribution.There are

no grounds on which to

maintain this hypothesis.
2)

In the above form, only one outcome can be
accommodated.

3)

Though other forms may be developed that accommo­
date more than one outcome, the computational dif­
ficulties are enormous since it becomes difficult
to specify a maximum likelihood estimator.

90
4)

Given the number of outcomes and attributes
involved in this analysis, the number of equa­
tions to be estimated would be unrealistically
large since there is no theory to relate cer­
tain outcomes to given attributes.

In logit analysis the functional form is:

e a + ex
P =

1

+ e“ + ex

which transforms to:
In j-z-p = a + BX
subject to the constraint P > 0.
The objections to employing this form are similar
to those detailed under probit analysis.

Both approaches

assume the data conform to given specific distributions
which may or may not be the case.

We desire an algorithm

that has no such distributional assumptions.
the literature on information theory.

One exists in

It is called the

entropy minimax algorithm and is used as a hypothesis dis­
covery procedure.

Once relationships between outcomes and

attributes are discovered, using entropy minimax, they may
be tested using the logit analysis, especially where single
outcomes are involved.

Such testing would seek to demon­

strate that for a given outcome, coefficients of attributes
were significant.

To ensure the absence of contrived rela­

tionships, the testing of the discovered hypotheses (if any)
is to be conducted on a second 'test' sample of data.

Other

91
clustering algorithms might have been chosen such as factor
analysis.

These were not adopted since, in a recent survey

of tests on clustering algorithms, the entropy minimax
algorithm was found to converge more quickly than the others
(JOHNSTON 1976, GIFT 1978a). It had a smaller error rate and
was not constrained by the assumtion of an apriori distribu­
tion.

III.

Background on the Entropy Minimax Algorithm
Since little has been published on the entropy mini­

max pattern-detection algorithm, the description of the
background and procedure employed here is somewhat more
detailed than would be the case with a more commonly used
form of analysis.

Much of the following discussion is based

on papers by Schonbein and Gift (SCHONBEIN 1978, GIFT 1978b).
The discussion here diverges from theirs insofar as the
application is different in both subject and interpretation
procedures.
Entropy minimax is employed as an application of
statistics in the field of communication.

It was developed

by Christensen and enables a researcher to simplify the
structure of a data source and reduce uncertainty about the
data (CHRISTENSEN 1972, 1973).

Its major utility has been

realized in seeking patterns or knowledge in seemingly ran­
dom and complex data.

To the extent that knowledge can be

gleaned from apparently random data, the degree of random­
ness (or entropy as it is referred to in information theory)

92
will be reduced.

The specific amount by which the random­

ness or entropy is reduced can be measured.

This measure is

an indirect indicator of the quantity of knowledge extracted
from the data after applying to it the entropy minimax
pattern detection procedure.
Entropy, in the informational theoretic setting, is
similar in concept to that of thermal energy in physics.
In physics, entropy is a measure of the unavailability of
a system's thermal energy for conversion into mechanical
work.

Entropy, as defined in information theory, is a

measure of the unavailability of a system* s random data for
conversion into knowledge.
For any system of data, there are two components:
(i) entropy or uncertainty, and (ii) knowledge.

Seemingly

random data would appear to yield no knowledge, that is,
to consist entirely of entropy (uncertainty).

After apply­

ing a pattern recognition algorithm to the seemingly random
data, it may be possible to detect patterns or gain knowledge
or, equivalently, eliminate some uncertainty.
knowledge is gained, entropy is reduced.

To the extent

In this approach,

knowledge per se cannot be measured; only the reduction in
uncertainty can be quantified.

The reduction in uncertainty

is measurable and is called 'information.'

A more general

definition of information is, "the change in the random state
of knowledge."
Uncertainty is at a maximum when complete randomness
is evident, that is, when all events are equally likely.

93
Uncertainty is zero when an event is certain, either to
occur or not occur.
For analytic convenience, it is helpful if measures
of uncertainty are additive across the number of possible
events in the data.

A commonly used measured of entropy,

and one meeting the additive criterion, was developed by
Shannon (SHANNON 1948).

It is represented by the expected

or average amount of information one would receive upon
observation of an event occurrence from the system of data.
For example, in the case of chore services we might, by
examining a client profile of attributes (an event occurrence),
gain information about probable services appropriate for
that client.
Data to which the entropy minimax procedure is
applied is broken down into two categories; an attribute
list or inputs, and an outcome or class membership list.
Attributes are commonly measurements or observations on
sample cases such as sex, age, income, functional status,
etc.

The outcome signifies the classification of a system

of events; in this research the full range of the types of
services received by clients such as light cleaning, laundry,
meal preparation, etc.

The data source is a sample from the

population of clients.
Assumptions associated with the employment of the
entropy minimax procedure in this research are the follow­
ing:

Individual samples drawn from the larger popula­
tion of events are independently and identically
distributed.
Statistical regularity in the population with
respect to client management decisions is evi­
dent and the conditional probabilities for
various outcomes exist.
Clients with similar attribute profiles are
assigned similar services signifying consistency
in decision making.

This assumption implies

that in approving certain services for clients,
the social worker making the assignments, makes
his/her decision on the basis of the client's
recorded functional, socio-economic and medical
status.

This is a key assumption since, should

no patterns be detected, the implication could
be that this assumption is violated.

It might

then be hypothesized that the social worker's
assignment of services is based on other than
Ji

the recorded functional, socio-economic and
medical status of the client.
Attributes characterizing the client profile are
significant in relation to outcomes and are
important or controlled - to obviate affecting
the results.

Attribute vectors are assumed to

contain a sampling of factors affecting the
decision-maker's choice of outcome.

95
Unlike Assumption C above, this assumption
implies there is a relationship between a client's
attributes and the services assigned to him/her.
An underlying assumption is that a social worker,
if consistently employing the attribute profile
of the client, would assign services on a
systematic and statistically detectable basis.
The absence of detectable patterns would signify
a violation of this assumption.

Such findings

could flow from a consistent social worker
seemingly assigning services on the basis of
attribute characteristics but there being no
systematic relationship between the two.

Such

a violation would suggest the specific attribute
profile analyzed to be of no value in assigning
services.
An inherent limitation of the procedure lies in the
necessity for judgement and intuition in the specification
of components of the attribute vector.

A related problem is

the identification of a client's characteristics and the
accurate transformation of them into the attribute profile
format necessary for manipulation in the entropy minimax
procedure.

IV.

The Entropy Minimax Procedure
This section of the chapter describes how the entropy

minimax procedure operates conceptually.

The data set of

96
interest is classified according to N clients, M individual
attributes, and K mutually exclusive outcomes.

A schematic

representation of the decision process is presented below:

Decision
Process ^ O u t c o m e s

(Q1,Q2*-*QK )

Data processed by the entropy minimax procedure are
generally in binary form; therefore, continuous variables
are transformed into two or more parts, each part becoming,
in effect, a newly specified attribute.

The outcomes should

be mutually exclusive but there are means of running the pro­
cedure when this restriction is not met.
The set of observable data would appear as illustrated
in Table 6.1.

We are interested in testing the hypothesis

that a patterned relationship exists between attributes and
outcomes.

We are also interested in generating a hypothesis

to the effect that a given set of attributes is probabilis­
tically related to a given outcome or set of outcomes.

This

hypothesis could be then tested on different data using
classical statistical methods such as regression analysis,
in particular, logit analysis.
Since the entropy minimax procedure measures the ex­
tent of any statistical relationship between attributes and
services, it would appear to be a useful tool for comparing
one attribute profile format with another format.

Each for­

mat would presumably have different categories or subcategories

97

TABLE 6.1.--Data format for individual client attributes
and their outcome states
OUTCOME STATE

ATTRIBUTE VECTOR
Client

0

al

a2

a3 ..... aM

Qi

q2

Q3 ..... * Q]

1

0

0

1

0

1

0

...... ..

n

2

1

0

1

0

0

1

...... ..

0

3

0

0

1

1

0

0

...... ..

0

4

1

1

0

0

1

0

....... .

l

1 indicates the attribute or outcome is present;
it is not.

98
and perhaps different specifications of variables.
ous

profiles

The vari­

of activities of daily living could be compared

with each other on the basis of how accurately they predict
outcomes, i.e., services.
To simplify the explanation of the entropy minimax
procedure we will take as an example, a sample of clients,
each characterized by an attribute profile of three identical
categories.

A point in three dimensional space would thus

encompass all three attribute categories.

The purpose of

employing the entropy minimax pattern detection procedure
is to divide up the space or volume (a process known as
partitioning, screening or analogical screening) into blocks
such that each group or individual classification of outcomes
is uniquely represented by one of the blocks.

In terms of

the chore service program, after such a screening program
has been run, we should be in a position to take an additional
client’s attribute profile and predict:

(i) in which block

it should be placed, i.e., which services would be utilized
by that client, and (ii) the probability of the client fall­
ing into that block, i.e., actually being assigned those
services represented by that block.
For example, in Figure 6.1 we have a three dimensional
attribute space:

A = (a^, a2 , a^)•

Let us assume the dimen­

sion a^ represents the sex of the client and equals "f" if
the client is female, "M" if the client is male.

Let the

second dimension a 2 represent the relationship of the client
to the provider, where a 2 equals "r" if the provider of

99

nr

nw

f or

1

nr or

1

nw or

0

FIGURE 6.1.— Screening of a three dimensional space into two
outcomes

services is a relative and equals "nr" if the provider is a
non-relative.

The third dimension a^ represents mobility

where a^ equals "w" if the client is mobile and equals "nw"
if the client is immobile.
i

There are potentially eight elementary cells for
which there is only one attribute value for each cell.
we assume two outcome

If

states, say meal service represented

by the small detached block in Figure 6.1 and other services
(OS) represented by the remaining seven-eights of the block,
then the tabular representation of the results would appear
as in Table 6.2.

Let the probability of employing meal

services be P(M).

The conditional probability

represents the probability of employing meal services given
that the profile An is observed.
In this case, cell number seven is partitioned from
the rest of the attribute space and meal service is provided
to clients falling into that cell according to a quantified
conditional probability.

Other services are provided to

other clients according to a different conditional proba­
bility.
To take a more complicated example, a different
screening has been performed on the three dimensional attri­
bute space partitioned in Figure 6.2.

This latter screening

has partitioned the attribute space into four outcomes;
Q-^, Q2 , © 3* and Q4>

These are shown in Figure 6.2.

From Figure 6.2 we could draw the conclusion that
within the class of clients for whom the value of a 2 =

0

101

TABLE 6.2.— Conditional probabilities of specific outcomes
given characteristic attribute profiles
Outcome State
Attribute
Vector

(observed)
M

1)

0

a2 a3
0 0

2)

0

0

3)

0

4)

al

Q_ (not observed)
Q

P[M/(ai=0,a 2=0,a 3=0)]

P[Q/ ^ =

1

P[M/(a 1= 0 fa 2=*0,a3=l)]

P[Q/(a^= 0,a2= 0,a3=l)

1

0

P[M/(ai=0,a 2=l,a 3=0)]

P[Q/(a1=0,a 2=l,a 3=0)

0

1

1

P[M/(a x=0,a2= l ,a 3=l)]

P[Q/(a 1=0,a 2=l,a 3=l)

5)

1

0

0

P[M/(3^

P[Q/(a 1=l,aa=0,a 3=0)

6)

1

0

1

P[M/(a 1=l,a 2=0,a 3=l)]

P[Q/ (3^

7)

1

1

0

P[M/(3^

p[Q/(a 1=l,a 2—l,a 3= 0)

8)

1

1

1

p[M/(ai=l,a 2=l,a 3=l)]

1,32= 0,83= 0)]
1,32= 1,83= 0)]

P[Q/ (3^

0 ,82= 0,33= 0)

1,82= 0,33= 1)
1,82= 1^ 3= 1)

102

nv

P [Q3 |a^— 0 r 2

/&

P[Q

nw

1

FIGURE 6.2.— Screening three dimensional space into four
outcomes.

I

103
(those with relatives as providers), the values of the other
two attributes, a 1 (sex) and a 2 (mobility) are immaterial in
predicting the outcome Q^.

In the case of outcome C^, two

attributes a^ and a 2 are pertinent in the determination of
that outcome? the mobility vector a^ is immaterial.
Q 3 and

Outcomes

are both dependent on the level of all three attri­

butes.
The entropy minimax procedure consists of a stepwise
algorithm to partition the attribute space.

The first step

is to find the most populous sub-volume with the lowest
entropy; in Figure 6.2 this volume would be represented by
P (C^/aj^O).

This sub-volume is then removed together with

all the cases (clients) in it.

The next step searches for

the next most populous sub-volume, e.g., that associated
with outcome Q 2 which turns out to have the lowest entropy
for its size.

These steps continue until the pre-set limit

of steps is reached or until no more volume of attribute
space remains to be searched.

The number of partitions per­

formed on the space can also be limited by a minimum degree
of significance attributable to the last sub-space removed.
Each volume or space identified is characterized by:
(i) the attributes within that space;
ciated with that space?

(ii) the outcome asso­

(iii) the conditional probability

relating a specific outcome to a specific vector of attri­
butes (A.),
i.e., P(QV/A.)?
(iv) the amount of entropy or
X
-K 1
uncertainty removed from the total entropy as a result of
removing the sub-space volume.

It is also possible to

104
estimate to what degree the entropy removed is significant.
Possible extremes that can be achieved in the partitioning
or screening process are:

(i) for the space to be divided

into the number of partitions equal to the number of events
(clients), in which case the amount of data in any one cell
is so small that conclusions as to probabilities cannot be
determined;

(ii) to take all the data and treat it as one

cell or one volume thus ignoring potential information asso­
ciated with independent variables.
Probabilities are based on directly observable fre­
quencies , there being many logically consistent sets of
probabilities.

Probability estimates assigned to conditional

relationships between attributes and outcomes depend on the
specific screening used to partition the sample data; that
is they depend on the way in which the space is "chopped up."
The entropy of the total sample space, when that space
is treated as an undivided cell, is a measurable entity con­
stituting the maximum entropy associated with that space.
When the entropy of partitioned space is lower than that of
unpartitioned space the existence of a patterned structure
within the seemingly random data is evident.

The measure of

the degree to which entropy is reduced by the partitioning
is an indicator of the unquantifiable amount of knowledge
gained by partitioning the space.

Entropy is thus both a

measure of the reduction in uncertainty resulting from the
screening, and a useful criterion by which to measure the
relative efficacy or "goodness" of each screening.

The "best"

partitioning is signified by that screening yielding the
maximum amount of entropy removed.

The entropy minimax

algorithm selects a screening which maximizes the informa­
tion extracted from the sample and minimizes the amount of
"bias"* in the result.

When classical statistical procedures

are used to analyze seemingly random data, it is common prac­
tice to ignore the screening problem.

That is, the data is

divided into variable categories on theoretical grounds or
intuitively before classical techniques are applied.

Where

no theoretical grouns exist for such divisions, the entropy
minimax procedure would likely yield results superior to the
intuitive approach.

Furthermore, it is much less likely to

result in spurious relationships.

V.

The Mathematics of Entropy Minimax
Entropy, otherwise known as informational entropy or

the expected value of information is commonly notated as
H(Q ;A) and is defined by the following equation:
_
_
_
H{Q;A) = - I
S P(Qt ,A.) I(Q.,A.)
k=l i=l
K 1
* 1

EQUATION
(6.1)

*In the context of entropy minimax, bias refers to the
possible selection of a screening in which the maximum entropy
has not been determined or arrived at before the entropy of
that screening is compared with the entropy of other screenings.
Unbiasedness indicates that for any given screening the maximum
entropy of that screening is determined and compared with the
maximum entropies of other screenings.
It is the minimum en­
tropy among these maximum entropies that indicates the best
screening...thus the term Entropy 'Minimax.'

106
where I

, commonly referred to as 'mutual information'

represents the amount of information with respect to Q^, and
is defined as:

—

N

Manipulation of Equation 6.1 (SCHONBEIN 1978) leads to the
following equation:
H (Q; A) = H (Q) - H( q |a )

^6^3)1 ^

where H(Q) represents the self information of the outcome
states or the maximum value of entropy in the data.

H(Q A)

is the conditional entropy of uncertainty remaining after
the attribute vector has been observed.

We seek to minimize

this measure of entropy.

This measure might be considered
2
to be the information-theoretical counterpart of 1-R in

regression analysis.
The residual uncertainty H(Q| a ) is that entropy re­
maining after observing an attribute vector A when that vector
fails to completely predict an outcome.

Certain prediction of

an outcome Q that is based on observation of attribute vector
A would result in the entropy H( q Ja ) becoming equivalent to
H(Q) thus rendering total entropy H(Q;A) = 0.
For any given partition the algorithm seeks to maxi­
mize the entropy? equivalently, this entails the minimization
of H( q |A).

After recording the entropy for the first parti­

tion or the first cell of the algorithm, the algorithm will
continue scanning a variety of candidates for first cell until

107
it encounters one of a lower maximum entropy which it records.
The scanning procedure continues and terminates when it en­
counters no cell of lower maximum entropy than that previously
recorded.

The program records the probability of the outcome

identified with that cell given the attributes associated
with the cell.

It also records the amount of entropy removed

from the total entropy as a result of removing that cell.
The data associated with that cell is then dropped from the
complete set of original data and the search procedure starts
again on the remaining data to identify a second cell.

The

second cell will usually be found to remove less entropy
from the remaining data than did the first cell from the
original data.

After recording the relevant statistics asso­

ciated with the second cell, the data embodied by that cell
are discarded and the search procedure continues until a
third cell is identified.

The process can continue until

some predetermined number of cells has been identified or
until there is no entropy left in the data.
The entropy minimax procedure is different from
classical decision making in that in the latter, the signifi­
cant or relevant attributes are assumed to be known.

In

addition, in classical procedures, a priori information with
respect to the distributions or the likelihood of observing
various outputs as a function of certain inputs is also
assumed.

In the entropy minimax procedure, no a priori

information, or theories as to which attributes are strongly
related to which outcomes, is assumed.

Nor are the

108
distributions of outcomes assumed.

The procedure merely dis­

covers aggregations of attributes that are strongly associated
with different outcomes of which there may be up to six or
seven in number.

The decision rules associating given attri­

bute vectors with given outcomes is assumed to be implicit
in the data and will be discovered.

Such a discovery, or

the detection of a pattern would lead to a hypothesis perti­
nent to the nature of that decision rule.

The hypothesis can

then be tested by classical methods.
Schonbein has shown that strategies based on the
maximization of likelihood ratios such as minimizing the
probability of error, also have the property of maximizing
mutual information and visa versa (SCHONBEIN 1978) .

Since

discriminant analysis techniques are essentially likelihood
ratio-maximizing techniques, it is clear that a technique
which is optimal in information theory must simultaneously
be an optimal discriminant analysis technique.
Schonbein has also shown that outcomes may be pre­
dicted by fewer attributes than those characterizing the com­
plete attribute vector (A).

Such a truncated attribute

vector, let it be labelled g(A), is known as a sufficient
statistic in that it conveys all the information that would
be conveyed by observation of the complete attribute vector.
Any vector of attributes g(A) conveying no less than the full
attribute vector G(A), is a sufficient statistic and could
be any vector of Boolian logical functions, e.g.,

109
G(A) = [g^(X2=l)/ g 2 (X^=0,Xy=l),
g 3(X1-0,X 2= 0 /X 3=l)]

EQUATION
<6*4)

Cells are defined in attribute space by each of these
individual Boolian expressions for which there exists a unique
set of outcome probabilities; each outcome probability being
a function of only those attributes in the cell.
From Equation 6.3f the following expression for
entropy can be derived:
H[Q;G.(A)] = - I

P[Qk ]logeP[Qk ]

k*"l

+

Z

k=l

P[g..(A)] Z P[Qk ;j± .(A)]
^
i=l
K

logep[Qk ;gi j (S)

EQUATION

1

i.U

where Gj (A) specifies the j

set of Boolian expressions

{gij) which are mutually exclusive and span attribute space.
Ptgj^jtA)] is the probability of choosing at random an attri­
bute vector that is identical to that vector of the attribute
of the i

cell or Boolian expression in the j

screening.

For each partitioning, indeed before any partition­
ing, the self information of the outcome set H(Q) is the
same; thus, it can be ignored.

The goal of the entropy mini­

max algorithm is to minimize H[Q;Gj(A)] and thereby to de­
termine the sufficient statistic with the minimum number of
attributes.
To determine that the sufficient statistic, condi­
tional entropy, is minimized:

110
H .[Q |G .(A) ] 3

3

E

i=1

P[g^(A)] E
iD

k =1

P[Q.|
*

gi;j'(A) ]log P[Qk |gi;j(A) ]

EQUATION
(6 .6 )

= HjtQyGjfA)] - H[Q]
Since a priori probability distribution of outcomes
(Qk ) need not be known in order to achieve a solution, the
entropy minimax procedure is superior to classical proce­
dures in this analysis.
In order to minimize conditional entropy, it is neces­
sary to choose an estimator P . . for the probability P[Q,J
th
gij ^ ^ where P^ j represents the probability that in the j
partitioning, attribute vector i falls in the same cell as
output k.

It must do this according to the principle of

maximum uncertainty which states, that information from one
additional sample with an identical vector of attributes to
that in the cell, would constitute the maximum amount of
information necessary to make a decision as to the determi­
nation of the outcome associated with that cell.
Prom another perspective (P i.j) *s
probabilities which, in the j

set of

screening, maximizes the

remaining entropy after all available data has been ob­
served.
Through a process known as the entropy of variation,
an estimator is found which maximizes the entropy H [Q |Gj(A)].
This estimator is

111

_k
n n
ID
where:

n ij

+

ni j + 1

the nura^©r of observed outcomes of type k
in the i

nij

cell of the j

4*Vi

screening

the nuin^er of outcomes of all types in the
ith cell of the

t

EQUATION
(6 .8 )

screening

is the a priori probability of an outcome
state k.

The probability P[g^j(n)] is
p. . =

ij

where:

n. . +

1

EQUATION
(6.9)

-------

n + J

J

,th
is the number of cells in the j
screening

n

is the total number of cases in the sample

or the number of events.
Av
It is known that P ^ converges to a maximum condi­
tional entropy for each partition and then identifies the
minimum entropy among all possible maximum entropies.

The

estimator also converges in probability and is, therefore, a
consistent estimator in the statistical sense, thus assuring
us that the estimator of conditional entropy will also con­
verge to the minimum entropy partitioning.
We seek to minimize
{H.[Q|G.(A)]} by minimizing {E P . . E Pk .. log

i i i

j

n

xi

Pk ..>
ID
In so doing, we will determine if a patterned relationship
exists between outcomes (services) and vectors of client

112
attributes.

We will learn which attributes are associated

with specific service outcomes.

Finally, we will learn the

extent of the knowledge gained by determining, for each
successive cell in the chosen partition, the quantity of
entropy removed relative to the total entropy found in the
unpartitioned data.

Knowledge of such relationships should

be of value in analyzing cost of chore services.

VI.

The Application of the Entropy Minimax Algorithm in
Pattern Detection
The conceptual and theoretical utility of the entropy

minimax pattern detection algorithm was explained in previ­
ous sections.

This section addresses the manipulation of

the chore service data into forms appropriate to the detec­
tion of patterns and the generation of hypotheses.
Basically, the aim of using the procedure is to
attempt to detect systematic relationships between a client's
profile (encompassing categories of functional status and
socio-economic status) and service categories.

Description

and justification of the alternative specifications of out­
come classification (service categories and their combina­
tions) and client attributes are found in the following sub­
sections of this chapter.
A.

Selection of Outcome Classes.
The potential number of outcome classifi­
cations in this analysis totaled 14.

Three of

the service categories (guide dog, interpreter,

113
and other) were dropped from the analysis because
very few clients employed them.

Ideally, each

outcome class would be represented by each of
the remaining 11 service categories.

In prac­

tice, the accuracy and reliability of the entropy
minimax computer program markedly decreases as
the number of outcome classifications rises above
five or six.

11

Means were sought to aggregate the

service categories into between three and six

outcome classifications.

Five procedures were

followed:
1.

Those service categories were aggregated
which seemed to occur together in the data.

2.

Individual service categories were em­
ployed as proxies for other service cate­
gories.

3.

The choice of outcome classification was
based on service categories that did not
appear to be associated with each other.

4.

Choice here was based on those service cate­
gories occurring most frequently in the
data.

5.

Finally, the choice was similar to that
mentioned in number

2,

above, but a highly

frequent service category was also added.
Possibly, other service category combina­
tions could be justified and tested.

The

114
limitations on computer funds and the largely
exploratory nature of this application of the
entropy minimax algorithm suggested further
research should proceed only after thorough
evaluation of the present results.
The careful reader will have noted that the
assumption concerning mutual exclusivity of out­
comes has been violated.

This problem was over­

come by designating each outcome as an individual
case.

Thus, in the case where a client was

receiving five services, the client was 'split'
into what amounts to five clients with the same
profile, each with a different outcome.*
1.

Aggregation of Service Categories.
It was recognized in the early stages
of this research that certain outcome classes
would probably be associated with each other
and it was on this basis the first classifi­
cation of outcomes was made,
a)

In the first outcome group, if clients
could not perform heavy cleaning, it was
unlikely they would do their own shop­
ping or laundry.

Thus, such services

*In a private communication, I was assured by Mr.
Schonbein, of the Department of Radiology, College of Human
Medicine, Michigan State University, that the pattern de­
tection procedure would still function appropriately and
detect patterns if any existed.

115
would probably be associated with each
other.

Table 6.3 compiled from the

full data set of 628 cases, lays out
the frequency of services employed by
clients according to the number of
services employed by clients according
to the number of services they received.
A visual scan of the table indicates
that the first five services are associ­
ated with each other, especially among
those clients receiving more than four
services.

A further confirmation of

the common association of the first
five most frequently utilized services
(shopping, laundry, heavy cleaning,
light cleaning and meal preparation)
was observed in a frequency count in
the training sample in which all five
were observed among 234 clients out of
a sample total of 428.

Only six clients

failed to receive any of these services.
Together, laundry, heavy cleaning, meal
preparation and shopping were received
by 256 clients; laundry, heavy cleaning
and shopping by 302 clients,
b)

Possible associations between other
classifications of outcomes were sought.

TABI.E 6.3.— Frequency of services received by clients according to total nunber of services provided

Total
No. of
Services

TYPE OF SERVICE
Laundry
(I.)

Shopping
IS)

Heavy Clng. Light Clng. Heals
OIK)
<M0
(H)

Non-Nursing
Personal
(NNP)

Trans.
ITT)

Fin. Hgt.
(FH)

Attendant
IA)

House
Maint.Rep.
(HHR)

Yard
Work
IV)

1

0

I

2

0

1

6

0

0

0

0

2

2

10

4

13

4

5

6

2

0

0

0

2

3

31

20

26

15

8

11

8

0

2

3

2

4

55

52

47

34

23

15

18

3

1

7

5

5

96

84

72

74

75

36

24

13

6

11

4

6

135

134

116

116

119

76

55

23

20

20

8

7

112

113

102

105

105

85

68

43

26

19

11

8

83

84

83

82

83

76

65

42

37

22

15

9

39

39

39

39

39

37

36

28

25

18

12

10

12

12

12

12

11

12

12

6

11

12

B

11

7

7

7

7

7

7

7

7

7

7

7

580

550

519

488

476

367

295

165

135

119

78

Col.
Total
Percent­
age of
Clients

92.4

87.6

82.6

77.7

75.8

58.4

47.0

26.3

21.5

18.9

12.

There appeared to be an association be­
tween the use of financial management
services and non-nursing personal ser­
vices since together they were utilized
by
c)

88

clients,

The classification of the third outcome
was made by associating home repair
and maintenance services with yardwork,
these being less frequently required
than other services and being associated
in 30 cases.

Neither service was used

by 314 clients.

The classification of

the (d) fourth and (e) fifth outcomes
were attendant services and transporta­
tion, respectively.
The Use of Proxy Service Categories to
Classify Outcomes.
Since the computer analysis associated
with the entropy minimax computer runs was
relatively complicated compared to the cost
analysis which utilized regression techni­
ques, the two procedures were developed and
run simultaneously.

This approach facili­

tated some interaction between the two
procedures.

The choice of outcomes or

service category proxies was thus based on
the regression of services on total monthly

costs (TCM).

These regressions, explained

in detail in Chapter

8,

yielded significant

coefficients in the categories:

light

cleaning (LK), meal preparation (MP), atten­
dant (A), and non-nursing personnal services
(NNP).

These four outcome categories were

used as four individual outcome classifica­
tion in the entropy minimax algorithm.

The

remaining five outcome categories were not
designated as outcome classifications and
were left out of the analysis.

It was de­

cided that if the four included categories
resulted in the discovery of significant
patterned relationships between client
attribute profiles and outcome classifica­
tions, then further work would proceed on
relating these service categories to other
service categories.
Outcome Classifications Represented by
Service Categories That Were Unassociated
with Each Other
In this classification, service cate­
gories chosen were those that appeared to
be clearly not associated with each other
in the sense that they seldom occurred to­
gether for any one client.

It was hypothe­

sized that such a lack of association may

lead to easier separation of data in pattern
detection.
Three service categories were chosen:
transportation, attendant, and non-nursing
personal services.

The remaining six ser­

vice categories were left out of this com­
puter run.
Outcome Classifications Represented by the
Categories of the Four Most Frequently
Utilized Services
According to Table 6.3, the four most
frequently used service categories were
laundry {92.4 percent of clients), shopping/
errands {87.6 percent), heavy cleaning (82.6
percent) and light cleaning (77.7 percent),
respectively.

These were designated outcome

classifications for this run.

This does not

imply that these services, relative to other
services, occupied the most time of the pro­
vider.

It was hypothesized here that by in­

cluding only the most frequently used services
in the computer run, large cells would be
constructed by the pattern detection
algorithm.

120
5.

Outcome Classification Based on a Modifica­
tion of the Proxy Approach Used in Method
(2) of Outcome Classification
The only modification made to Approach
(2), described above, is the addition of the
shopping/errands service.

This was done to

see if the addition of service categories
made any difference to the amount of entropy
removed from the total data entropy.
B.

Choice of Attributes
Attributes were limited to categories of
SES and functional status.

Medical status was

not included because (as mentioned in the litera­
ture review) other studies found no relationship
between medical status and use of non-medical
chore-type services.

Furthermore, results from

the regression analysis of costs in this research
showed no relationship between health services
and costs of services (see Chapter

8).

Each attribute category was transformed
into a binary variable.

This approach is some­

what different from that used in the regression
analysis where each category was sometimes di­
vided into five subcategories, each being repre­
sented by a binary variable.

An effort was made

within each category to subdivide the category
between those subcategories where the difference

121
between one subcategory and an adjacent sub­
category was at a maximum.

In the case of the

impairment indicators, mobility, dexterity,
sensory, and comprehension, these judgements
were based on the array of data in Table 6.4.
Home management, which does not appear in the
array, was divided on the same basis.
Considering the socio-economic variable
first, age was divided between those over 80
and those under 80 because it was thought the
older person would use more services due to
circumstances purely related to age.
Location was divided between urban and rural
since it was felt those clients in urban areas
would be more likely to request services for any
given functional status than those in rural areas.
This was based on the proposition that with
respect to transaction costs for clients, ob­
taining services in the city was reckoned to be
less costly than for those clients in rural
areas.
A client's living arrangement with respect
to the provider of services was divided between
those who lived with the provider and those
living separately from the provider.
The client's relationship to the provider
was divided between clients who were relatives

TABI.E 6.4.— The number of clients At different impairment levels and the service categories employed by them
TYPES AND LEVELS;o f IMPAIRMENT (INCREASING FROM I TO 5)

Service
Category

1

Mobility
i
2 • 3
4
a

Dexterity

Sensory

Comprehens ion
J

5

1

2

3 i
11
i 4

5

1

2

3 i 4
a

5

1 1 2
1

3

4

5

Laundry

SI

17

152

121

239

44

57

111

243

125

238

96

178

48

20

245

96

82

79

78

Shopping/E,

49

19

141

111

230

42

54

105

233

116

212

96

171

46

18

229

91

78

77

75

Heavy Cleaning

36

16

137

111

219

29

49

103

228

110

200

94

162

45

IB

243

89

72

54

61

Light Cleaning

34

10

122

103

214

29

38

96

211

114

183

89

157

41

18

208

86

71

56

67

Heal Prep.

41

9

116

97

213

37

37

86

204

112

175

88

151

46

16

182

77

74

65

78

Non-Nursing
Personal

33

6

67

69

193

25

27

60

146

109

142

66

104

40

15

110

52

63

70

72

Transport

31

11

71

58

124

28

28

47

130

62

108

45

100

33

9

102

48

45

51

49

Financial Hgt.

32

3

24

26

70

29

11

29

55

41

54

22

57

26

6

7

22

30

49

57

Attendant

16

4

26

24

65

15

10

24

49

37

51

20

46

11

7

45

19

23

20

28

llome Hgt. t Rpr.

2

1

35

24

57

1

12

19

55

32

39

23

37

13

7

55

22

18

9

15

Yardwork

4

1

14

19

40

1

4

14

38

21

20

25

22

7

4

37

14

16

3

8

123
of the provider and those who were not rela­
tives.
The dichotomization of categories of the
functional status variable was less clear cut
than was the case with the SES variable.

In

the raw data, each functional status indicator
had five levels of impairment.

Frequency counts

were run on each level of each category, see
Table 6.4.

Judgements were made as to where

the cut-off between relatively non-impaired and
the relatively impaired should be.

Mobility

was divided between the second and third levels
of impairment.

Dexterity between third and

fourth; sensory between third and fourth? com­
prehension between first and second; home manage­
ment was divided between the second and third
levels.
The nine actual computer runs utilizing the
entropy minimax algorithm are described in the
next Chapter where the computer printouts are
presented.

CHAPTER 7
RESULTS PROM APPLICATION OF THE ENTROPY MINIMAX ALGORITHM

I.

Introduction
In the last chapter the theory underlying the en­

tropy minimax principle was discussed.
the empirical results.

This chapter examines

The first section lays out the speci­

fic attributes and outcomes as they were entered into each
computer run.

This is followed by a description of the

a priori probabilities of attributes and outcome classes in
the context of the computer printouts.

Input and cell en­

tropies are then analyzed after which the outcome probabili­
ties are examined.

Finally, the results are discussed in

light of the methodology employed and the data base.

II.

Attributes and Outcome Classes
Nine pattern detection runs were conducted on vari­

ous formats of the data.

These are listed in Table 7.1.

The first computer run was conducted using aggregations of
the outcome classes in clusters.
run,

2

In addition to the first

series of four runs were conducted; one series used

a format of functional status attributes including mobility,
dexterity, sensory and comprehension.

The other series

dropped mobility, dexterity and sensory attributes, replacing
124

TABLE 7.1.— Forms of outcomes (service
Minimax Computer Runs

2

1

Run No.

(LK,HK,MP,
L,S) (FM,
NNP)
(HMR,Y)
A, TT

LK
MP
A
NNP

mixes) and client attributes employed in Entropy

3

4

5

6

TT
A
NNP

LK
HK
L
S

LK
MP
S
A
NNP

LK
MP
A
NNP

7
TT
A
NNP

8
LK
HK
L
S

9
LK
MP
S
A
NNP

Impairment
Categories
P
P
P
P
P

P
P
P
P
P

P
P
P
P
P

P
P
P
P
P

P
P
P
P
P

0
0
0

0
0
0

0
0
0

0
0
0

p
p

p
p

P
P

P
P

P
P
P
P

P
P
P
P

P
P
P
P

P
P
P
P

P
P
P
P

p
p
p
p

p
p
p
p

P
P
P
P

P
P
P
P

SocioEconomic
Status
Age
Relationship
Living Arr.
Location
Client Attribute

—0

indicates the attribute was not included in the run
P indicates the attribute was included in the run

125

Mobility
Dexterity
Sensory
Comprehension
Home Mgt.

126
them with the home management attribute.

The socio-economic

attributes, age, relationship, living arrangement, and loca­
tion had the same specification throughout the 9 computer
runs.
Before examining the results of the runs, the com­
puter printouts will be explained.

Pour printouts have been

reproduced in Figures 7.1, 7.2, 7.3 and 7.4.

The important

features of Figure 7.1 are the total number of events or
clients in the sample (NTOT 428) and the number of outcome
class members (NOUT).
taken from run number
in number:

In an actual printout of Figure 7.1,

2,

the outcome class members are four

light cleaning (LK), meal preparation (MP),

attendant (A), and non-nursing personal services (NNP).

The

key process control parameter in Figure 7.1 is LSTEP, indi­
cating the maximum number of processing steps through which
the algorithm cycles before terminating.

In all of the com­

puter runs, with the exception of the first, processing steps
were limited to
a cell.

10,

each step constituting the creation of

The cells were considered sufficient since any use-

able information usually appears in the first 5 or

6

cells

created.

III.

A Priori Probability of Attributes and Outcome Classes
The utilization of the equal A PRIORI WEIGHTING

FACTORS (see Figure 7.1) and their magnitudes (see Figure
7.2) is based on the assumption of no known a priori reduc­
tion in uncertainty characteristic of the data.

Use of

127
****** Entropy Minimax Pattern Detection.
RUN TITLE.

WARD TRAINING SAMPLES —

Date.

January 1976 Version.

run number 2.

22 August 1978

Parameters From Tape 9.
Nentry
NTOT
NV1
NV2
NCO
NOUT

428
428

8

0
1
4

Number of Row Entries in D Array.
Total Number of Events.
Number of Binary Variables.
Number of Scaler Variables.
Number of Outcome Classes.
Number of Outcome Class Members.

Process Control Parameters.
NORD
LTEST
LSTEP
KCODE
PERR

8
3
10
0
1.00

Processing Order.
Preprocessing Order.
Number of Processing Steps.
Scaler Variable Code 1=A/D 2=Midpoint.
Error Varience Limit.

Apriori Weighting Factors.
WV(1) =
.25
W V (2) =
.25
W V (3) =
.25
W V (4) =
.25
Total Weighting Factor WW = 1.00
MAX. ARRAY DIMINSIONS, FPVCTR(11734) INVCTR{879)
Apriori Probability Array.
=
1.767
A P P ( 1)
=
A P P ( 2)
1.690
s
A P P ( 3)
.233
=
A P P ( 4)
.837
A P P ( 5)
.472
.984
A P P ( 6)
.864
A P P ( 7)
=:
1.721
A P P ( 8)
s
A P P ( 9)
1.685
=
A P P (10)
1.649
=
.444
A P P (11)
=
A P P (12)
1.251
—
—
—

Figure 7.1.

Part 1 of computer printout from run number 2.

S T E P - W I S E

A P P R O X I M A T I O N
P A T T E R N
D I S C O V E R Y
BILL SCIIONBF.IN
DEPARTMENT OF RADIOLOGY
MICHIGAN STATE UNIVERSITY

P R O G R A M

INPUT VARIABLES
INDICATED NUMBER OF DATA SETS IN INPUT SAMPLE

387

COMPUTED TOTAL NUMBER OF DATA EVENTS IN INPUT SAMPLE

973

INDICATED NUMBER OF QUALITATIVE(BTNARY) ATTRIBUTES

8

INDICATED NUMBER OF QUALITATIVE(SCALAR) ATTRIBUTES ,

0

COMPUTED TOTAL NUMBER OF ATTRIBUTES

8

INDICATED PROCESSING ORDER (I.E. MAX NUMBER OF VARIABLES USED TO DEFINE A ATTRIBUTE)

8

INDICATED PREPROCESSING ORDER (FOR ATTRIBUTE SUnSET SELECT ION BEFORE EACH PROCESSING STEP)
INDICATED NUMBER OF OUTCOME CLASSES UNDER CONSIDERATION

3

4

.250

.250

.250

.250

INDICATED NUMBER OF DATA EVENTS A CELL MUST CONTAIN IN ORDER FOR THE CLASS FREQUENCIES FOR THESE EVENTS
TO CONTAIN THE SAME AMOUNT OF OUTCOME INFORMATION FOR TIIE CELL AS THE A PRIORI CLASS PROBABILITIES
1.
BINARY VARIABLES LIST.
VARIABLE N., L. MOBILITY
VARIABLE N., 2. DEXTERITY
VARIABLE N., 3. SENSORY
VARIABLE N., 4. COMP REBF.HSTON
VARIABLE N., 5. AGE (80 YEARS OR OLDER:)
VARIABLE N., 6. RELATIONSHIP OF PROVIDER (RELATIVE?)
VARIABLE N., 7. LIVING ARRANGEMENT (SHARE HOUSE?)
VARIABLE N., 8. LOCATION (URBAN?)
OUTCOME CLASS NAME.
Figure 7.2.

OUPIJTS

(BASED ON FIRST MINIMAX RUN)

Part 2 of computer printout for run number 2.

128

INDICATED A PRIORI CLASS PROBABILITIES.

***** 1STEP =

1

IN=387

INR=428

OUTCOME TOTALS DY CLASS MEMBER. T(
T<
T(
TC
D ARRAY AFTER REDUN. JN= 8
JNR=

1)=
2)=
3)=
4)=
8

IW=

973

326,
319,
86,
242.

PREPROCESSOR RESULTS. LTEST= 3
RESULTS FROM ENTRPY. CELL DEFINITION ICELL=
NO.OF OUTCOMES TN CELL XM=
ENTROPY OF CELL PB=

15
2.0
.836988EI00

EVENTS SATISFYING ALL THE FOLLOWING

HAVE ESTIMATED FREQUENCIES
+ .217
.083
.019

I

LK

.088

.750

MP
.265

+ .207
.083
.019
+ .207
.083
.019

AT
NNP

ESTIMATED PROBABILITY OF EVENT FALLING IN THIS CELL = .002
RESULTS FOLLOWIHG DECODE, IEND- 0

Figure 7.3.

Part 3 of computer printout for run number 2.

129

BINARY VARIARL=
3 =, 1
SENSORY
BINARY VARIABLE
2 =, 0
DEXTERITY
BINARY VARIABLE
1 =, 0
MOBILITY
AGE (80 YEARS OR OLDERH)
BINARY VARIABLE
5 =, 0
TUB FOLLOWING ATTRIBUTE(S) ARE CONSTANT ON THIS CELL BUT WERE NOT USED IN THE CELL DEFINITION
BINARY VARIABLE 8 =, 1
LOCATION (URBAN=)
THE FOLLOWING ATTRIBUTE(S) WERE SELECTED BY CHOOSE AS SIGNIFICANT BUT WERE HOT USED IN THE CELL DEFINITION.
BINARY VARIABLE 4 (CONPREIIENSION
).NE.O IN THIS CELL WITH PROB.= .459 APRIORI PROB.= .4J9
BINARY VARIABLE 6 (RELATIONSHIP OF PROVIDER (RELATIVES)
).NE.O IN THIS CELL WITH PROB.= .496 APRIORI PROB.= .492
BINARY VARIABLE 7 (LIVING ARRANGEMENT (SHARE HOUSED
).NE.O IN THIS CELL WITH PROB.= .466 APRIORI PROH.= .432

TERMINATED BECAUSE LIMIT OF 10 STEPS WAS REACHED.
STEP, 11
REMAINING EVENTS AGGREGATED INTO SINGLE CELL GIVE FOLLOWING RESULTS
ANY REMAINING EVENTS
HAVE ESTIMATED FREQUENCIES
+ .015
.332
LK
.017
+ .015
.323
MP
.017
130

+ .012
.092
AT
.001

+ .015
.253
NPN
.005
ESTIMATED PROBABILITY OF EVENT FALLING IN THIS CELL = .954
RESULTS FOLLOWING DECODE, IEND = 5
D ARRAY

Kl=

429

K2=

13

IN=

360

JN=

8

Figure 7.4— Part 4 of computer printout for run number 2.

131
other than equal weighting factors might have been specified
if previous research had indicated such weights were justi­
fiable.
The A PRIORI PROBABILITY ARRAY in Figure 7.2 lists
the client attributes and outcome class members (or services)
by code.

Listed first are the client attributes coded APP

(1) to APP (8).

They are respectively:

mobility, dexterity,

sensory, comprehension, age, relationship, living arrange­
ment and location.

Lower down the list from APP (9) through

APP (12), the service outcomes are listed.

They are respec­

tively: , light cleaning (LK), meal preparation (MP), attendant
services (A), and non-nursing personal services (NNP).

The

number of the right hand side of the coded list represent
the a priori probability of the attributes or outcomes being
observed.

The actual a priori probabilities of the attributes

or outcomes can be calculated by dividing the numbers associ­
ated with the list by two.

For example, the probability of

a client with a significant impairment in mobility appearing
in the list is .05 x 1.767 = 0.888.

IV.

Entropy
It is from the probability data in the A PRIORI

PROBABILITY ARRAY that the total entropy of the input data
set is calculated before partitioning is initiated.

For

example, in run number 2, Figure 7.1, the entropy of the
input data

*-s calculated using only probabilities

associated with the outcome classifications APP (9) to APP

(12) .

132
Calculation of the input data entropy H^npUt is con­
ducted according to the following equation which was derived
from Equations 6.1 and 6.2:
H

= S P
. outcome.

input

X

I

loo P
ye outcome.

x

EQUATION
(7.1)

Restating the right hand side of the equation in terms drawn
directly from the A PRIORI PROBABILITY ARRAY we get:
APP.

APP.

i

„

_
input ”

r
.

i

2
APP.
*
jl
Z~5

i

ge

L APP. J
v
x

x

- _

_

2

r

x

2

APPi iog
tA.P.P.L-]
i ?APPi
e ?APPi

r1.685 .
5.029
9e
,1.649, .
5.029

EQUATION
(7.2)

EQUATION
<7 *3)

,1^685. . 1.649 .
5.029
5.029 loge
.1.25
5.029

,1.25 , n
oge l5.029;j

= 1.292
which is the magnitude of the entropy in the input data.
The features of the computer printout illustrating
an actual cell,

(Cell No. 1 in run number 2) are illustrated

in Figure 7.3.

For our purposes, the pertinent characteris­

tics are the following:
A.

NUMBER OF OUTCOMES IN CELL XM * 2.0 indicating
that only

2

events fall into the first cell.

Indications of an emerging pattern would be sug­
gested by a cell encompassing a much higher
number of events.

133
B.

ENTROPY OP CELL BB ■ .836988E+00.
this figure signifies little.

By itself,

In combination

with the next characteristic it is important.
C.

ESTIMATED PROBABILITY OP THE EVENT FALLING IN
THIS CELL = .002.

Multiplying this figure by

the ENTROPY OP THE CELL BB, we obtain a measure
of the entropy remaining in the cell relative
to that entropy in the total data.

In the case

of Cell Number 1, this weighted entropy is
0.836988 x .002 = .0017.

This is a low figure

implying little entropy is associated with this
cell and little entropy has been removed from
the total entropy of the input data.
After the data have been partitioned into the 10
cells, each of which embodies some entropy within itself,
a final cell is constructed, Figure 7.4.

It encompasses

the data remaining after the data associated with the first
10 cells was removed.

This last cell also embodies an

entropy which is calculated in a similar manner to that of
the input entropy HinpUt*

Le^

entropy in the last cell

be designated Hla#t CQll, then

p (Qk)

P(Q>)
loge (2P(Qk )}
k

where Qk - LK or MP or A
ZP(Qk ) = 1

or NNP

K

H last cell “ “ tO*332 loge 0.332 + 0.323 loge
0.323 + 0.092 logQ
6 0.092 + 0.253 log^6
0.253] = 1.298
Multiplying this entropy by THE ESTIMATED PROBABILITY
OP EVENT FALLING IN THIS CELL = 0.9.54 (see Figure 7.4), and
adding this result to the weighted entropies remaining in the

10

partitioned cells, resulted in generating the total entropy

remaining in the data.

The entropy in each of the 10 cells

and the probability of an event falling into those cells is
recorded in Table 7.2.

For example, the top left hand prob­

ability of .083 is the probability of the light cleaning ser­
vice appearing in cell number 1.

In run number 2 this entropy

amounted to 1.285 (Table 7.3).
The entropy removed (Hremoved ) from the data as a
result of the partitioning was calculated by subtracting the
sum of the weighted entropies embodied in the cells (in­
cluding the last cell) from the total input entropy

^removed

H input ~?H i

•
EQUATION
(7.4)

where H^ = weighted entropy in cell i
H

removed

1.292 - 1.285 = 0.007

This result indicated that using the entropy minimax algorithm on data characterized by the attributes:
mobility, dexterity, sensory, comprehension, age, relation­
ship, living arrangement and location; and also characterized

TABLE 7.2.— Array of outcome classifications, attributes and probability and other
results from run number 2

Cell Number
I

II

III

IV

V

VI

VII

VIII

IX

X

Last
Cell5

(9)
Light
Cleaning

.083

.464

.375

.050

.313

.563

.529

.083

.417

.438

.332

(10)
Meal
Prep1n

.750

.464

.542

.450

.063

.313

.296

.417

.083

.438

.323

(11)
Attendant

.083

.036

.042

.050

.063

.063

.029

.083

.417

.021

.092

(12)
Non-Nursing
Personnel

.083

.036

.042

.450

.563

.063

.146

.417

.083

.104

.253

5

4

3

3

7

2

2

11

384

.008

.002

.002

.011

.954

No. In Cell
Prob. of
Cell

2
.002

6
.006

.005

.004

.003

*Probability of event falling in last cell.

.003

TABLE 7.2.— Continued

Entropy

.84

.95

.96

1.10

1.00

1.00

1.10

1.10

1.14

1.00

0

-

0

-

1

0

-

0

0

-

(2) Dexterity

0

0

-

0

-

0

0

0

1

-

(3) Sensory

1

-

0

0

-

0

-

-

1

1

(4) Compre­
hension

0

-

0

1

0

0

0

1

1

1

(5) Age

0

-

-

0

0

-

0

0

0

0

(6) Rel

0

-

1

1

0

0

1

0

0

-

(7) Liv. Arr.

0

0

-

1

1

0

0

-

-

0

(8) Location

0

0

-

0

-

1

1

1

1

-

136

(1) Mobility

TAOLE 7.3.

Summary of results from nine computer runs of pattern detection algorithm.

Run
Number
Names of Variables
in the Run

1

6

7

B

9

LK
UK
I.
S

K
MP
S
A
NNP

LK
MP
A
NNP

TT
A
NNP

I.K
1IK
I.
S

LK
MP
S
A
NNP

10

10

10

10

10

10

10

3

I.K
HP
A
NNP

TT
A
NNP

20

10

(I.K,liK,MP,L,
S) (FM,NPN)
(IIMR.Y)
A
TT

Number
of Steps

5

2

4

Mobility
Dexterity
Sensory
Comprehension
llome Mgt.

1
1
1
1
0

1
1
1
1
0

1
1
1
1
0

1
I
1
1
0

1
I
1
1
0

0
0
0
1
1

.0
0
0
1
1

0
0
0
1
1

0
0
0
1
I

Socio­
economic
Status

Age
Relations!! ip
Living Arrt.
IfOcation

1
1
1
1

1
1
1
1

1
1
I
1

1
1
1
1

1
1
1
1

1
1
1
1

t
1
1
1

1
1
1
1

1
1
1
1

Probability1 of being
member of last cull
at end of run
Entropy
of Data
Entropy
in Cells
Entropy
Removed
Total % oF
Entropy Removed
Entropy in
Cells Other
Than I.asl
Coll

.954

.954

.898

.975

.957

.932

.875

.923

.947

1.418

1.292

1.021

1.384

1.525

1.292

1.021

1.384

1.525

1.338

1.285

.925

1.323

1.579

1.292

.805

1.377

1.518

.080

.007

.095

.060

.006

.000

.116

.007

.007

5.600

0.500

9.400

4.400

0.400

11.400

0.500

0.500

.080

.047

.076

.027

.055

.101

.099

.068

0.00
.082

137

Impairment
Levels

138
by the outcome classifications:

light cleaning, meal prepara­

tion, attendant, and non-nursing personal services; entropy
removed was negligible, therefore, no relationships were de­
tected on which to base and test hypotheses.

In more con­

crete terms, the assignation of services LK, MP, A, and NNP
to clients with the above profiles appeared to be almost com­
pletely random.

Therefore, the client's need for light

cleaning, meal preparation, attendant and non-nursing per­
sonal services could not be predicted on the basis of the
client's attribute profile.

Similar results were obtained

using the other 4 combinations of outcome classification and
the alternative attribute profile,

(see Table 7.3).

The configuration of outcome classifications and
attributes yielding the largest reduction in entropy was
that of run number 7 where the entropy removed totaled
0.116 (Table 7.3).
Since entropy was not appreciably reduced (no pat­
terns were discovered) it was judged to be of no value
basing hypotheses on these results.

V.

Probability of Outcome Classes
Had the entropy of the data been significantly re­

duced by the subtraction of a cell and the events it em­
bodied, then we would have examined closely the printout
labelled HAVE ESTIMATED FREQUENCIES (see Figure 7.3).

For

example, in CELL 1 (indicated by ISTEP = 1) we had the like­
lihood of Light Cleaning (LK), Meal Preparation (MP),

139
Attendant (A), and Non-nursing Personal (NNP) services fal­
ling into the cell with the probabilities of 0.083, 0.750,
0.083 and 0.083, respectively.

The upper and lower range

figures to the right of each probability in the printout
represent one positive and one negative standard deviation
from the mean.

Since some of these standard deviations are

large relative to the magnitude of the mean probability of
an event falling into the cell, there is still considerable
uncertainty about the magnitude of the probability.

This

accounts for the large amount of entropy (0.836988) associ­
ated with the cell.
Another cause for uncertainty (but not high cell
entropy) stemmed from the relative magnitudes of the cell
probabilities.

Taking an example from Table 7.2, the

probabilities of outcomes falling into cell number
displayed.

2

are

Here the probability of a person with a given

set of attributes receiving Meal Preparation (MP) services
was 0.464, the same probability for receiving Light Cleaning
(LK) services.

Such a client was slightly less likely than

not to have received the services LK and MP.

Probabilities

in the region of 0.50 are characterized by a high degree of
uncertainty.

If the probabilities had been close to zero

or unity, there would have been more certainty about the
relationship between the client's attributes and the outcomes
associated with those attributes.

For example, from Cell

Number 2, it is reasonable to conclude that clients with
attributes characterizing that cell, were highly unlikely to

TABLE 7.4.— Array of outcome classifications, attributes and results from run number 1.

Cell Number
I

II

III

IV

V

VI

VII

VIII

IX

X

Service Categories in
Outcome Classifications
(9) Light Cleaning, Heavy Cleaning,
Meal Preparation, Laundry,
Shopping/Er rands
(10) Financial Mgt.
Non Nursing Personal
(11) Home Main, and Repair
Yardwork
(12) Attendant
(13) Transportation
Number in Cell

.050

.733

.067

.408

.733

.440

.300

.480

.050

.300

.050

.067

.067

.008

.067

.040

.050

.040

.300

.050

.050
.050
.800

.067
.067
.067

.067
.067
.733

.008
.088
.488

.067
.067
.067

.040
.040
.440

.050
.050
.550

.040
.040
.440

.050
.050
.550

.050
.050
.550

3

2

2

24

2

4

3

4

3

3

Probability of Cell

.005

.003

.003

.037

.003

.006

.005

.006

.005

.005

Entropy

.777

.949

.949

1.000

.949

1.100

1.130

1.100

1.140

1.140

Attributes
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)

Mobility
Dexterity
Sensory
Comprehension Attribute
Age
Relationship
Living Arrangement
Location

0
0
1
0
0

-

0

-

0

-

-

0

-

-

-

-

0
1

0
-

0

-

-

-

0

1
1
0

1
-

0
0
0

1

-

1
0
0
1
0
0
0
1

0
0
0
0
1
-

"

"input = 1.418

Total Entropy of Data Ret.

"output = 1.418 - .080 = 1.338

0

_
—

_
0
0
0

0
0
I
0
1
1
0

1
1
0
0
0
I
0

141
have received Attendant (A) or Non-nursing Personal

(NNP)

services because of their low probabilities, both of which
were 0.036.
The outcome probabilities are the estimates of P ^ ^ ,
Ak
namely P ^

which are calculated in the computer program but

not laid out explicitly in the printout.

The constituent

parts of the equation used to estimate P^j can be implicitly
determined by observing some results.

By examining Cell

Number 1, in run number 1, Table 7.4, the probability of ob­
serving the composite outcome classification (LK, HK, MP, L,
S) was 0.050; that is almost zero.

Since there were only 3

client events in this cell, it was concluded that this out­
come was highly unlikely to appear in the cell.

The same

result applied for 3 of the other 4 outcomes.
Prom Equation

6.8

we have the estimated probability

p ij!
Jk
if
where n .. =

= n ij * t
iO
n.j + 1

0,

the number of observed outcomes in the i
cell of the j

fch

partitioning; in this cell

a.w

the k

outcome type is characterized by

the outcome set (LK, HK, MP, L, S ) .
n . . = 3, the number of outcomes of all types in the
j.u

i
t =

0.2,

4*Vl

cell of the j

partitioning,

the a priori probability of outcome k appear­
ing in the cell, there being 5 possible out­
come states.

142
The estimated probability of the outcome set k,
JaU

HK, MP, L, S) appearing in the i

(i.e., LK,
4-V*

cell of the j

partition­

ing is:
P

—

ij

Q +
3+

The same applies to the

^

g QCQ

1
3 of the 4 other outcomes.

The final outcome listed is Transportation (TT) with
a probability of 0.800.

From this, it can be concluded that

all of the outcomes in the cell were Transportation services
ir
(TT). Thus n - = 3, the number of client events in the
cell.

Hence,
P.ij. = |3 ■
% “*■1
?■ = 0.800
+
The algorithm searched out this cell first, consider­

ing it to be the cell removing the most entropy from the
input data and a cell with minimum entropy for all cells
screened.

The algorithm then drops from the data set those

client events in Cell Number 1 and goes on to search the re­
maining data in order to construct the next cell.

VI.

Discussion
No pattern was found to systematically link client

attributes with the range of services assigned to clients.
No testable hypotheses were discovered.

In the light of the

results of the regression analysis discussed in Chapter
these results were not totally unexpected.

In Chapter

was shown that with few exceptions, client attributes,

8,
8,

it

identical to those employed above, were poor predictors of
monthly costs. It was, therefore, not surprising they would
also be poor predictors of assigned services.
Explanations of the above results could emanate from
several sources:
A.

The specification of client attributes on the
survey form DSS-3492 (Rev. 2-75) could be in­
appropriate with respect to guiding the social
worker in assigning services.

If this is the

case, a different profile of attributes might
yield more systematic relationships with
assigned services.

This explanation constitutes

a violation of Assumption D above.
B.

The attribute profile may be appropriate but
not used by the social worker in the assignment
of services, thus violating Assumption C above.
Here, two forces may be operating:
1.

Social workers may utilize the client's
attribute profile in assigning services but
do so in different ways from each other re­
sulting in the inconsistent matching of
services to clients attributes.

The train­

ing of the social workers may have been in­
consistent.
2.

Social workers may choose to ignore much of
the recorded client profile, preferring in­
stead to assign services on the basis of

144
other criteria.

Another hypothesis might

be that they assign services on the basis of
services required.

Thus, instead of checking

out each attribute and deducing

from the

observations the types of care required, the
social worker may make direct observations
about the type of appropriate service re­
quired.

For example, the social worker may

observe directly that the client cannot pre­
pare his/her own meals in which case it may
be appropriate to assign meal services.

In

such an event, the social worker may be con­
tent to record sufficient profile characteris­
tics that seemingly justify the assignment
of meal services.

However, the justification

of meal service may vary across clients super­
vised by one social worker or across social
workers.
C.

The specification of the service outcome mixes
for purposes of entering into the algorithm, may
have been inappropriate.

The combinations of

assigned services were selected on the basis of
five types of criteria as described in Chapter 7.
Other criteria and combinations might have pro­
duced more defined patterns.
D.

The attribute characteristics transformed into
binary categories for the purpose of entering

145
them into the entropy minimum algorithm may
have been inappropriate.

The specific trans­

formations used were based on judgements as to
the nature of discontinuities within each cate­
gory.

The dichotomization of each category may

have been inappropriate.

CHAPTER

8

RESULTS OP REGRESSION MODELS

I.

Introduction
The regression models were specified in Chapter 5.

Three basic models were estimated, Model A, Model B and
Model C.

Rather than discuss these models equation by equa­

tion we shall view the results in several steps as variables,
variable categories, or subcategories, are simultaneously
added or deleted from the models.
The results of the regression analysis are discussed
at various levels of aggregation.

The analysis is first

focused on examining the effects of the inclusion or exclu­
sion in the model of the 3 variables:

functional status (in

its 3 alternative forms), socio-economic status, and medical
status.

In this approach, the emphasis is placed on the

changes in the adjusted coefficient of multiple determination
—2
R .

Here also the signs and stability of the coefficients

are assessed with a view to making judgements as to the de­
gree of multicollinearity present.
Second, the results are examined to determine the
most significant categories within each variable.

In the

case of functional status, these results are examined in

_2

the same context as the analysis of R
146

referred to above.

147
Third, the coefficients of sub-categories are exam­
ined to determine the relationship between various sub-cate­
gories.
Each of the endogenous variables, Total Cost per
Month (TCM) , Total Hours per Month (THM) , and Cost per Hour
(CH) will be examined within each of the above sections.
Finally, the results on the 'test data1, as distinct
from the 'training data', will be assessed.

It may be recalled

that 428 observations were selected randomly from a total of
628 cases and used to estimate the equations.

The 200 re­

maining observations were saved to compare the "best” models
from the 'training data' result with their equivalents in
the 'test data.'

II.

The Effects of Variables on the Variation in Total Cost
per Month, Total Hours per Month and Cost per Hour
Of interest in this section, is the effect of the

different forms of functional status on variation in the
endogenous variables TCM, THM, and CH in Models A, B and C,
respectively.
Due to the results of previously mentioned research
(ANDERSON 1974), it was believed that the exogenous variable,
Medical Status (HS), would have little or no effect on the
variation in either costs or hours of service.

For this

reason and to reduce computer costs, Medical Status was not
included in the early computer runs on the models.

Later

computer runs confirmed the efficacy of this approach.

148
The method of analysis used was to examine the com­
ponent parts of the models with a view to learning which of
the variables, functional status, socio-economic status or
medical status, most fully explained the variation in each
of the 3 endogenous variables.

Then component categories

of variables were deleted or added to determine those cate­
gories found to account for most of the variation resulting
from the parent variable.

These were then brought together

into each of the full models.
This analysis is replete with considerable adjust­
ments to equations in the sense that categories were dropped
and added before the full model was estimated.
several reasons for this approach.

There were

First, the early computer

runs were some of the first for this analyst, and testing the
model with a few variables left less room for error than if
all the variables had been entered in the first few runs.
Second, computer time was minimized using this approach.
Third, the data had been divided up
'training set' and a 'test set.'

into two groups, a

Should

the results from

the 'training set' turn out to be contrived due to the ex­
cessive manipulation of the data, the 'test set' would probably
fail to confirm the results based on the 'training set.'
For the sake of clarity and flow of exposition, the
order in which the computer runs in

each model are discussed

is as listed in Tables 8.1, 8.2 and 8.3.

TABLE 8.1.— Results of Hodel A, total costs per month (TCM)
Computer Run Number

R2
R2

At

All

AIII

AIV

AV

.239
.229

.08
.07

.221
.217

.273
.236

.436
.420

AVI

AVI I

AVI II

AIX

AX

.149
.116

.334
.299

.308
.278

.365
.304

.495
.461

AXI

AXI I

AXIII

AXIV

AXV

AXVI

.511
.474

.536
.476

.525
.481

.512
.451

.4)8
.412

.492
.477

MOB

669
(.091)

1006
(.017)

627
(.102)

DKX

400
(.360)

412
(.233)

652
(.127)

SEN

131
(.686)

934
(.048)

374
(.259)

COMP

1228
(.000)

1092
(.000)

974
893
(.001) (.001)

277
(.307)

623
(.071)

352
(.119)

IIOM

3492
(0)

4195
(.000)

3053
3872
(.000) (0)

1450
(.001)

1620
(.001)

2595
(.000)

-437
(.856)

139
(.953)

1615
(.432)

M3

1020
(.611)

749
(.705)

96
(.955)

M4

1179
(.579)

1041
(.618)

-57
(.977)

M5

2174
(.209)

1779
(.384)

-67
(.970)

02

-2012
(.364)

-1218
(.582)

-180
(.927)

03

-2905
(.186)

-2192
(.310)

-1194
(.535)

04

-1400
(.566)

-262
(.906)

443
(.822)

D5

-25
(.992)

1379
(.557)

1266
(.543)

S2

-501
(.613)

-240
(.802)

-341
(.690)

S3

233
(.796)

909
(.311)

404
(.615)

149

M2

TABLE 8.1 (continued)
Computer Run Humber
A1

All

AIII

AIV

AV

AVI

AVII

AVIII

AIX

AX

AXI

AXII

1437
(.305)

1710
(.215)

707
(.560)

S5

-351
(.876)
2997
(.004)
2655
(.013)
3265
(.005)
3904
(.003)
-4121
(.383)
1736
(.691)
3464
(.410)
8034
(.OSS)

-385
(.863)
2594
(.011)
2428
(.024)
2562
(-033)
3611
(.007)
-5387
(.238)
-711
(.866)
996
(.805)
5288
(.190)

1034
(.596)
2020
(.026)
1608
(.099)
1282
(.260)
888
(.490)
-5730
(.165)
-1474
(.697)
-2059
(.579)
182
(.960)
-2347
(.009)
762
(.451)
-1242
(.133)
-4732
(.000)
-1548
(.200)
-117
(.906)
-406
(.647)
486
(.450)

C2
Cl
C4
CS
K2
K3
K4
K5
LK
ItK
IIHIt
MP
L
S
FH
TT

-3238
(.000)
845
(.369)
-1560
(.058)
-5298
(0)
-2344
(.051)
-412
(.678)
-993
(.198
1128
(.080)

-2986
(.000)
1457
(.134)
-1391
(.085)
-5403
(.000)
-1960
(.097)
-434
(.656)
-947
(.238)
474
(.458)

-2161
(.014)
1017
(.293)
-1189
(.137)
-4986
(.000)
-1665
(.154)
-403
(.677)
-518
(.554)
485
(.443)

2123
(.015)
1744
(.061)
1451
(.179)
952
(.435)
-5200
(.191)
-1380
(.707)
-1891
(.597)
731
(.836)
-2153
(.014)
648
(.513)
-1390
(.082)
-4669
(.000)
-1783
(.129)
474
(.622)
-384
(.661)
460
(.465)

AXIV

AXV

-1846
(.069)
378
(.730)
-1387
(.138)
-5183
(0)
-1191
(.384)
-985
(.416)
-240
(.806)
5J6
(.461)

-3226 -2013
(.000) (.011)

AXVt

150

S4

AXllt

-6044 -5410
(.000) (.000)

TABLE 8.1 (continued)
Computet Run Number
A1
A
Y
NNP
A2
A3
A*
1NC2

INC4
INCS
CLT2
CLT3
CLT4
RL2
RL3
RL4
LOC
SF

A11I

AIV

AV

AVI

AVII

AV1II

A1X

-1836
(.021)
1008
(.290)
-5042
(0)
-1685
(.134)
-12B
(.907)
512
(.625)
-3031
(.065)
-2166
(.175
-2426
(.187)
-944
(.771)
1868
(.420)
-562
(.802)
-4636
(.009)
-4809
(.000)
241
(.880)
-2994
(.002)
4190
(.000)
481
(.591)

-1575 -994
(.124) (.333)
-873
-47.2
(.391) (.962)
-362
-1175
(.234) (.703)
-2709
-2891
(.065) (.052)
-2615
-2631
(.067) (.069
-3602
-3697
(.030) (.028)
-2775
-2711
(.343) (.357)
-1644
-1456
(.427) (.488)
-235
-617
(.907) (.998)
-3130
-2891
.048
(.072)
-3611
-3541
(.002) (.002)
167
334
(.907) (.818)
-1548
-1516
(.089) (.100)
3888
3766
(.000) (.000)
250
347
(.754) (.668)

-1411
(.175)
-862
(.403)
-900
(.369)
-2374
(.112)
-2319
(.118)
-3839
(.025)
-3772
(.207)
-1512
(.476)
262
(.897)
-2887
(.073)
-3309
(.004)
586
(.689)
-994
(.289)
3986
(.000)
366
(.655)

AX
-1635
C035)
448
(.640)
-5154
(.000)
-1360
(.126)
320
(.712)
-1016
(.223)
-2006
(.124)
-2519
(.047)
-3348
(.023)
-2789
(.275)
-620
(.738)
692
(.701)
-1124
(.436)
-1728
(.090)
165
(.897)
370
(.654)
3620
(.000)
667
(.351)

AXI

AXI I

AXI II

AX1V

-1508
(.050)
499
(.598)
-4661
(.000)
-1154
(.192)
328
(702)
-1150
(.164)
-1997
(.121)
-2591
(.039)
-3577
(.014)
-3153
(.212)
-720
(.695)
673
(.705)
-1041
(.465)
-1684
(.095)
127
(.919)
334
(.689)
3550
(.000)
578
(.412)

-1648
(.037)
1019
(.313)
-4357
(.000)
-1232
(.178)
-295
(.746)
-1515
(.086)
-1770
(.180)
-2399
(.065)
-3684
(.015)
-4350
(.095)
-533
(.778)
899
(.618)
-988
(.496)
-1721
(.097)
10.9
(.993)
399
(.641)
3601
(.000)
451
(.535)

-1649
-1141
(.032)
(.195)
1153
359
(.238)
(.753)
-4548
-4691
(.000)
(0)
-1043
-535
(.508)
(.238)
164
525
(-849)
(.619)
-1277
-738
(.477)
(.37)
-3752
-2045
(.110)
(.012)
-2735
-3580
(.028)
(.014)
-3822
-3937
(.009)
(.018)
-3760
-3709
(.137)
(.221)
-490
' 164
(.789)
(.937)
750
896
(.673)
(.661)
898
649
(.528)
(.693)
-1709
-830
(.091)
(.481)
-172
1566
(.891)
(.284)
448
1088
(.248)
(.589)
3730
3399
(.000)
(.000)
554
-144
(.434)
(.857)

AXV

AXVI

-1917 -1502
(.013) (.042)

-5172 -4592
(.000) (.000)

-1107
(.112)

-892
(.208)
-1773
(.081)

-1305
(.115)
-1792
(.031)

3629
(.000)

151

INC3

All

TABLE 8.1 (continued)
Computer Run Number
AI

All

All I

AIV

AV

AVI

AVII

AVIII

AIX

AX

AXI

AXI I

AXIII

IIS4

-123
(.948)
-89
(.922)
992
(.471)
4905
(.082)
-1866
(.408)
186
(.974)

1155

1156
1157
iisb

IIS9

Omitted variables:

AXIV

AI, INCl, CLT1, RL1. HI, Dl, SI, Cl, Kl, LOC (Rural), SF (Male), IIS3 (lleart)

Parentheses Indicate the level of significance of coefficients using an f-test (two-tailed).

AXV

AXVt

TABLE 8.2.— Results of Model R, total hours per montli (TIIM)
Computer Run Number
DI

Dili

R2

.140

R2
MOD

.129
.128
188
(.083)
-118
(.325)
- 64
(.472)
405
.377
(0)
(.000)
547
604
(.000)(.000)

DEX
SEN
COMP
ilOM
M2

M4
H5
D2
03
04
05
S2
S3
S4
S5
C2
C3

DV

DVI

DVII

BVIII

BIX

DX

BXI

BXI I

BXI1I

BXIV

DXV

DXVI

.177

.185

.214

.274

.265

.303

.297

.312

.348

.321

.305

.163

.225

.301

.134

.163

.184

.236
222
(.031)
-165
(.149
18
(.835)
186
(.015)
470
(.000)

.232

.23B

.249

.261

.264

.258

.218

.155

.201

.276

-104
(.874)
591
(.282)
630
(.280)
773
(.178)
-135
(.837)
-734
(.223
-709
(.253)
-450
(.491)
-113
(.677)
-200
(.419)
525
(.172)
-882
(.151)
308
(.276)
446
(.131)

177
(.016)
524
(.000)

100
(.225)
351
(.009)
146
(.816)
863
(.106)
949
(.092)
1022
(.064)
355
(.552)
-654
(.261)
-552
(.359)
-407
(.519)
- 74
(.771)
- 26
(.912)
511
(.169)
-394
(.512)
- 55
(.840)
34
(.906)

81
(.460)
410
(.01)
228
(.715)
882
(.096)
990
(.077)
908
(.097)
458
(.442)
-619
(.292)
-496
(-409)
-424
(.504)
-175
(.500)
-211
(.390)
933
(.368)
-287
(.630)
- 75
(.785)
-110
(.710)

DXVI I

103
201
(.003) (.152)
335
352
(.015) (.007)

153

M3

.133

BIV

-87
(.760)

TABLE 8.2 (continued)
Run Nuiabec
Coiaputer I
BI
C4
C5
K2
K3
K4
K5
LK
HK

HP
L
S
FH
TT
A
Y
NNP
A2
A3
A4

BIV

BV

BVI

BVI I

BVIII

1301
(.000)
1456
(.000)
-372
(.774)
942
(.432)
681
(.554)
1589
(.165)

BIX

BX

BXI

BXII

BXIII

318
(.232)
- 24
(.934)
142
(.558)
-799
(.002)
-248
(.485)
13.9
(.962)
21
(.937)
- 53
(.780)
-579
(.014)
-278
(.335)
-306
(.153)

611
(.079)
428
(.275)
-261
(.835)
854
(.460)
775
(.493)
1208
(.283)
266
(.330)
-126
(.601)
232
(.357)
-828
(.002)
- 56
(.878)
29
(-921)
- 26
(.922)
- 55
(.998)
-664
(.006)
-388
(.208)
-216
(.338)

562
(.091)
348
(.354)
17.2
(.989)
907 .
(.423)
731
(.507)
1274
(.202)
308
(.253)
- 55
(.855)
104
(.670)
-811
(.002)
-250
(.488)
6.5
(.983)
40
(.880)
- 40
(.836)
-606
(.011)
-213
(.478)
-269
(.214)

509
(.117)
- 97
(.780)
210
(.481)
-851
(.009)
-367
(.401)
107
(.781)
- 27
(.930)
-141
(.544)
-508
(.071)
-186
(.609)
-386
(.131)

168
104
90
(.745) (.698) (.533)
401
399
228
(.412) (.128) (.126)
261
219
219
(.418) (.301) (.383)

115
(.678)
356
(.199)
222
(.409)

194
(.475)
424
(.111)
266
(.297)

369
(.245)
560
(.097)
447
(.178)

688
(.033)
793
(.028)
-563
(.647)
737
(.516)
681
(.532)
1319
(.225)
88
(.741)
356
(.222)
- 27
(.914)
-944
(.000)
-500
(.179)
21
(.945)
-532
(.026)
174
(.381)
-545
(.026)
- 76
(.797)
-731
(.001)

123
(.629)
92
(.755)
93
(.702)
-910
(.000)
-317
(.375)
19
(.948)
-128
(.599)
- 58
(.762)
-616
(.009)
-294
(.313)
-435
(.040)
50
(.857)
276
(.309)
378
(.146)

146
(.595)
271
(.321)
209
(.481)

171
(.528)
285
(.278)
246
(.331)

BXIV

BXV

nxvi

BXVIl

172
252
179
(.454) (.491) (.289)

154

IIHR

Bill

-1119 -882
-810
(.000) (.000) (.001)

- 653 -579
-577
(.006) (.014) (.010)

- 909 -518
-297
(.000) (.016) (.150)

82
76
(.886) (.718)

TABLE 8.2 (continued)
Computer Run Number
BI
INC2
INC3
INC4
INC5
CLT2
CI.T3
CLT4
RL2

R1.4
I.OC
SF
IIS1

IIS2
IIS 4
IIS5

use
I1S7
IISS
IIS9

BIV

BV

BVI

DVII

132
48
(.906) (.737)
128
156
(.692) (.730)
668
800
(.079) (.136)
329
389
(.628) (.675)
- 93
126
(.827) (.866)
-620
-568
(.266) (.294)
-334
-10B
(.442) (.798)
-1350
-1532
(.000) (.000)
969
1020
(.014) (.008)
-1240
-1502
(.000)
(0)
103
204
(.427) (.079)
- 80
- 99
(.715) (.642)

BVIII

BIX

BX

BXI

388
61
92
94
(.875) (.473) (.816) (.809)
82
376
1.67
- 16
(.829) (.346) (.997) (-965)
882
584
583
516
(-190) (.056) (.192) (.245)
125
544
67
- 26
(-872) (.523) (.930) (.973)
-114
- 51
153
135
(.926) (.842) (.783) (.809)
-522
-483
-240
-239
(.334) (.377) (.662) (.658)
- 70
-212
211
235
(.868) (.624) (.630) (.588)
-1316
-1286
-1201
-1224
(.000) (.000) (.000) (.000)
1022
1173
1057
1060
(.008) (.003) (.007) (.006)
-1233
-1165
-1097
-1086
(0)
(.000) (0)
(.000)
134
84
159
135
(.590) (.744) (.536) (.596)
-157
-102
-16.1
- 41
(.632) (.478) (.941) (.847)

BXII

BXI 11

BXIV

284
(.480)
269
(.497)
836
(.069)
349
(.660)
138
(.810)
-167
(.761)
129
(.770)
-1256
(.000)
1171
(.002)
-1090
(.000)
37
(.889)
- 113
(.609)

94
(.810)
- 21
(.954)
514
(.249)
131
(.866)
89
(.874)
-230
(.674)
213
(.625)
-1128
(.000)
1127
(-004)
-1055
(.000)
127
(.621)
- 48
(.825)

50
(.915)
- 84
(-855)
411
(.438)
216
(.823)
-159
(.810)
-460
(.480)
- 21
(.968)
-1205
(.001)
804
(.083)
-1109
(.000)
22
(.943)
- 15
(.953)
324
(.497)
85
(.900)
673
(.265)
226
(.440)
470
(.276)
180
(.841)
-583
(.418)
145
(.699)

BXV

BXVI

BXVI I

-157
-139
(.486) (.526)
352
551
(.088) (.268)
-222
(.748)

237
244
(.355) (.348)
-559 -1109
(.034) (.000)
1066
(.005)
-1039
(.000)
91.3
118
(.719) (.625)

155

RL3

Bill

TABLE 8.3.— Results of Model C, costs per hour (C?l)
Computer Run Number
CIV

Cl

CHI

R2

.086

.000

.129

R2
MOB

.075
-6
(.196)
4.6
(.372)
4.3
(.261)
-14.2
(.000)
-16.6
(.006)

.075

.083

DEX
SEN
COMP
non
M2

M4
N5
D2
03
04
D5
S2
S3
S4
S5
C2

0.6
(.983)
-4.4
(.853)
-4.5
(.857)
-17.9
(.468)
-16.0
(.541)
9.3
(.721)
21.2
(.428)
-1.3
(.964)
-4.3
(.789)
8.2
(.422)
-8.7
(.599)
15.6
(.555)
-5
(.968)

CVI I lCVIII

.099

.116

.160

.074

.082

.116
-7.3
(.117)
6.8
(.185)
2.2
(.583)
8.7
(.011)
16
(.008)

CIX

CX

.153

.202

.116

.126

-8
(.015)
-17
(.002)

CXI

CXII

CXIII

CX1V

CXV

CXVI

CXVII

.168

.188

.233

.207

.213

.073

.120

.167

.111

.128

.135

.134

.116

.064

.093

.135

-6.9
(.067)
-15
(.015)
-1.9
(.946)
-8.9
(.710)
-11.1
(.659)
-22
(.353)
-30.9
(.248)
9.7
(.711)
18.2
(.501)
-1
(.971)
-3.6
(.758)
5.1
(.637)
-8.7
(.600)
6.8
(.799)
11
(.370)

-6.6
(.165)
-15.6
(.026)
-6.5
(.820)
-9
(.709)
-13.1
(.605)
-20.1
(.402)
-26.3
(.331)
14.1
(.598)
21.1
(.426)
7.1
(.806)
-1.8
(.881)
6.1
(.583)
-8.3
(.623)
7.7
(.775)
10.5
(.402)

-9.1
(.005)
-15.8
(.010)

-5.8
(.081)
-16.4
(.006)

156

M3

-13.1
(.000)
-17.9
(.001)

CVI

CV

8.9
(.465)

TABLE 8.3 (continued)
Computer Run Humber
CI

CJ
C4
C5
K2

K3
K4
K5

IIK

IIHR
HP
L
S
FM
TT
A

CIV

CV

CVI

CVIII

CIX

ex

4.4
(.737)
32.4
(.026)
-30.2
(.061)
-53
(.328)
-87.9
(.065)
-89.6
(.067)
-107.6
(.028)

-4.9
(.700)
-46.9
(.001)
-48.6
(.002)
-52
(.351)
-81
(.117)
-77.2
(.120)
-102.6
(.038)
-7.8
(.509)
-32.8
(.011)
14
(.210)
17.8
(.117)
26.8
(.102)
1
(.944)
15.4
(.142)
- 3.4
(.699)
23
(.033)

Y

5.3
(.681)

NNP

21.7
(.023)

A2

CVI1

CX1II

CXIV

8.7
(.500)
-30.5
(.043)
-24.8
(.146)
-80.5
(.846)
-105.7
(.040)
-99.5
(.047)
-117.8
(.017)
-15.8
(.195)
-18.6
(.177)
8.9
(.423)
16.8
(.152)
19
(.222)
- 1.3
(.926)
- 5.6
(.644)
-11.8
(.194)
26
(.015)

-22.2
(.114)
-11.5
(.449)
6.3
(.624)
11.1
(.428)
18.3
(.335)
- 6.4
(.705)
- 1.6
(.906)
- 4.8
(.633)
18.9
(.121)

8.2
14.8
(.532)(.290)

10
(.461)

12.5
(.430)

13.6
7.4
4.2
(.157) (.448)(.683)
- 9.5 - 7.8
- 5.7
(.639) (.438) (.536)

6.4
(.516)
-10.7
(.386)

2.1
(.848)
- 8.7
(.528)

(.441)
-22.2
(.099)
10
(.366)
18.8
(.102)
24.2
(.138)
- 1.9
(.890)
3.5
(.751)
- 9.8
(.266)
27.2
(.011)
9.2
(.490)

-2.2
-8.0
-5
-7.2
(.859) (.517) (.55)) (.690)

CXII

9.4
(.486)
-30.3
(.055)
-23.3
(.192)
-74.2
(.194)
-110.1
(.037)
-111.7
(.030)
-125.1
(.014)
-16.9 -13.7
(.164) (.271)
-16.4 -15.8
(.222) (.259)
8
5.4
(.472) (.635)
13.4
17.6
.249 (.138)
21.6
16.9
(.184)(.314)
- 0.6 - 3.5
(.963)(.801)
-6.4 - 3
(.595)(.807)
-10.3 -11.6
(.241)(.194)
25.2
25.1
(.019)(.021)

-9

.

CXI

CXV

-16.5
(.117)

CXVI

CXVI I

-17.5 -20.1
(.117) (.067)

25.4
(.019)

15.4
13.1
(.161) (.226)

25.1
(.017)

22.3
.033

28.5
(.002)

14.5
(.130)

22.3
(.030)

7.2
(.440

157

LK

cut

TARI.E 8.3 (continued)
Computer Run Humber
*

Cl
A3
A4
INC2
1NC3
INC4
1NC5
CI.T2
C1.T3
CLT4

RL3
Rt>4
LOC
SF

1151
1152
1154
1155
1156

1157

IIS8
IIS9

CIV

cv

CVI
- 7.8
(.516)
1.2
(.916)
-18.7
(.298)
-20.5
(.242)
-33.4
(.099)
-16.6
(.642)
- 9.7
(.703)
- S.9
(.811)
-.9
(.961)
37.4
(.007)
-25.5
(-145)
51.9
(.000)
13.4
(.241)
- 1.7
(.862)

CVII

CVI II

-10
(.398)
4.2
(.724)
-21
(.233)
-19
(.257)
-26.7
(.183)
-15
(.671)
-11
(.655)
- 9.2
(.706)
- 9.8
(.608)
29.3
(.033)
-29
(.095)
40
(.000)
17.5
(.120)
- 1
(.927)

- 8
(.495)
6
(.596)
-19
(.283)
-17.7
(.304)
-24.5
(.220)
- 7
(.840)
12.8
(.608)
-10
(.682)
-10.6
(.579)
28.6
(.037)
-29
(.096)
40
(.283)
16.2
(.151)
- 1
(.931)

ex

CXI

CXI I

CXI1I

CX1V

- 8.9
(.478)
- 7
(.952)
-26.2
(.147)
-27.3
(.127)

-13.8
(.250)
2.7
(.817)
-20
(.261)
-15
(.390)

-33.1
(.109)
-26.5
(.462)
-14.7
(.567)
-15.1
(.538)
- 8.9
(.648)
24.1
(.085)
-36.4
(.041)
37.8
(.001)
15.7
(.178)
0.5
(.962)

-23.7
(.244)
-10.5
(.765)
17.7
(.491)
-16
(.520)
-18.4
(.358)
27.9
(.048)
-30.8
(.081)
39.3
(.001)
14.6
(.214)
- 1.4
(.884)

-13.5(.255)
5.2
(.653)
-20.5
(.252)
-14.1
(.415)
-20
(.321)
- 6
(.863)
-17.4
(.494)
-16.3
(.511)
-19.8
(.318)
26
(.004)
-32
(.069)
37.2
(.001)
16
(.167)
.14
(.999)

-14.9
(.237)
- 0.3
(.983)
-27.2
(.137)
-23
(.200)
-29.1
(.163)
-23.9
(.507)
-21.2
(.418)
-22.5
(.368)
-20.4
(.311)
23.2
(.105)
-38.8
(.030)
36.5
(.002)
16
(.186)
.7
(.942)

-15.8
(.189)
2.0
(.864)
-21.3
(.232)
-14.3
(.408)
-21.4
(.290)
-17.8
(.614)
-14.2
(.580)
-16.9
(.496)
-18.9
(.341)
21.8
(.122)
-37
(.036)
36.2
(.002)
15.3
(.193)
- .5
(.965)

- 9.4
(.521)
- 3.7
(.795)
-17.1
(.407)
-17.8
(.373)
-21.8
(.344)
-6.7
(.874)
-5
(.862)
.3
(.992)
5.5
(.808)
38.7
(.018)
-23.1
(.251)
45.8
(.001)
15
(.264)
- 5.9
(.599)
- 3
(.907)
- 3
(.918)
-25.3
(.334)

CIX

2.6

(.840)
-13.8
(.469)
38
(.329)
38.7
(.215)
7.7
(.636)

CXV

CXVI

CXVTI

10.5
9
(.288) (.351)

- 2.5
(.803)
-14.6
(.311)

-2.9
(.771)
-7.7
(.598)
9.1
(.772)

- 3.2
(.782)
5
(.670)

-3.1
(.786)
23.8
(.078)

-33.1
(.054)
34.9
(.001)
17.3
16.3
(.127) (.144)

158

RL2

c m

Functional Status*
The first results to be examined in these
tables were observed in the first five equations;
equations which embody various alternative forms
of the variable functional status, together with
combinations of these forms.

Here we were seek­

ing to determine which specific functional status
indicator was most appropriate for inclusion in
each of the models.
Using the five functional status indicators,
each of which was characterized by five levels
of impairment:

mobility (MOB), dexterity (DEX),

sensory (SEN), comprehension (COMP) and home
management (HOM) in Equation AI, Table 8.1, we
observed that the adjusted coefficient of multi_2

pie determination (R ) in Model A was 0.229.
Most significant were the sub-categories COMP
and HOM.
Since multicollinearity was suspected be­
tween on the one hand HOM and COMP and on the
other, the first three categories of functional
status, MOB, DEX and SEN, the latter were entered
into the equation alone in Model A, Equation All,
—2

and yielded and R

of 0.07.

Equation AIII, in

which only COMP and HOM were entered, yielded an
!K of 0.217.

Multicollinearity appeared to be

present and the categories MOB, DEX and SEN of

160
the functional status variable explained little
of the variation in cost.

Another indicator

of multicollinearity between the

2

groups of

variables was indicated by large changes in both
the coefficients and the significance among the
MOB and SEN categories; in the first two equa­
tions in Model A, less change was evident among
COMP and HOM categories which retained high
degrees of significance in the first and third
equations.

Thus, COMP and HOM appeared to be

the most appropriate indicators of the variable
functional status in its implicit cardinal form.
Equation AXV presents the results of speci­
fying functional status utilizing binary cate­
gories for each level of impairment. There was
_o
little difference between the R in Equation AI
(0.229) and the 0.236 level of Equation AIV.
This suggested equivalence between the two
approaches.

To simplify matters, the categories

COMP and HOM still seemed to best explain varia­
tion in the endogenous variable.
Tables 8.2 and 8.3 provided comparisons
among functional status specifications in Models
B and C.

The relationships between the various

specifications of functional status categories
_2
were similar to those for Model A, but R was
not as high in either model as in Model A.

The

161
_2

R

fell in the range for Equations BI to BIV,

of between 0.128 and 0.134 and the Equations Cl
to CIV of between 0.075 and 0.083.
The third alternative indicator of func­
tional status, the services provided to the
client, when entered into Model A alone, Equation
_2

V, resulted in an R

of 0.42.

Clearly, this was

a superior indicator of variation in Total Cost
per Month (TCM)

to

the impairment level indi­

cators examined above.
However, when using the services indicator
of functional status in Model B and Model C,
there was only a marginal gain in the explana­
tion of the variation in total hours worked per
month (THM)

(Equations BI to BV).*

0.134 to 0.163.

R 2 rose from

There was no gain in the explana­

tion of the endogenous variable cost per hour
(CH) in Model C, (Equations Cl to CV) where the
R 2 varied between 0.075 and 0.083.
B.

Socio-Economic Status.
Before combining the socio-economic status
variables (SES) with the above alternatives of

♦Usually, with the exception of the endogenous vari­
ables, identical Equations were run for all 3 models. Several
more equations than those listed in Table 8.4 were run but
were dropped because they yielded no significant increase
in information than that shown in the tables of equations,
Tables 8.1, 8.2, and 8.3 and Table 8.4.

162
the functional status variables, the former was
entered alone into the Models (Equations AVI,

_2

BVI, and CVI) where R

was found to be 0.116,

0.184 and 0.082, respectively.

From these re­

sults, it appears that SES was more important
than functional status in explaining the varia­
tion in hours worked (THM) than it was in ex­
plaining month costs (TCM) or hourly costs (CH).
The effect of entering the alternative
functional status indicators into the equations
of all 3 models, together with the SES variable,
is shown in Equations VII to XIII.
In Equation AVII, the 5 cardinal functional
status indicators MOB, DEX, SEN, COMP and HOM
were combined with all the socio-economic status
categories.
0.299.

This raised the R

2

from 0.229 to

In Models B and C, the R2 changed from

0.129 to 0.236 and from 0.075 to 0.116, respec­
tively.

When COMP and HOM alone were combined

with the socio-economic status categories in
Equations AVIII, BVIII, and CVIII, R2 rose from
0.217 to 0.278, from 0.128 to 0.2 32 and from
0.075 to 0.116, respectively.

Clearly, in these

equations, socio-economic status was an important
variable in explaining all 3 endogenous variables,
especially hours worked (TCH).

163
The binary form of the functional status
categories were combined with socio-economic
status in Equations AIX, BIX, and CIX. The
_2
magnitudes of R in each of these equations dif­
fered little from those in Equations AVIII,
BVIII, and CVIII.

However, the coefficients

were much more unstable suggesting high degrees
of multicollinearity in this form.

It is worth

noting that the coefficients of the various
binary formulations of comprehension and home
management (e.g. C2 , C 3, C^, Cg, and K 2 , Kg)
were more stable than the equivalent coeffici­
ents of mobility, dexterity and sensory per­
ception.

These results coincided with the

relatively stable coefficients for COMP and
HOM in the cardinal form of the functional status
variable.
The coefficient of multiple determination,
_2
R , displayed a significant rise to 0.461 when

the third alternative indicator of functional
status namely, services, was combined with
socio-economic status in Equation AX.

In Model

B, the same variable categories resulted in only
_2
a marginal increase in R to 0.249.
In Model C,
the same functional form resulted in a marginal
_2
decrease m R to 0.111.

164
In Chapter 7 no patterned relationship was
found linking client attributes to services.
This outcome indicates little correlation between
attributes such as functional status ("cardinal"
or binary indexes), or socio-economic status
and services provided.

Yet, intuitively, it

would seem that in a regression frame work
there is likely to be a high degree of multicollinearity between the cardinal or binary
indicators of functional status and services
rendered.

In Equations XI and XII, in all models,

this seems to be the case.

In Equation XI, the

COMP-HOM form of the cardinal functional status
index has been entered into the equation together
with the alternative, but not mutually exclusive,
functional status indicator, services.

There

was a marginal gain of 0.013, 0.012 and 0.017
_2
in the magnitude of R for Models A, B, and C,
respectively.

These marginal gains when viewed

together with the large changes in coefficients,
associated with COMP and HOM appeared to confirm
the above mentioned intuition with respect to
multicollinearity.

The relatively large amounts

of cost or time variances explained by the ser­
vices categories compared with those of the
impairment level categories suggested that the
service index was the more powerful predictor.

This result was reinforced by the observation
that the coefficients of the services indicator
of functional status were relatively more stable
than those of the alternative specifications of
functional status.

These results were also con­

firmed in Equations XII where the binary form of
functional status was substituted for that of
the cardinal form as in Equation XI.

This sub­

stitution made little difference to the magni—2

tude of R .

Neither was there much further

change when only the C 2 to C 5 and K 2 to K,.
binary components of the functional status were
entered into Equation XIII together with services
categories and socio-economic status.
Medical Status.
As expected, the introduction of the vari­
able medical status into the models (see Equa­
tion XIII), did not add explanatory power.

In

all models the decrease in degrees of freedom
_2
served to cause a decrease in the R . For
example, in Model A it dropped from 0.474 in
Equation XI to 0.451.
The Search for an Optimal Model.
Two types of criteria were taken into
consideration in defining an optimal model sub­
ject to constraints of the available data:
technical criteria and (2) policy criteria.

(1)

166
1.

Technical criteria.
The number of degrees of freedom used
up in the estimation of the models had an
__2
effect on the magnitude of the R . This
was apparent in the estimation of Equation
XIII which included the Medical Status
variable.

It was apparent that by dropping

what appeared to be insignificant categories,
the explanatory power of the models might
be increased.
2.

Policy criteria.
The policy maker seeks to determine
anticipated costs on the basis of a minimum
amount of information.

Cutting down the

amounts and types of information required,
reduces the propensity to commit errors and
increases the time effectiveness of staff
especially social workers who record the
necessary information.

Thus, an optimal

model would preserve a high degree of pre­
dictive power and base it on a minimum of
information.

There is a direct trade-off

to some extent between predictive power and
information requirements.
Bearing in mind these criteria, two further
forms of the model were estimated.

Equation XV

included only 4 categories of services, light

167
cleaning, meal preparation, attendant and non­
nursing personal services.

These specifications

reduced R 2 to 0.412, 0.201 and 0.093 in Models
A, B, and C, respectively.

It is clear that

—2
though the reduction in R is evident, the four

categories accounted for a large proportion of
the variance in costs and hours worked.
By adding COMP and HOM together with one
category of Age (80 years and above), 2 cate­
gories of income (INC3, INC4), one category of
client contribution (CLT4), one category of the
clients relationship to the provider (RL2), and
—2
location, the R was raised to virtually its
highest level in Model A, that is 0.477.
In
_2
Model B, the level of R rose even higher than
that previously recorded to 0.276.
_o

to Model A, the R

Similar

in Model C remained at its

previous highest recorded level of 0.135.
The results from Equations XV and XVI
indicated the data requirements for cost predic­
tions could be significantly reduced from current
data recorded.

The Equations explaining the

largest amounts of variance in the endogenous
variables were Equations XI, XII, XIII and XVI
in all 3 models.

168
III.

Effects of Variable Categories on the Variation in
Total Cost Per Month, Total Hours Per Month and Cost
Per Hour
The effect of including and excluding functional

status categories was partially covered in the above section.
It was found that the categories COMP and HOM in both the
cardinal form and binary form, explained more of the varia­
tion in costs or hours than MOB, DEX, or SENS or their
binary form equivalents.
The significant service variables, light cleaning
(LK), meal preparation (MP), attendant (A), and non-nursing
personal (NNP), when entered into the Model A along (Equa—2
tion AXV) resulted in an R of 0.412.
—2

an R

This compares with
•

of 0.420 when all service categories are entered into

the equation together {Equation A V ) .

The coefficients of

LK, MP, A, and NNP and their level of significance, remained
relatively stable whether or not the other service variables
were present suggesting little or no multicollinearity
between the

2

groups of service categories.

Throughout all equations in Model B, the LK category
had a significant coefficient.

The effects of services alone

in the equation accounted for an R
0.163.

2

in the range of 0.155 to

Otherwise, the results were similar to those found

in Model A.

In Model C, the most significant service cate—2
gory was Attendant (A) but the level of R varied between
.064 and .074.

Consequently, little importance can be

attached to the different forms in which the service cate­
gories were entered into this model.

169
To estimate the effects of the different categories
of socio-economic status, each category was dropped from
Equation XI in each of the 3 models.

Not more than one SES

category was dropped from the equation for any one computer
run.

The results are presented in Table 8.4, run numbers

XVII to XXI.

In Model A, the location (LOC) category appeared

to account for much of the variation attributed to SES,
—2

causing the R

to drop from 0.471 to 0.450 when it was omitted.

In Models B and C, the variation in hours and hourly cost
can be largely attributed both to the relationship between
the provider and client and their living arrangements rela­
tive to each other.
in the next section.

These results are discussed more fully
—2

The R

dropped from 0.261 to 0.177 and

from 0.128 to 0.086 when the relationship and living arrange­
ment category (RL2, RL3 and $L4) were dropped from Models B
and C, respectively.

IV.

An Examination of Coefficients
Due to the occurrence of singularity in the estima­

tion of coefficients in a model in which binary variables
appear, certain subcategories of variables must be excluded.
Estimation of coefficients would otherwise be impossible.
Thus, the coefficients themselves cannot be interpreted with
respect to their individual values.

However, it is possible

to gain some further knowledge of the inter-relationships
among subcategories of variable categories by examining the

_2
TABLE 8.4.— A comparison of R for all models
Training runs

A(TCM)
Run No.
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
XVII

MODELS
B (THM) C(CH)

R2

R2

MOB, DEX, SEN, COMP, HOM

.229

.129

.075

MOB, DEX, SEN

.07

COMP, HOM

.217

.128

.075

.236

.134

.083

.420

.163

.074

.116

.184

.082

.299

.236

.116

.278

.232

.116

All FS binary, all SES

.304

.238

.126

All services, all SES

.401

.249

.111

COMP, HOM, all services, all SES

.474

.261

.128

All FS binary, all services, all SES

.476

.264

.135

C2-C5, K2-K5, all services, all SES

.481

.334

.134

COMP, HOM, all services, all SES, all HS

.451

.218

.116

LK, MP, A, NNP

.412

.155

.064

Same as run XI without A2-A4

.472

.262

.128

Variables and Categories

M2-M5, D2-D5, S2-S5, C2-C5, K2-K5 (i.e., all FS,
binary)
LK, HK, HMR, MP, L, S, FM, TT, A, Y, NNP (i.e. all
services)
A2-A4, SF, LOC, INC2-INC5, CLT2-CLT4, RL2-RL4,
(i.e. all SES)
MOB, DEX, SEN, COMP, HOM, all SES
COMP, HOM,

all SES

R2

TABLE 8.4 (continued)
Training runs
A(TCM)

R2

Same as run XI without CLT2-CLT4

.475

.263

.132

Same as run XI without INC2-INC5

.471

.261

Same as run XI without RL2-RL4

.471

.177

.086

Same as run XI without LOC

.440

.262

.126

COMP, HOM, LK, MP, A, NPN, and all SES minus A,, A
INC2, CLT2, CLT3
3

.474

.276

.135

XVIII
XIX

XXII

171

R2

Variables and Categories

XXI

C(CH)

R2

Run No.

XX

MODELS
B (THM)

172
relative values of coefficients.

These comparisons are use­

ful to the degree that the coefficients are significant and
remain relatively stable with respect to each other.

A low

level of confidence attributed to a coefficient would indi­
cate the coefficient to be subject to large changes in magni­
tude.

For example, in Models A and B, the consistently large

positive magnitude of HOM relative to COMP indicates that
the physical ability of the client to manage their home is
more important in explaining variation in costs per month
and hours per month/ than is their mental ability.
The relative values of HOM and COMP coefficients
were reversed in Model C when compared with Models A and B.
Also/ where the binary form of functional status was employed
in Models A and B, the costs appeared to increase as the
level of impairment increased.

The opposite was the case

in Model C where, as the level of impairment increased, the
hourly cost of providing services decreased.

This result

could have been induced by the $270 monthly payment ceiling
imposed by the Michigan State Government.

If the ceiling

were raised, it is conceivable hourly rates could also rise.
Model C is of particular interest with respect to the binary
representation of mental ability C2, C3, C4 and C5.

The

upper levels of impairment C4 and C5 showed both stability
and relatively high level of significance.

There was an

inverse relationship between hourly costs and level of im­
pairment.

173
It is interesting to note that when services were
included in the Model A, for example Equation AXII, the rela­
tive magnitude within the Mobility subcategories (M2 to M5)
and comprehension subcategories (C2 to C5) were reversed
resulting in a decline in TCM as impairment within categories
increases.

This suggests a multicollinear effect between

Mobility and Comprehension, on the one hand, and Services
on the other.

By the same token, some of the coefficients

of service subcategories also changed in Model A when the
binary form of functional status categories was added to the
service and socio-economic status variables in the trans­
formation from Equation AX to AXII.

Heavy Cleaning (HK),

Financial Management (FM) and Yardwork (Y) were especially
affected.

Though this observation also suggested the pre­

sence of multicollinearity, it should be viewed with caution
since the levels of significance were relatively high.

The

same kind of effects were apparent when the truncated
"cardinal" form of functional status (COMP and HOM) was
added to the service and socio-economic status variables,
Equations AX and AXI.

The coefficients and significance of

COMP, HOM, HK and FM were all affected.

The probable explana­

tion for the multicollinearity stems from the apparent rela­
tionship between the functional status category home manage­
ment (HOM) or its binary equivalent K2 to K5 and service
category heavy cleaning (HK); also between COMP or C2 to C5
and service category, financial management (FM).

174
Though there was apparent multicollinearity, the
relative level of significance of COMP and HOM and the slight
increase in explanatory power due to their presence, indicated
it was useful to keep them in the models together with the
service categories.

Of the relatively significant categories

among services (LK, HMR, MP, S, A and NNP) the attendant ser­
vices, meal services and non-nursing personal services appeared
to have the most effect on cost per month.
In Equations BXI, BXII, light cleaning (LK) appeared
to have the most effect on hours worked by a provider.
Laundry (L), meal preparation

(MP),and attendant

vices seemed to have the most impact on costs per
Model C.

(A) ser­
hour in

These statements should be viewed with caution in

light of the low level of confidence associated with the
coefficients.
Among the SES categories in Model A, location (LOC)
and Relationship and Living Patterns between providers and
clients (RL)

were found to be often significant.

Urban

clients were

$30 to $40 more costly on a monthly basis than

rural clients, but were not significantly different from
rural clients with respect to hours worked.

Hourly costs

were marginally greater for urban than for rural clients,
on the order of 16 cents more per hour.
>

As evident in Equations AXI, AXII and AXIII, services
provided to the client who was related to, but living separ­
ately from, the provider (RL2), cost less per month
than the other 3 relationship-cum-living patterns.

The

175
coefficient for the related but separate provider was signi­
ficant according to the F test at the 0.1 level.

The other

3 categories of relationship-cum-living pattern were substan­
tially different from each other.

The monthly costs of an

unrelated client living separately from the provider (RL4)
was only marginally higher in cost than the living-in related
provider (RL1 the omitted subcategory) or the non-relative
in the same house (RL3) .

Since neither the coefficients of

RL3 nor RL4 were significant, no firm conclusions can be
drawn.
In Model B, all 3 relationship-cum-living pattern
subcategories were significant at less than the 0.05 level
for most computer runs.
Providers living separately from clients (RL2 and
RL4) worked fewer hours than those living with the client.
But non-relatives living with the client (KL3) supplied more
hours of services than live-in relatives.
Cost per hour in Model C showed, as expected after
observing the results in Models A and B, an inverse relation­
ship to those described in Model B.

Non-relatives providing

services to clients living separately (RL4) resulted in the
highest hourly cost of services.

The next highest hourly

costs were realized by provider's relatives living separately
from the client, followed by the relative living with the
client (RL2).

The lowest hourly costs were incurred by the

non-relative living with the client (RL3).

176
V.

Results from the 'Test' Sample
Many equations were analyzed using data from the

training set of data.

The results were tested using a separ­

ate test set of data.

The reason for this was to test whether

the results based on the training sample were contrived.
The 200 case test set sample was analyzed by employ­
ing 3 equation specifications identical to 3 of the equations
in each of the 3 models.

The 'test' set equations and their

training set equivalents, respectively, are as follows:
AtXII

(AXII); AtXIII

(AVII)?

ATXVI (AXVI);

BtXII

(BXII); BtXIII

(BXIII); BTXVII (BXVII);

CTXII

(CXII); CTXIII

(CXIII); CTXVII (CXVII)

The 'test* set results are presented in Table 8.5 and desig­
nated by the subscript T.
—2
In the case of Model A, R in the 'test'

compareswell with that

sample

of the 'training' sample results.

Equations in Model A:
MODEL A EQUATIONS
AXII
R2

.476

AtXII

AXIII

.494

.481

AtXIII

AXVI

A^VI

.453

.477

.435

In Model B the results were unusual because the test
results are better than those from the training set.
MODEL B EQUATIONS

R2

BXII

BtXII

BXIII

BTXIII

BXVII

BTXVII

.264

.312

.258

.334

.276

.315

TABLE 8.5.— Test results - Models A, B, C
Model B

Model A

R2
MOB
DEX

ATI

T
A II

T
AMII

BT1

0.617

0.551

0.471

0.479

0.494

0.453

0.435

0.312

Model C
BTU T

CTI

0.458

■0.319

0.334

0.315

bt h

T

T

C*II

C'lII

0.514

0.460

0.350

0.359

0.342

0.300

SEN

COMP

508
(.091)
1016

1I0H

125
(.260)
32
(.874)

(.101)
M2

3351
(.307)
5936
(.012)
6749
(.010)
5788
(.021)
-2197
(.323)
-3131
(.167)
-2659
(.259)
270
(.914)
-1020
(.429)

M3
M4
M5
D2
D3
D4
DS
S2
S3

-I860
(.126) .
-1197
(.529)

S4
S5

-9339
(.000)

C2

2588
(.046)
-206
(.899)
2076
(.213)

C3
C4

•

1886
(.149)
15
(-992)
1146
(.471)

10
(.993)
-364
(.654)
-367
(.683)
- 61
(.943)
-603
(.434)
425
(.588)
77
(.925)
131
(.880)
-553
(.217)
-324
(.441)
-435
(.510)
111
(.899)
- 85
(.848)
174
(.757)
505
(.382)

- 73
(.863)
- 40
(.937)
343
(.510)

- 7
(.061)

0
(.998)
46
(.256)
12
(.674)
13
(.670)
- 19
(.526)
24
(.383)
0
(.986)
10
(.710)
29
(.347)
15
(.345)
1
(.962)
45
(.054)
- 6
(.826)
16
(.305)
7
(.706)
- 36
(.082)

16
(.307)
14
(.457)
- 29
(.124)

TABLE 8.S (continued)
Model D

Model A
at i

cs
K2
K3
K4
R5
LK
IIK
IIHR

L
S
FH
TT

A
»
NNP
A2
A3
A4
INC2

1994
(.196)
-18004
(.008)
-18054
(.004)
-15334
(.012)
-13600
(.023)
- 674
(.578)
- 765
(.535)
1240
(.324)
- 5510
(.000)
369
(.854)
- 1112
(.469)
260
(.827)
1881
(.058)
-2418
(.024)
2051
(.171)
-5208
(.000)
148
(.907)
- 295
(.818)
1591
(.227)
2339
(.288)

AT III

- 437
(.696)

-5305
(.000)

-1731
(.078)

-5208
(.000)

1414
(.154)

DTI
310
(.586)
-1532
(.549)
-3263
(.173)
-2135
(.370)
-2054
(.386)
- 374
(.371)
- 678
(.115)
104
(.819)
- 963
(.016)
1115
(.148)
- 116
(.827)
- 566
(.176)
634
(.072)
- 454
(.216)
-1014
(.055)
- 324
(.377)
192
(.663)
- 24
(.958)
- 187
(.698)
1437
(.057)

T

B II
353
(.483)
-1506
(.497)
-2961
(.150)
-2236
(.258)
-2040
(.293)
- 313
(.429)
- 731
(.071)
223
(.589)
- 848
(.024)
585
(.374)
- 199
(.691)
- 533
(.157)
521
(.017)
- 450
(.197)
- 922
(.060)
- 451
(.179)
127
(.759)
- 165
(.693)
- 266
(.535)
1315
(.069)

BTIII

- 570
(.127)

- 885
(.012)

- 416
(.202

- 483
(-130)

7
(.982)

CTI
- 34
(.093)
48
(.597)
106
(.212)
102
(.228)
86
(.306)
30
(.044)
24
(.110)
- 24
(.136)
19
(.168)
- 31
(.259)
11
(.554)
13
(.353)
- 11
(.352)
13
(.311)
60
(.002)
19
(.143)
- 9
(.551)
- 1
(.923)
- 4
(.815)
- 70
(.009)

CT11
- 29
(.118)
63
(.436)
103
(.173)
114
(.117)
98
(.172)
27
(.066)
29
(.050)
- 26
(.085)
19
(.158)
- 17
(.461)
15
(.393)
8
(.568)
- 7
(.524)
12
(.327)
52
(.604)
21
(.085)
- 5
(.702)
1
(.947)
2
(.890)
- 62
(.019)

T
C*III

36
(.010)

22
(.089)

10
(.383)

22
(.065)

1
(.938)

178

HP

3996
(.016)
3089S
(.000)
-32223
(.000)
-30547
(.000)
-29626
(.000)
- 1156
(.337)
- 257
(.835)
1102
(.402)
- 5093
(.000)
- 368
(.868)
-2254
(.145)
624
(.603)
769
(.447)
-2634
(.014)
2419
(.111)
-4519
(.000)
- 208
(.870
- 257
(.847)
2042
(.144)
1782
(.409)

T

All

Model C

TABLE 8.S (continued)
Model A
T
A I

ATll

Model B
T
A 111

bt i

BT1I

Model C
T

b 'iii

CTI

T
C*II

T

c 'iii

2424
(.220)

2332
(.245)

1087
(.377)

1002
(.145)

824
(.210)

- 268
(.525)

- 57
(.021)

44
(.066)

- 1
(.955)

INC4

2125
(.332)
422
(.927)
-2533
(.394)
- 84
(.977)
-3067
(.186)
-1692
(.288)
-1483
(.398)
-1246
(.324)
2019
(.242)
- 527
(.627)

2281
(.308)
678
(.885)
-3427
(.245)
-1241
(.667)
-4462
(.058)
-1755
(.277)
-1748
(.321)
-1316
(.301)
864
(.619)
286
(.791)

777
(.616)

1047
(.169)
- 717
(.656)
-1859
(.073)
-2263
(.025)
-1159
(.150)
-1706
(.002)
162
(.789)
-1978
(.000)
234
(.695)
597
(.114)

815
(.265)
- 728
(.636)
-1900
(.050)
-2464
(.010)
-1164
(.130)
-1683
(.002)
300
(.602)
-1916
(.000)
- 191
(.731)
562
(.114)

- 445
(.408)
-1731
(.208)

- 63
(.020)
26
(.650)
52
(.156)
70
(.051)
23
(.418)
30
(.050)
- 40
(.065)
41
(.008)
7
(.716)
- 19
(.145)

- 51
(.056)
32
(.563)
53
(.135)
72
(.038)
16
(.558
38
(.050)
- 45
(.036)
45
(.003)
3
(.865)
- 14
(.285)

- 2
(.919)
68
(.184)

INC5
CLT2
CLTJ
CLT4
Rt.2
RI.3
RL4
LOC
SF

-2558
(.078)
- 741
(.532)

1924
(.214)

489
(.320)
-1757
(.000)
238
(.671)
-1798
(.000)
268
(.603)

- 22
(.224)
46
(.012)
- 42
(.043)
44
(.002)
1
(.927)

179

INC3

180
It Is in Model C that the results have been found
difficult to logically explain because the "test" results
are clearly superior:
MODEL C EQUATIONS

R2

CXII

cTx n

CXIII ctx iii

.135

.359

.134

.348

CXVII

cTxvn

.135

.300

In Model

C, efforts were
made todetectoutliers
_2
causing the increase in R , with no success. One feature
that is noteworthy is the difference in means, and to a
lesser extent, standard deviations of the endogenous variables
TABLE

These are detailed in Table

8.6.—

8.6.

Means and standard deviations of endogenous
variables

Training Sample

Test Sample

Mean

Std. Dev.

Mean

Std. Dev.

17939

7948

18465

7162

(2>

1708

2047

1915

213:

MODEL C (3)

183

85

165

79

MODEL A (1>
MODEL

b

The standard deviations are relatively large, indi­
cating the differences in means to be acceptable.
^ I n Model A, the mean and standard deviation are
measured in cents; thus, 17939 indicates $179.39/month.
(2)
'In Model B, the mean and standard deviation are
measured in tenths of an hour; thus, 1708 indicates 170.8
hrs/month.
(3)
In Model C, the mean and standard deviation are
measured in cents; thus, 183 indicates $1.83/hour.

181
In comparing variable categories and subcategories
between the two samples, each model will be taken up in turn.
Only the seemingly most revealing results will be presented,
the criteria for their choice being the degree of significance
and the extent of similarity between coefficients.

The sub­

categories or categories have been divided into 3 groups.
The first group (Group I) is comprised of those coefficients
with similar magnitudes and high significance.

The second

group (Group II) embodies those coefficients which are less
similar in magnitude or significance than those in the first
group but for which interpretation of the results remains
basically similar.

The third group (Group III) shows con­

tradictory results.
The comparison of results in Model A is presented
in Table 8.7.

Two equations in each sample are modified

and used to demonstrate the similarities and differences
between the two samples.

The variable categories showing

the highest degree of correspondence (designated Group I)
were meal preparation (MP) and non-nursing personal services
(NNP).

Agreement between the 2 samples was not so clear in

the categories LK, A and LOC and subcategory RL2 in Group II.
Nevertheless, the interpretation of the results remain
essentially similar.

The magnitude of the location coeffi­

cient decreased by almost half and the significance dropped.
The most common result of all the coefficients in Group II
was the difference in significance of coefficients between
the 'training' set and the 'test' set.

Since the latter

182

TABLE 8.7.— A comparison of selected categories and subcategories between "training" and "test" samples
from two equations in Model A
Category

Equations
AXII

Group I

Group II

AXVI

A tXVI

MP

-4732
(.000)

-5093
(.000)

-5410
(.000)

-5305
(.000)

NNP

-4357
(.000)

-4519
(.000)

-4592
(.000)

-5208
(.000)

LK

-2347
(.009)

-2013
(.011)

- 437
(.696)

A

-1648
(.037)
-1721
(.097)

-1156
(.337)
-2634
(.014)

-1502
(.042)

-1692
(.288)

-1305
(.115)

-1731
(.078)
- 741
(.532)

LOC

3601
(.000)

2019
(.242)

3629
(.000)

1924
.241)

m3

96
(.955)

5936
(.012)

Mf
4l

- 57
(.977)

6749
(.010)

M5
d

- 67
(.970)

5788
(.021)

RL2

Group III

a txii

(Incomplete)

183
had fewer than one-half the cases of the 'training' set,
the drop in significance should not be surprising.
The contradictory results characterizing Group III
showed up only in the case of the binary variables repre­
senting mobility:

Mg, M 4 , and Mg.

Significance increased

to a significant level with the test results and the signs
of two coefficients changed.

These results, as with those

of the other categories and subcategories not listed in
Table 8.7 suggest these variables should be ignored in
future research.
The comparison of training set and test set results
in Model B is presented in Table
as that used for Model A.

8.8

using the same format

Again, meal preparation (MP)

appeared to be the most significant predictor of hours of
service provided per month to a client.

Coefficients in

the training set are Attendant services (A), all relationshipcum-living arrangements categories (BL2, RL3, and RL4),
yardwork (Y), and non-nursing personal services (NNP).

In

each case, the significance and signs were such that inter­
pretation of the results of the two sets were virtually the
same.
The anomalies evident in the Group III occurred in
the category HOM, and subcategories Mg, M4 , and Mg, the latter
3 being the same as those in Model A.
In Model C, the same number but not the same specific
variable categories and subcategories were consistent across
the training and test sets (Table 8.9).

184
TABLE 8.8.--A comparison of selected categories and sub­
categories between "training” and "test" samples
from two equations in Model B
Category

Equations (Incomplete)
BXII

b txii

BXVI

btxvii

Group I

MP

- 828
(.002)

- 963
(.016)

- 810
(.001)

- 885
(.012)

Group II

A

- 664
(.006)

- 454
(.218)

- 577
(.010)

- 416
(.202)

RL2

-1256
(.000)

-1109
(.000)

-1757

1066
(.005)

238
(.671)

-1039
(.000)

-1798
(.000)

352
(.007)

32
(.872)

GROUP III

RL3

1171
(.003)

-1706
(.002)
162
(.739)

RL4

-1090
(.000)

-1978
(.000)

Y

- 338
(.208)

-1014
(.055)

NNP

- 216
(.336)

- 324
(.377)

HOM
M,
J

882
(.096)

- 364
(.654)

M,

990
(.077)

- 367
(.683)

908
(.097)

- 61
(.949)

%

(.000

185

TABLE 8.9.— A comparison of selected categories and sub­
categories between "training" and "test" samples
from two equations in Model C
Category

Equations (Incomplete)
CXI I

Group I

COMP

cTxvn

- 5.8
(.081)

- 7.0
(.061)

- 29
(.124)
30
(.131)

23.8
(.078)

46
(.102)

RL3

- 38.8
(.033)

- 40
(.065)

- 33.1
(.054)

- 42
(.043)

RL3

36.5
(.002)

41
(.008)

34.9
(.001)

44
(.002)

A

25.1
(.021)

19
(.168)

22.3
(.030)

(.383)

- 13.7
(.271)

30
(.044)

- 20.1
(.067)

36
(.010)

K3

-110

103
(.173)

K4

-111
(.030)

114
(.117)

K5

-125
(.014)

98
(.172)

RL2

Group III

CXVII

- 30.3
(.055)
23.2
(.105)

C4

Group II

cTxn

LK

(0.037)

10

186
—2

Due to the differences in R

between the 'training'

and 'test' sets, the results should be viewed with more
caution.

The significance of the relationship-cum-living

subcategories RL2, RL3, and RL4 was clearly consistent across
the two sets; hourly costs being predictable to some extent
using these subcategories.

Client comprehension in both one

binary subcategory (C4) and the 'cardinal' category (COMP)
also appeared consistent suggesting that within the relevant
range hourly costs were inversely related to mental impair­
ment.
Only Attendant (A) service coefficients could be
interpreted as similar (but not convincingly so) in Group II.
In Group 3, inconsistencies were found in the coeffi­
cients

of light cleaning (LK) and 3 binary subcategories of

Home Management (Kg, K^, and K,.).
Further discussion of these results appear in the
conclusion.

CHAPTER 9
CONCLUSIONS, FURTHER RESEARCH AND POLICY IMPLICATIONS

I.

Introduction
This study has focused on the analysis of non-medical

long-term care services assigned to the impaired under the
Michigan Adult Chore Service Program.

The services were

supplied by providers who were hired by predominantly elder­
ly clients.

The client was financed by the Michigan Depart­

ment of Social Services (MDSS) to acquire one or more of
the following types of services:

light and heavy cleaning,

home repair and maintenance, shopping and errands, laundry,
meal preparation, financial management, yardwork, attendant,
transportation and non-nursing personal services.
The aim of the research was to examine two principal
relationships:

first, to determine whether or not there was

a systematic relationship between the client's attributes
and the services assigned to the client by the MDSS workers;
second, the estimation of the relationship between the client's
attributes and the cost of services.

Implicitly, the study

examines the decision making process by which MDSS workers
assign services to clients.
Under the MDSS program, the assignment of services
to clients by MDSS workers was purportedly based on the
187

188
following attributes:

functional status, socio-economic

status and to a lesser extent, the medical status of the
client.

Functional status attributes included the degree of

impairment in mobility, dexterity, sensory perception, com­
prehension and ability to manage the home.

Socio-economic

status covered income, age, sex, type of living arrangement,
relationship of client to provider, and location (urban/
rural}.

Medical status entailed diagnosis of a patient

according to criteria such as respiratory problems, heart
problems, cancer, rehabilitation problems, mental illness
and retardation and others totaling 9 groups of diagnoses.
If services are assigned to clients by MDSS workers on the
basis of client attributes, it should be possible to demon­
strate the types of services assigned to clients on the basis
of an attribute profile.

In addition, knowledge of the

clients' attributes should facilitate estimation of service
costs and hours of labor supplied by providers.
To determine whether systematic relationships existed
between client attribute profiles and assigned services, a
pattern discovery algorithm, called entropy minimax was
employed.

Stemming from developments in informational theory,

entropy minimax was used because it could manipulate several
assigned services and multiple attributes simultaneously and
produce probabilistic relationships between assigned services
and attributes.

It also had the advantage of obviating the

necessity of assuming a priori distributions in the data.
The results appear in the next section.

189
The relationship between the client attributes as
explanatory variables and service costs was estimated using
regression analysis.

The goal of the regression analysis

was to identify, if possible, predictors of cost that would
indicate where costs might be controlled.
were seeking answers to such questions as:

For example, we
Do services

provided to clients by relatives cost less than those pro­
vided by non-relatives?

Is cost related to age of the client

or to whether the provider lives with the client?

Is cost

related to whether the provider lives in a rural or urban
area?

In the hypotheses detailed in Chapter 5, theories

on these and other questions have been postulated, e.g.,
assuming otherwise identical profiles, clients taken care of
by relatives were less costly to care for than client's re­
ceiving services from non-relatives.
The two thrusts of the thesis are discussed below
together with alternative explanations of the results.

This

is followed by a retrospective look at the results in the
context of the aims of the thesis and future research.
Finally, policy implications of this study are briefly dis­
cussed.

II.

The Relationship Between Client Attributes and
Assigned Services
The objective of this analysis was to seek to identify

and utilize a methodology in order to determine if a system­
atic relationship could be detected between client attributes

190
and assigned services.

The entropy minimax procedure was

the method used to search for patterns of service among a
sample of 428 MDSS Chore Service clients or approximately
4% of the total client population in 1975-1976.
Using the available data on the Michigan Chore
Service Program clients, together with the attribute pro­
file associated with that program, no systematic relation­
ship was discovered between client attributes and assigned
services.

Employment of the entropy minimax algorithm did

not detect a patterned relationship between client attri­
bute profiles and assigned services.

Several features of

the analysis conducted in this study might account for these
results being inconclusive.
Methodological problems could have stemmed from misspecification of attribute categories.

This implies the

profile was inappropriate and that indicators other than,
say, dexterity or mobility, might have better characterized
the client.

For example, the client's ability to dress him­

self might be a better indicator of impairment than dexterity.
Since some attributes were cardinal in nature and
necessitated transforming to a binary form, a further
methodological shortcoming of the analysis may have stemmed
from inappropriately dichotomizing the category.

The speci­

fic scale on which the transformation was performed may also
have been inappropriate.

Table 6.4 in Chapter

some of the specific categories transformed.

6

presents

191
Another methodological problem may have resulted
from the specification criteria employed to generate the
five alternative outcome mixes.

The reliability of the

results of the entropy minimax computer program diminishes
when more than 5 or

6

outcome categories are entered into

the program.

For that reason, it was necessary to either

aggregate the

11

services into groups or employ some out­

comes (services) as proxies for others.

The criteria by

which this specification of outcomes was accomplished is
more fully described in Section VI-A of Chapter

6.

The regression analysis of Models A, B, and C
tended to confirm the absence of a patterned relationship
between client attributes and services rendered.

This ob­

servation was based on thefinding that in regression Model
A the service variable alone accounted for more variation
—2

in the costs per month (R
2

tional status alone (R
—2
combined (R = .304).

= 0.420) than did either func-

= 0.116) or both of these variables

When functional status, socio-economic
—2

status and services were combined, R

= 0.474.

Those cate­

gories of the functional status variable associated with
almost negligible amounts of variation in monthly costs were
mobility, dexterity and sensory perception.

The implication

of these findings is that the level of a client's dysfunc­
tion with respect to mobility, dexterity, and sensory percep­
tion were poor predictors of the client's assigned services.
The unexpected results of no relationships found by
the entropy minimax analysis may stem from a lack of

192
consistency among MDSS workers in their assignment of ser­
vices.

For example, MDSS workers may have no common working

definitions of the variable categories, although the program
had been running since 1972.

Even if the definitions were

common, the scaling of them may differ from worker to worker.
Alternatively, the MDSS worker may assign services by impli­
citly taking into account more or fewer client attributes
than those listed.

Those key attributes used in each deci­

sion may vary from client to client and from worker to worker.
Another approach for the MDSS worker might be to
inquire as to what services are perceived as required by
the client, e.g., cleaning, non-nursing personal services,
etc.

In other words, to seek to determine what it is the

client cannot do that needs to be done in order to maintain
(produce) an independent life style.

The inability to cope

with some everyday tasks seems to be the primary motivation
of the person requesting the MDSS services in the first
place.

Clearly it is not mandatory that a client need be

mobile or dextrous to be independent.

Neither does it follow

that because the client is immobile or lacks dexterity that
the MDSS will fund services such as cleaning or meal prepara­
tion.

The specific assignment of services to a client by

the MDSS worker would depend on both the client's inability
to perform such services herself and on the MDSS worker's
perception that without such services the client cannot
continue to live appropriately in an independent setting.
It is conjectured the MDSS worker reviews both the client's

193
request for services and the consequences of doing without
those services before assigning services.

Implicit in this

conjecture is the belief that the services are assigned to
a client primarily on the basis of what the client is per­
ceived to need by the MDSS worker rather than on the basis
of the attributes of the client.

Client attributes can sub­

sequently be specified by the worker to justify the employ­
ment of services assigned by them to the client.

Specific

attributes need not be prerequisites for specific services.
The one exception to this might have been the attribute
comprehension which correlated with financial management
services (r = .55).
As pointed out in the thesis, several approaches to
determining long-term care are based on different client
attribute profiles.

In view of the foregoing, these

approaches should be tested to determine if systematic
linkages exist between attributes and services assigned.
These methods of determining appropriate care are indirect
approaches in that it is presupposed that the attribute pro­
file of the client is first specified and then utilized in
the assignment of services.

A direct approach to assigning

services would be to classify clients according to the
services they require in order to maintain relatively in­
dependent lifestyles.

Such an approach would only implicitly

take into account functional, socio-economic and medical
status.

Thus, a person might be classified as requiring

meal services, cleaning, laundry and shopping services.

A

194
more refined format might specify in the case of meal ser­
vices, which meals are needed and the average length of time
it takes to prepare them.

This subjectivity of the decision

making process in assigning non-medical services to clients
is in apparent contrast to the more "objective" approach of
assigning medical services used by the medical profession.
The approach to the assignment of subsidized ser­
vices based directly on service needs might, due to its
"subjectivity," jeopardize the program by rendering it more
vulnerable to charges of abuse or fraud.

The direct approach

of stating needs for services might be a less "objective"
justification for government assistance than a profile of
readily observed attributes on which "need" or the assign­
ment of services is supposed to be based.

The formal speci­

fication and recording of the attribute profile together
with the assigned services would appear to make abuse or
fraud more difficult to perpetrate.

Employed in this way,

attribute profiles might serve less to justify the assign­
ment of specific services than to justify services per se.
The profile itself becomes an accountability check on the
MDSS worker.

If the worker views it exclusively as such,

then his/her approach to assigning services is direct in
that it is in direct response to the service needs requested
by the client.

The justification of services by the detail­

ing of a client's attribute profile would appear to respond
to the MDSS requirement that the MDSS worker, and in turn
MDSS itself, be accountable to the legislature for

195
responsible allocation of public funds.

The primary purpose

of utilizing an attribute profile thus becomes one of en­
suring government accountability, not the justification of
specific services.

It provides an auditable record of why

services were assigned.

According to the results of pattern

detection analysis, the attribute profile does not provide
decision criteria as to what specific services ought to be
assigned to the client.

Another use to which the attribute

profile may be put is the prediction of client outcome over
time, given necessary support services to keep the client
out of an institution.

III.

The Determination of Categories Influencing Costs
The regression analysis was performed on three

'behavioral' as distinct from 'technical' cost functions.
The distinction between these types of functions is explained
in Chapter 5.

Each of the cost functions had a different

endogenous variable:

Costs per month (Model A ) , hours per

month (Model B ) , and costs per hour (Model C).
Model A best fitted the data in so far as it explained
more variance (almost 50%) than the other models (33% and 13%,
respectively).

As noted above, the most significant variable

in Model A was assigned services.

Important categories of

the service variable appeared to be meal preparation, light
cleaning, attendant services and non-nursing personal ser­
vices .

196
Among the categories of the socio-economic status
variable, only location was significant in Model A, indicat­
ing higher costs in urban areas.

This result was unconfirmed

in the "test data," as distinct from the "training data."
The specific functional status variable categories
mobility, dexterity and sensory perception were not as power­
ful explanatory categories as were the more general cate­
gories comprehension and ability to manage the home.

Com­

prehension could be considered an aggregate measure of
mental abilities.

Home management could be an aggregate

indicator of physical impairment.

These findings question

the value of creating more disaggregated indicators of
physical and mental impairment with respect to estimating
monthly costs, at least as understood by MDSS workers.
In Models B and C where the endogenous variables
were hours of service employed and costs per hour, respec­
tively, as hypothesized, the socio-economic status variable
was more important.

Surprisingly, the lowest hourly cost

of services was incurred by non-relative providers living
in the same residence as the client.
worked the longest hours.

Such providers also

Fewer hours at higher cost were

provided by relatives living with clients.

Even fewer hours

were supplied by relatives living separately from clients
but at higher cost per hour than the previous two arrange­
ments.

Providers supplying the least hours at the highest

hourly cost were non-relatives living separately from clients.
This seeming indirectly proportional relationship between

197
costs per hour and hours worked explained why monthly costs
remained relatively constant.

The provider related to the

client was not less costly on a monthly basis than the
non-related client.

As hypothesized, hourly costs were

higher for those clients living separately.
Variable categories that contributed significantly
to the explanatory power of Models B and C were comprehen­
sion, home management and attendant services.

Hours worked

were higher for physical disabilities than for lack of com­
prehension but hourly costs of providing services to com­
pensate for physical impairments were lower.
As expected, the medical status indicator appears to
play no role in explaining monthly costs of chore services.
This does not mean it plays no role in explaining costs of
long-term care.

Medical status was not addressed adequately

in this analysis because the quality of the data was poor.
The primary medical diagnosis underlying the client's impair­
ment was not always recorded.
ly.

Neither was it done systematical­

This deficiency in data is a clear indication of the lack

of systematic training among MDSS workers.

The lack of ade­

quately trained MDSS workers might also have affected the
accuracy with which other client attributes, especially func­
tional status, were recorded.

This deficiency in turn might

account for the lower explanatory power of functional status
categories.
The functional status categories of mobility, dex­
terity and sensory perception were particularly poor predictors

198
of cost.

In this study, more comprehensive or general indi­

cators of functional status such as level of comprehension
or ability to manage the home were better categories with
respect to explaining variation in costs.
From the regression results, it was apparent that
services assigned to clients best explained variation in
monthly costs.

It was but a short intellectual leap to pro­

pose that classification of a client's functional status
might better be based on those services required by the
client to maintain an independent lifestyle.

This approach

to classifying clients more directly addresses the client's
service requirements but might be subject to more abuse as
discussed above.

IV.

Other Conclusions and Implications for Research
This research started out with the assumption that

a profile of client attributes including non-medical and
medical attributes could be used to identify an appropriate
package of care from among the whole spectrum of long-term
care type services, medical and non-medical.

This study

did not address the provision of medical services which are
assigned according to patient signs and symptoms and to a
lesser extent, according to circumstances characteristic of
the client.

However, the procedure of observing the patient's

signs and symptoms (or medical attributes)

followed by the

assignment of medical services based on those attributes is
referred to in this study as the medical model of service

199
assignment.

The procedure by which MDSS purported to assign

non-medical services to clients appeared to be based on a
medical model.

Prom the results arrived at in this study,

it now seems that it is inappropriate to base the assignment
of non-medical services on the basis of "signs and symptoms"
of functional status.

Future research, employing a pattern

detection method such as entropy minimax should focus on the
detectability of relationship between other forms of attri­
bute profile and other specification of services.

If future

research also confirms the results of this study, the utility
of current approaches to assigning services for long-term
care clients on the basis of attribute profiles similar to
that apparently used by MDSS is called into question.
One of the general aims of this dissertation was to
suggest a methodology by which all long-term care clients or
patients might be classified.

Prom the foregoing discussion

it-is clear the client's attributes can be divided into at
least

2

general categories:

fication of clients.

medical and non-medical classi­

The classification of the client's

inability to perform necessary tasks associated with living
independently appeared to be a superior method to that of
classifying them according to physical and perhaps mental im­
pairment attributes.

The classification of clients according

to deficiencies in service requirements rather than bodily
or mental impairments or, with few exceptions, socio-economic
status (e.g. location), seems to be the best approach to pre­
dicting service requirements and their costs.

200
Further research should be addressed to determining
the best classification of clients according to their service
requirements.

Alternatively or concurrently the classifica­

tion of services might also be clarified.

One test of the

efficacy of the classifications used is to examine the
accuracy with which costs or hours worked can be estimated
using those categories as explanatory variables in a regres­
sion analysis.

From the research conducted here, it appears

the more direct the relationship between client attribute
classification and service rendered, the more powerful the
explanatory power of the variables (categories) used.

Thus,

instead of basing the assignment of, say, dressing services
to a client on a dexterity impairment index, it would be
more appropriate to classify the client as being unable to
dress himself.

Dressing services in the context of the MDSS

form would be subsumed under non-nursing personal services.
But non-nursing personal services also covers bathing ser­
vices, toileting services and others.

The question is to

what extent the "needs" of the client should be aggregated.
Is it better to detail client "needs" such as dressing,
bathing and toileting services or aggregate them under the
heading non-nursing personal services?

This also is a ques­

tion for further research.
The

first

consideration in assigning services

(either medical or non-medical) to any client is the medical
status of the client.
observed first.

The medical status of the client is

If the diagnosis indicates instability

201
necessitating professional medical care, then the decision
as to where it is best provided is considered.

The diagnosis

may necessitate hospitalization in which case non-medical
attributes are of little importance.

The medical condition

of the client is always of great importance with respect to
services required; therefore, it and implicitly medical
services "needs," are considered first.
At the other end of the spectrum of care, after it
has been observed

the client is medically stable, the non­

medical attributes assume importance in assigning services.
A program like that of the MDSS studied here can meet such
needs.

It is for clients who fall between these extreme

cases of hospitalization and employment of minimal non-medical
service assignments that an accurate attribute profile becomes
critical.

A specific attribute profile may make a client

eligible for a nursing home or eligible for chore type ser­
vices and home health visits.

As detailed in the review of

literature, Chapter 3, it is claimed that 20-50% of patients
in nursing homes are inappropriately placed.

The implication

is that many of these could have been cared for appropriately
in a home setting if they had sufficient services to support
them.

Perhaps, also, there is another explanation for so

called inappropriate institutionalization of people in nurs­
ing homes.
Perhaps considerable confusion arises from the fact
that with age, the number of unstable episodes of illness
increases and alternates with stable conditions.

When this

202
fluctuation between stable and unstable medical condition is
frequent, the medical model takes precedence and professional
health staff tend to take over.

Since these staff usually

work in institutions, the predisposition to institutionalize
patients becomes logical.

This may explain why, at any one

time, some persons in institutions appear to be inappropri­
ately placed.

They may have been passing through a relatively

shortlived stable episode of medical status when the assess­
ments were made.

Institutionalization of the medically un­

stable would not be inevitable if professional medical staff
offered services in the homes of the chronically ill and dis­
abled during periods of medical instability.
An alternative interpretation of the non-detectable
relationship between client attributes and assigned services
might be pertinent.

Perhaps the specification of the pro­

file outline and the assigned services is appropriate but
the MDSS workers do not use it consistently.

Implicit in

this view is that if the MDSS workers consistently employed
the attribute profile in the assignment of services, then
patterns between attributes and services would become detect­
able.
Further research might focus on the actual means by
which workers assigning services make their decisions.

What

criteria do they in fact use on which to base service assign­
ment?

This decision related research should encompass not

only the workers making assignments of services but the
clients themselves, their families and third party payors.

203
The objective functions of these groups were posited in
Chapter 2.

Just what specific criteria are considered by

these groups and how are they weighted when decisions on
assignment of services are necessary?

When examining the

basis on which decisions are made by the workers assigning
services, it should be borne in mind that they must not
only assign services to the client but maintain some form
of accountability to the third party payor, in this case
the state government.

V.

Policy Implications
The present official MDSS approach to assigning

services to clients on the basis of the current attribute
profiles seems to be ineffective in that there appears to
be no detectable relationship between client attributes and
assigned services.

The functional status variable and

socio-economic status variable are less useful predictors
of costs than the services themselves.

It is probable that

the actual utility of the functional and socio-economic
status variables derives from their use for justification of
service assignment per se rather than specific services.

In

this role, attribute records fulfill an accountability func­
tion and should be retained, at least in part, for that
purpose.

They meet the accountability concerns of the third

party payor, in this case the state government.
Further emphasis might be given to specification of
the client's service requirements within the MDSS Form DSS-3492.

204
With a view to more consistently documenting attributes and
services assigned, the MDSS workers should be trained more
systematically.
be simplified.

To facilitate this, the MDSS form might
The parts of the form documenting types and

levels of impairment might be removed or altered.

More

detail might be appropriate in the documentation of service
assignment.

For example, the estimated time required to

perform each type of assigned service would be helpful in
estimating costs and would also constitute a consistency
check among MDSS service workers.
Third party payors such as the government, also seek
to provide service packages for eligible clients at minimum
cost.

Within the context of the MDSS chore service program,

the functional status categories that were significant in
explaining costs were comprehension and ability to manage
the home.

These were broad indicators of mental status and

physical impairments, respectively.

The explanatory variable

explaining the most variation in cost was the service vari­
able.

The most significant categories of that variable were

light cleaning, meal preparation, attendant services and
non-nursing personal services.

That these categories were

significant indicates they may be of value in establishing
policies with respect to cost.

For example, instead of the

single monthly cost ceilings nowadopted by the MDSS for its
chore service program, there might be several ceiling.

Bach

ceiling might be associated with the assignment of one or
more, but not all, of the above service categories.

Clients

205
for whom meal preparation is assigned might be subject to a
higher cost ceiling than those for whom transportation or
light cleaning is assigned.

The higher cost ceilings for

more labor intensive services such as meal preparation and
non-nursing personal services might induce persons to remain
in independent settings longer and thus delay possible entry
into nursing homes.

From the perspective of the third party

payor (MDSS in this case) the appropriate cost ceiling for
non-nursing personal services might be a percentage of the
cost to the state of an average month of care in a nursing
home.

Thus# if the average cost of nursing care for Medicaid

patients is $ 30/day and the state pays $16 of that, then a
maximum ceiling cost for non-nursing personal services might
be 16x30=$480 per month.

Assuming medical costs constitute

part of nursing home costs, the actual ceiling on a mix of
services that include non-nursing personal services, may
appropriately be reduced to between $300 and $450 per month.
A lower ceiling might apply to a mix of services that does
not include non-nursing personal services.

The reason for

suggesting the nursing home cost-related ceiling for non­
nursing personal services was because these services most
nearly approximate those provided in a nursing home, and
therefore, might substitute for them.

If the state offered

this option for people who are clearly eligible for state
subsidized nursing home services, and if the client opted
not to enter a nursing home, then there would be a clear
saving of federal dollars and a marginal saving of state
resources.

206
Other

lower ceilings than the current $270 might be

imposed on service mixes which did not include
non-nursing personal services.

The overall cost of the Chore

Service Program might rise or remain the same.

As long as

the rise was more than offset by demonstratable savings in
nursing home costs, the application of multiple ceilings
that depended on service mixes would be appropriate.

On the

other hand, the monetary savings to the state might justifi­
ably be negligible if it can be demonstrated that the bene­
fits associated with home care are greater than those derived
from nursing homes.

207

INSTRUCTIONS:
1. File original in service c u e tilt.
2. Submit copy to S.O- attached to
whit* OSS* I3C

ELIG IBILITY AND NECESSITY
FOR ADULT PAID SO CIAL SERVICES
S ta te o f M ichigan
D epartm ent o f Social Service*
ilintMQava

cuinrsnaait

toctac ucuettv nutaaik

£il£tU NuMtia

1
---------------------------------------------------------------------------- 1. ELIG IB ILITY --------------------------------------------------------------------------C. COMPUTATION (for ootentiel recipient’*oniyl
A. STATUS OF ADULT
i Chock applieaoia boaetl

1 O

T O T A L INCOMC FO R W A R D E D FR O M INCOM E BOX

> ■ _______

SSI Recipient

M.A. PATIENT PAY AMOUNT
(SubtrictI
AVAILABLE INCOME
(Subtotal I
INCOME BASE
(Subtract)
TOTAL CLIENT PAY AMOUNT

Don recipient meet I Vet No
Potential SSI Recipient SSI Resource.Criteria11 |~1 al~l
sotsntiai SSI raciewni ctieck on* ooa.

□
it

Q Aatd 2 O Disabled aCH Blind
B. INCOME for *11 client*.
SSI .

RSOI +_
Other Pension* +_

0 . SERVICE COSTS
COST OF CHORE SERVICES

EerntdNet +_

I e n te r t o u t h o r n o ack l

TOTAL CLIENT PAY AMOUNT
(E n te r fro n t c o m p u ta tio n ) (Subtract) —
Other +
-lATOTAL•
TOTAL A U TH O R IZ ED
(i n s e r t i n c o m p u t a t i o n s o x o n u n i * i i - « STATE PAYM ENT
II. NECESSITY
A. LIVING ARRANGEMENTS (Chflck applicabl* boxnl
[~~1 Houteholder / Independent Living
2 U
Non-Hou*ehold*r / Living in household of another,
NUMItaosrooms
vtcii* in u g ia ia n
n
Owned

!!

-pRiCTBOTusarr

□

Rented

8, HEALTH (if pervinenti

SSCTTWyiHiSiZIIelSr-

"" "

-PMONINO

IiUmiiw trptiiorv
{Ooei eiient nnd

I h o ftru tu tw luprwtfon Vtt

C. CLIENT LIMITATIONS
(Qnek Appucabii 8o«t>i
SOMI 1 MUCH j
OCSCR'^TiOfw

1 I IiwnT D

*TWe rn rw t N * •-•W *tM«*t «* W)i Seen " • • » « ■ " < « >

OttCPIPTlON
Walk

1 NON!
•

1 MONI

SOMI

MUCH

u □

s n

•a F I

1 Manage Finances
! Remember Instructions

[25 □

26 n

i 2? n

'9 □

i Undertone Instructions

‘ 28 □

29 □

| 3o Q

Lift

» □
io Q

8 □
" □

« n

: Oo Light Cleaning

■31 Q

32 0

!3 3 Q

Brno

130

14l

Climb Stairs
Graip

') □

See
Hear

3S$>3*97

n O

J*fSi P'tviou* •omOrt

Of utM

2 P

• a
2 0 fl

l a p

1
« □
:2i n

! » □

23 C

I2 4 0

Do Hesvv Cleaning

34 □

35 □

la e D

Understands English

37 □

38 □

!3 a Q

• 40 Q

41 n

j 42 n

Otner (Soecifv Belowl

(TURN OVER AND COMPLETE BACK)

208

II. NECESSITY (CONTINUED)-------O. SERVICES NEEDED (Chtck aoolicaoia bon)

’ Q

8. SJioooing ana/or ottitr arrtndt

2. Htivv Cltininq

2 □

7, Guido Dog

3. Minor hausatioid rteain
4. Mod Praeancian

□
r>

' 1. Lignt Craning

< n

S. Laundry

« a

12. Non-nuriing ptnontl eon

H

t

8. Financial Managamant
9. Trontooruoan
10. Attandsnt for tronioortttion

!ll.Yardv.ork

*□
« n

171

to

1 13. Intorortior
i 14. Otltar ISeoeifv ealew)
!

'1 □
12 □
13 O

1« □

C. PROVIDER'S INFORMATION
DESCRIPTION

FIRST PROVIDER U N

N o in o

;

R a U n o n tltio t o

adult

; Aga l«oore»imit»l

1 SECOND PROVIOER (M l

THIRO PROVIDER (731

FOURTH M O V fO C ft

1

;(1
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3 'G O rw RRm m
'3 ~ 9 m * w S v * i_iN««.*Mm« I t C o i R i w t — •< U N » ii* i m

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«s0M|M«rrl«R t C " * * * * * " " j r G O m y ip r l—

|[

JO O m r

' Addrau

Ptiona____________
>Sarvica Providta
u n iarteo d a iaa in 0
:
abo«at
i Hgun ear day
1Day* oar w f c

:

I

j

Sxoactad duration

1

. Rata of pay

!

Mommy r u t of oav

'

Sffactiva data

|

.

j
!

F. APPROVED FOR: (Ckaek aoo<ieab(a box)
1. Chora Sarvicas ilnoiv. orawoani
2. Chora Sarvieas lAgancv oramooi
3. Homamakar tarvictl

•n
2□
3P

[ 4.

Family haioar larvicai

1 S. Attandant itrvicn
I 8. Bilingual imarorttar

4n

7. Guida dog

7 D

*n
•0

G. DENIED

Ration.'

H. REVIEW NEEDED
1•
i-i* 4**

" *-•***.

I. CERTIFICATION

|
; .csnmncron« :
r
«
*jau
i
r 1•
'
i
»
i3 5 !«rm.n«;-»r
i
i™ t t
a
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i
is
o
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t
i
l
i
a
t:
n
aioava■
moj
a
r
v
.
c
an
a
t
a
i
.
3
i«ienlynnc*orcnosrmi igr««a:
sscr*srmmy-aomradi
c
r
v
i
e
a
i
.
*ien«rvr.t orov51’ii
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.

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•4*J

APPENDIX A

APPENDIX B

209

SAMPLE COUNTY RATE
CHORE SERVICE PAYMENT SCHEDULE

Type ol* Service

Rate

1. Light housekeeping - meal preparation, shopping, laundry,
etc. - non-daily
$2.25/hr.
2. Heavy one-time house cleaning

2.75/hr,

3. Yard work - cleaning, snow shoveling, etc.

2.00/hr.

4. Daily household activities - include shopping,
transportation, etc. at least 6 hrs. a day - 5 days a
week

$200/mo.

5.* Live-in 24 hour personal care (ambulatory client) in­
cluding all household activities

240/mo.

6.* Live-in 24 hour bedfast or chair to bed - total care
including ail household activities

240/mo.

7.

A.

Adult with parents or relative (1st degree), attend­
ing workshop or day activities - personal care
needed (help dressing, eating, bathing, etc.)

150/mo.

Non-personal care, but cannot be alone extended
periods of time

100/mo.

Adult with parents or relatives (1st degree) not
attending workshop or day activities - personal
care required

200/mo.

Non-pcrsonul care - cannot be left alone extended
periods of time

150/mo.

Adults with parents or relatives severely retarded or
handicapped needing total care

270/mo.

U.
8.

A.

11.

9.

NOTE:

These are only a suggested rate schedule and could be adjusted
downward when possible.

*0wn arrangements to be made with client for time off.

PAID SOCIAL SERVICES
The following information complements Services Manual Appendix E
in the area of establishing county maximums under the Paid Social Ser­
vices Program. Many considerations were taken into account in arriving
at county maximums that are in line with the "going rate" for the cost
of such services in Mason County.
Chore Services have been broken down into specific task functions.
A particular client may be eligible for one or any combination of the
specified task functions. Eligibility for specified Home Services shall
be based on an evaluative interview between the social services worker
and the client. Eligibility for specified Home Services, is based on the
requirements described in Sections A and C of SM Appendix E. The narra­
tive in the services record is to indicate the services provided, and
must confirm the exact needs and duration of the specific services to
be purchased.
Task Function

County Maximum

Criteria

A.

MEAL PREPARATION

$5.00 per day

2 h -3 hrs. daily for 2
meals - client has tools

ii.

HOUSE CLEANING

$10.00 per week

3 hrs. incl. transportation
client has tools

C.

LAUNDRY (in-home)

$3.00 per day

as needed: every day, twice
weekly, once weekly, etc.

D.

SHOPPING FOR CLIENT

$4.00 per week

2 hrs. incl.transportation

£.

LAWN MAINTENANCE

$4.00 per week

2-3 hrs. - provider has tools

P.

GARBAGE DISPOSAL

$5.00 per month

provider transports

$105.00 per month
$130.00 per month
$160.00 per month
$54.00 per month

______
______
_______
personal needs plus $1.00
hh needs

LIVE-IN ATTENDANTS
a. 5 nights
I). 6 nights
c. 7 nights
d.

H.

relative

SNOW REMOVAL
a.

Manual or hand plow $2.00 per hour

b.

Automotive

$3-6 per hour

Single payment-provider
has tools
Single payment-provider
has tools

211

I.

NON-NURSING PERSONAL CARE

$2.00 per day

_______

Any combination of these services may not exceed $270.00

per month.

The services worker should take care in determining the client's
present needs and in projecting anticipated needs, such as a need for
snow removal in the winter, so that the total maximum of $270.00 is not
reached before adding the cost of snow removal.
11-17-73*

*Not updated since then.

Received by reviewer on 12-30-75

BIBLIOGRAPHY

BIBLIOGRAPHY

Anderson, N. N . , A Planning Study of Services to NonInstitutionalized Older Persons in Minnesota, The
Governor's Citizens Council on Aging, S t a t e o f
Minnesota, 1974.
Barney, J. L . , Patients in Michigan's Nursing Homes: Who
Are They? How Are They? Why Are They There?
Institute of Gerontology, University of Michigan,
Wayne State University, November 1973.
Barney, J. L., "The Well Being Report: A Look at Supportive
Services for the Elderly.T* Institute of Gerontology,
University of Michigan, Wayne State University, 1975.
Berger, E. J . , "Study and Analysis of Utilization and Cost
Data concerning the Provision of Home Health Service
and Extended Care Services.11' St. Louis Labor Health
Institute, St. Louis, Missouri, February 23, 1970.
Berkowitz, M. and Johnson, W. G., "Towards the Economics of
Disability: The Magnitude and Structure of Transfer
and Medical Costs." J. Human Res., Summer 1970,
5(3), pp. 271-97.
Blenkner, M. et al, "Protective Services for Older People,
Findings from the Benjamin Rose Inst. Study." in
Social Casework, October 1971, Vol. 52, No. 8.
Boulding and
, Redistribution to the Rich and the Poor,
Wadsworth Publishing, Belmont, California, 1972.
Burton, R. M . , et al, "Nursing Home Cost and Care: An
Investigation of Alternatives."
GSBA Paper No. 12
(Revised August 5, 1974) , Center for the Study of
Aging and Human Development, Duke University Medical
Center, Durham, NC.
Busse, E. W. and Pfeiffer, E., (eds.), Behavior and Adaptation in Late Life, Boston, Little Brown and Co.,
T 5W . ---------------

212

213
California Association of Home Health Agencies, Cost Survey
of California Certified Home Health Agencies and the
Related Effects of the California State Department
of Health Care Services. Schedules of Maximum
Allowances, March 1973.
Caro, F. G., Organizing and Financing Personal Care Services;
An Alternative to Institutionalization for the Disabled.
Levinson Gerontological Policy Institute, Brandeis
University, June 19 72.
Christensen, R. A . , "Entropy minimax Method of Pattern
Discovery and Probability Determination," Arthur D.
Little, Inc., Cambridge, Mass., 7 March 1972.
Congressional Budget Office:
"Long-Term Care for the Elderly
and Disabled," Budget Issue Paper, February 1977.
Emling, Diane Carpenter, Adult Chore Services. A Profile of
In-Home Assistance-! Studies in Welfare Policy No.
10, Michigan Department of Social Services, November
1976.
Lave, J. R., Lave, B. L. and Silverman, L . , "Hospital Cost
Estimation Controlling for Case Mix," Applied
Economics 1972, 4, pp. 165-180.
Evans, R . , "Behavioral Cost Functions for Hospitals,"
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1972a.
Fitzgerald, J . , "Home Health Services for the Aged in South
Eastern Michigan," The Comprehensive Health Planning
Council o£ Southeastern Michigan, November 1972.
Florida Department of Health and Rehabilitation Services,
"Community Care for the Elderly," 1971.
Genesee Region Health Planning Council, Survey of Need for
Inpatient Beds and Related Home Health Care Services,
Monroe County, New York, 1969-70.
Gift, D. A., Comparison of Classifying Power of New Neighbor
Clusterer, Entropy-Minimax, Pattern Detector and
Multiple Regression. Working Memorandum, Thyroid Pro­
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Gift, D. A . , "An Introduction to Entropy-Minimax Pattern
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