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Unwersnty dissertation entitled

 

FORECASTING CONSUMER ADOPTION OF
TECHNOLOGICAL INNOVATION:
choosing the appropriate diffusion models for new
products and services before launch

presented by

Lance Cameron Gentry

has been accepted towards fulfillment
of the requirements for the

Marketing and
PhD. degree in Supply Chain Management

 

 

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FORECASTING CONSUMER ADOPTION OF
TECHNOLOGICAL INNOVATION:
choosing the appropriate diffusion models for new
products and services before launch

By

Lance Cameron Gentry

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Marketing and Supply Chain Management

2003

ABSTRACT

FORECASTING CONSUMER ADOPTION OF
TECHNOLOGICAL INNOVATION:
choosing the appropriate diffusion models for new
products and services before launch

BY

Lance Cameron Gentry

Within the vast literature on various forecasting models, there is
consensus that no single diffusion model is best for every situation. Experts in
the field have asked for studies to provide empirically based guidelines for
recommending when various models should be used. This research investigates
multiple diffusion models and provides recommendations for which diffusion
models are appropriate for radical and really new products and services before
the launch of the innovation. In addition, a forecasting classification grid is

proposed.

Copyright by
Lance Cameron Gentry
2003

DEDICATION

This dissertation is dedicated to my family, my committee, and the
wonderful people in N370. I greatly appreciate the extra effort my wife, Allison,
has put forth to ensure I had uninterrupted time to work on this project. Luke,
Charles, Leah — you are the primary reasons why I went back to school and
pursued my doctorate. I hope and expect that the life of an academic will provide
ample opportunity to get to know you even better as your mother and I lead you
to adulthood.

Professor Calantone - Many thanks for your guidance over the last few
years. I appreciated the opportunity to get to know you better and I am grateful
you made time to serve as my chair. Professor Droge - Thank you for your
lessons on focus and your remarkable editing. I hope that I learn to teach my
students with the same clarity that you bring to your classes. Professor
Bohlmann - I appreciate your suggestions. Your assistance provided
reassurance when I had doubts about the output of some of the diffusion models.
Professor Page — You are a large part of the reason my research is aimed at the
diffusion of innovation among consumers. Thank you for making the study of
consumer behavior so interesting. Professor Levine - Thank you for your
willingness to serve on my committee even though the timing did not work out.
Professor Hoagland — Many thanks for your support, your stories, and the benefit
of your vast experience in forecasting.

I also want to thank all of those in N 370. You have made it easier to

succeed over the last four years and I appreciate it.

ACKNOWLEDGMENTS

First and foremost, I would like to thank those at the Consumer Electronics
Association. I was first introduced to you while serving at Philips and was
favorably impressed by your professionalism and effectiveness. I am pleased
that l was responsible for bringing Intel into your organization and believe this
was a win-win scenario for both Intel and the CEA. And I greatly appreciate your
willingness to give me access to your data for this study. The people at the CEA
have always been very friendly and helpful. I would especially like to thank Sean
Wargo for his diligence and patience in this project. Despite the number of
questions I asked about minutia (e.g., wasthe AVCO Cartrivision system
included in the 1974 VCR data?), he managed to get back to me in a prompt and
courteous manner.

I would also like to thank Richard Zwetchkenbaum (Intel), Angela Heam
(Satellite Broadcasting and Communications Association), and Ron Christianson

(Cyber Telephone Museum) for their help in obtaining data for this project.

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................... viii
LIST OF FIGURES ................................................................................................ x
LIST OF ABBREVIATIONS/DEFINITIONS .......................................................... xi
Chapter 1 ............................................................................................................. 1
WHAT THIS RESEARCH WILL ACCOMPLISH ................................................... 1
The Research Problem ........................................................................................ 1
Is Forecasting Part of Marketing? ................................................................. 1
Why is This an Important Problem for Academics & Managers? .................. 3
The Research Questions .............................................................................. 4
The Research Context ......................................................................................... 4
Data Sources ................................................................................................ 5
Chapter 2 ............................................................................................................. 7
LITERATURE REVIEW ........................................................................................ 7
Forecasting: Techniques and Methods ............................................................... 7
Classification Schemes in the Literature .............................................................. 8
Cetron and Ralph, 1971 - summary ............................................................. 8
Cetron and Ralph, 1971 - strengths and weaknesses ................................ 11
Martino, 1972 - summary ........................................................................... 11
Martino, 1972 - strengths and weaknesses ................................................ 13
Bright, 1978 — summary .............................................................................. 14
Bright, 1978 - strengths and weaknesses .................................................. 16
Armstrong, 1985 - summary ....................................................................... 17
Armstrong, 1985 - strengths and weaknesses ........................................... 20
Amtstrong, 2001 - summary ....................................................................... 21
Armstrong, 2001 - strengths and weaknesses ........................................... 23

A Forecasting Typology is Proposed .................................................................. 24
Predictions .................................................................................................. 27
Intentions ................................................................................................. 27
Conjoint Analysis ..................................................................................... 28
Expert Opinion ......................................................................................... 29
Scripts ......................................................................................................... 31
Role Playing ............................................................................................ 31
Scenarios ................................................................................................ 32
Correlations ................................................................................................. 32
Extrapolation ........................................................................................... 33
Analogies ................................................................................................. 34
Neural networks ...................................................................................... 36
Models ........................................................................................................ 38
Expert Systems ....................................................................................... 38
Econometric Forecasts ............................................................................ 42
Structural Models ..................................................................................... 43
Summary of Literature Review ........................................................................... 44

vi

Chapter 3 ........................................................................................................... 45

METHOD ............................................................................................................ 45
Hypotheses ........................................................................................................ 46
Data Sources ..................................................................................................... 48
Personal Computers (PCs) ......................................................................... 48
DBS Satellite Receivers .............................................................................. 50
CD Players .................................................................................................. 51
Camcorders ................................................................................................ 51
Projection Televisions (PTVs) ..................................................................... 52
VCRs ........................................................................................................... 52
Cordless Phones and Telephone Answering Device (T ADs) ...................... 53
Revised Classification of Innovations .......................................................... 54
Models ................................................................................................................ 55
Bass Model (B) ........................................................................................... 57
Bass Model Variants ................................................................................... 57
Simple Logistic (SL) & Gompertz (G) .......................................................... 58
Flexible logistic (F LOG) — Box and Cox (BnC) ............................................ 59
Selected Models and Proposed Forecasting Classification Grid ................. 59
Verification of Models ......................................................................................... 60
Process ........................................................ 64
Curve Fitting ................................................................................................ 64
Forecasting ................................................................................................. 64
Hypotheses Testing (Quadrant Analysis) .................................................... 65
Chapter 4 ........................................................................................................... 66
RESULTS ........................................................................................................... 66
Potential Fit of Models ................................................................................. 66
Optimal Parameters .................................................................................... 68
Actual Fit of Models (Forecasting) .............................................................. 70
Hypotheses Testing (Quadrant Analysis) .................................................... 79
Cell Testing (Hypotheses Testing) .............................................................. 82
Quadrant Analysis without PCs ................................................................... 83
Cell Testing (Hypotheses Testing) without PCs .......................................... 86
Chapter 5 ........................................................................................................... 87
DISCUSSION OF RESULTS ............................................................................. 87
Answering the Research Questions ................................................................... 87
Lessons From the Hypotheses ........................................................................... 88
Models ................................................................................................................ 89
Bass Models ............................................................................................... 89
Simple Logistic and Gompertz .................................................................... 91
Box and Cox ............................................................................................... 92
Contributions ...................................................................................................... 92
APPENDIX A ...................................................................................................... 97
Selecting Diffusion Models ................................................................................. 97
APPENDIX B .................................................................................................... 104
Diffusion and The Generalized Bass Model ..................................................... 104
Bibliography ..................................................................................................... 106

vii

Table 1:
Table 2:
Table 3:
Table 4:
Table 5:
Table 6:
Table 7:

Table 8:
Table 9:

Table 10:
Table 11:
Table 12:
Table 13:
Table 14:
Table 15:
Table 16:
Table 17:
Table 18:
Table 19:
Table 20:
Table 21:
Table 22:
Table 23:
Table 24:
Table 25:
Table 26:
Table 27:
Table 28:
Table 29:
Table 30:
Table 31:
Table 32:
Table 33:
Table 34:
Table 35:
Table 36:
Table 37:
Table 38:
Table 39:
Table 40:
Table 41:
Table 42:
Table 43:

LIST OF TABLES

Segmentation’s Effectiveness in Forecasting ...................................... 21
Summary of Forecasting Classification Schemes ............................... 24
Summary of Intentions Findings .......................................................... 28
Summary of Expert Opinion Findings .................................................. 30
Summary of Role Playing Findings ..................................................... 31
Summary of Scenario Findings ........................................................... 32
Ranking of Data Sources for Extrapolation by Intended Use (Armstrong,
2001) ................................................................................................... 33
Summary of Extrapolation Findings ..................................................... 34
Cellular Analogy (Lenz, 1962) ............................................................. 35
Bisexual Reproduction Analogy (Lenz, 1962) ................................... 35
Summary of Neural Network Findings ............................................... 37
Summary of Expert Systems vs. Judgmental Forecasts ................... 40
Summary of Expert Systems vs. Econometric Forecasts .................. 42
Summary of Econometric Findings .................................................... 42
List of Growth Curve Models ............................................................. 43
Diffusion Models Initially Considered ................................................. 56
Diffusion Models used in Research ................................................... 57
Minding p's and q's ............................................................................ 61
Camcorder Diffusion with Lilien Adjustment ...................................... 62
Model Abbreviations .......................................................................... 66
Curve Fitting Results ......................................................................... 66
Curve Fitting - Comparative Placement ............................................. 67
Curve Fitting - Optimized Parameters for B Model ............................ 68
Curve Fitting - Optimized Parameters for Bv Model .......................... 68
Curve Fitting - Optimized Parameters for GB Model ......................... 68
Curve Fitting - Optimized Parameters for GBv Model ....................... 69
Curve Fitting - Optimized Parameters for SL Model .......................... 69
Curve Fitting - Optimized Parameters for G Model ............................ 69
Curve Fitting - Optimized Parameters for BnC Model ....................... 70
Personal Computer Forecasting Results ........................................... 71
PC Forecasts — Comparative Results ............................................... 71
DBS Satellite Receiver Forecasting Results ..................................... 72
DBS Satellite Receiver Forecasts - Comparative Results ................ 72
CD Player Forecasting Results ......................................................... 73
CD Player Forecasts - Comparative Results .................................... 73
Camcorder Forecasting Results ........................................................ 74
Camcorder Forecasts — Comparative Results ................................... 74
Projection Television Forecasting Results ......................................... 75
PTV Forecasts — Comparative Results ............................................. 75
Video Cassette Recorder Forecasting Results .................................. 76
VCR Forecasts - Comparative Results ............................................. 76
Cordless Phone Forecasting Results ................................................ 77
Cordless Phone Forecasts - Comparative Results ........................... 77

viii

Table 44:
Table 45:
Table 46:
Table 47:
Table 48:
Table 49:
Table 50:
Table 51:
Table 52:
Table 53:
Table 54:
Table 55:
Table 56:
Table 57:
Table 58:
Table 59:
Table 60:
Table 61:
Table 62:
Table 63:
Table 64:
Table 65:
Table 66:
Table 67:

Telephone Answering Device Forecasting Results ........................... 78

TAD Forecasts - Comparative Results ............................................. 78
All Eight Innovations - Comparative Results ..................................... 79
Radical Innovations — Comparative Results ...................................... 79
Radical/High Priced Innovations - Comparative Results .................. 79
Radical/Low Priced Innovations — Comparative Results ................... 80
Really New Innovations — Comparative Results ................................ 80
Really New/High Priced Innovations — Comparative Results ............ 80
Really New/Low Priced Innovations — Comparative Results ............. 81
High Priced Innovations - Comparative Results ............................... 81
Low Priced Innovations - Comparative Results ................................ 81
Results of Cell Comparisons ............................................................. 82
All Seven Innovations - Comparative Results ................................... 83
Radical Innovations — Comparative Results ...................................... 83
Radical/High Priced Innovations - Comparative Results .................. 84
Radical/Low Priced Innovations — Comparative Results ................... 84
Really New Innovations - Comparative Results ................................ 84
Really New/High Priced Innovations — Comparative Results ............ 85
Really New/Low Priced Innovations — Comparative Results ............. 85
High Priced Innovations — Comparative Results ............................... 85
Low Priced Innovations - Comparative Results ................................ 86
Results of Cell Comparisons ............................................................. 86
Watching p's and q's ......................................................................... 90
Sum of Squared Errors for All Forecasts ......................................... 105

LIST OF FIGURES

Figure 1: Initial Classification of 8 Consumer Electronic Innovations .................. 5
Figure 2: Forecasting Methodology Tree (1985) ............................................... 18
Figure 3: Armstrong’s Methodology Tree (2001) ............................................... 22
Figure 4: Forecasting Classification Grid .......................................................... 26
Figure 5: Existing Forecasting Techniques and the Grid ................................... 27
Figure 6: How Descriptive Terms (Same, Horizontal, Vertical, & Opposite) Are
Used ................................................................................................... 46
Figure 7: Revised Classification of 8 Consumer Electronic Innovations ............ 55
Figure 8: Classification of Research Models ..................................................... 60
Figure 9: VCR Diffusion with Lilien Adjustment ................................................. 62
Figure 10: Cordless Phone Diffusion ................................................................. 63
Figure 11: Recommended Models by Context .................................................. 88
Figure 12: Comparison of Gentry and Lilien et al. Diffusion Forecasts for VCRs
........................................................................................................... 94
Figure 13: Extended Comparison of Gentry and Lilien et al. Diffusion Forecasts
for VCRs ............................................................................................ 95
Figure 14: Initial Look at Logarithmic Parabola Model ...................................... 98
Figure 15: Initial Look at Modified Exponential Model ....................................... 99
Figure 16: Initial Look at Observation-Based Modified Exponential Model ....... 99
Figure 17: Initial Look at Bass Model .............................................................. 100
Figure 18: Initial Look at Generalized Bass Model .......................................... 100
Figure 19: Initial Look at Simple Logistic Model .............................................. 101
Figure 20: Initial Look at Gompertz Model ....................................................... 101
Figure 21: Initial Look at Extended Logistic Model .......................................... 102
Figure 22: Initial Look at Log-Logistic Model ................................................... 102
Figure 23: Initial Look at the Flexible Logistic Inverse Power Transform Model
......................................................................................................... 102
Figure 24: Initial Look at the Flexible Logistic Box and Cox Model ................. 103
Figure 25: Initial Look at the Flexible Logistic Exponential Model ................... 103

Abbreviations

B
BnC
Bv
G
GB
GBv

SL

Definitions
Forecast

Prediction

Radical Innovation

Really New Innovation

LIST OF ABBREVIATIONS/DEFINITIONS

Bass model — see page 57

Box and Cox model - see page 59

Bass model variant - see page 57

Gompertz model — see page 58

Generalized Bass model (Price) — see page 57
Generalized Bass model (Price) variant - see
page 57

Simple Logistic model — see page 58

"a statement about a condition in the future,
arrived at through a system of reasoning
consciously applied by the forecaster and
exposed to the recipient" (Bright, 1978).

"a statement about the future based on
rationale, if any, that the predictor has not
made known" (Bright, 1978).

Radical innovations cause both macro-
marketing and macro—technological disruptions
(Garcia and Calantone, 2002).

Really new innovations cause either a macro-
marketing or a macro—technological disruption
(Garcia and Calantone, 2002).

xi

Chapter 1

WHAT THIS RESEARCH WILL ACCOMPLISH

The Research Problem
How does one know when or if consumers will accept a technological

innovation before the innovation hits the market? This research will evaluate
techniques for forecasting consumer adoption of really new and radical
technological innovations and develop a methodology for selecting the most
appropriate techniques. The focus is on the consumer adoption of a product or
service itself, not on the success or failure of a particular firm (e.g., will high-
definition televisions be adopted by most consumers, not will Philips capture 20%
of the HDTV market).

Forecasting is used in many contexts including predicting the weather, the
economy, the advancement of technology, the effect of medicine on a patient,
and even changes in fashion. A review and evaluation of the general forecasting
methods is necessary to determine which tools are appropriate for forecasting

the consumer demand for an innovation.

Is Forecasting Part of Marketing?
The core values of marketing state consumer “welfare is the ultimate goal

of all marketing activities” (Achrol and Kotler, 1999). Thus, forecasting would be
part of the marketing process if the ability to forecast consumer adoption of a
technological innovation benefits consumers. Perhaps the most basic consumer
benefits are the economic gains provided by forecasting. Forecasting improves

both effectiveness and efficiency in the production of goods.

Effective production - producing the right things - depends upon
manufacturers knowing what to produce. If firms produce the wrong product (i.e.,
products that fail), resources are wasted and losses are imposed on the firm.
Consumer welfare is reduced when the firm recoups this cost by increasing the
price of successful products. If a forecast dramatically underestimates the
market, manufacturers may decide not to meet this need at all. For example,
Univac pioneered commercial computers, but forecast a limited market potential
for this innovation because they thought computers would only be used for
scientific purposes. Based upon this assumption, Univac's market research
predicted that there would be a total of a thousand computers in use in the year
2000. Initially they were not even concerned when IBM developed a computer
platform designed for business applications (Schnaars, 1989).

Efficient production — producing things right given that the decision to
produce has been made — depends upon manufacturers knowing how much to
produce. If a forecast is too large, firms waste resources by over-investing in the
new offering. Likewise, if the forecast underestimates demand, firms waste
resources by catching up to the demand and consumers pay more for the
product and/or have to do without it for some time.

The more accurate the forecast, the more effectively and efficiently an
innovation may be brought to market. The more effectively and efficiently an
innovation is brought to market, the greater the consumer welfare. The greater
the increase in consumer welfare, the greater the marketing contribution of

forecasting.

Why is This an Important Problem for Academics 8. Managers?
Academics are in the business of creating knowledge. In other words,

researchers exist to reduce uncertainty. Gervvin (1988) listed three types of
uncertainty that he found useful in investigating technology: technical
uncertainty, financial uncertainty, and social uncertainty. Forecasting consumer
adoption of technological innovations - and assigning probabilities to these
estimates - is a necessary part of evaluating the technological, business, and
social implications of innovation.

Managers who can better understand the range of potential futures should
be better prepared for whatever future occurs. As previously discussed,
forecasts enable managers to more effectively and efficiently manufacture the
right products in the right quantities. In theory, firms with managers who better
prepare their firms for these future needs should have a competitive advantage
over firms whose managers did not foresee what might lie ahead. However, this
presumes that the forecasts do not lead the managers astray. According to
Hoagland (2001), false predictions of a Y2K disaster disrupted the supply chain
as firms and individuals stocked up on inventories as insurance for the expected
disruption. Hoagland’s research led him to conclude that the actions taken to
hedge against the predicted Y2K disruption actually caused the recent recession.

Academics and managers clearly need to know how much confidence
they should have in a forecast. It is likely that the need for a higher level of
confidence is related to the height of the barriers of entry and exit of a market.
For example, the barriers of entering the suborbital tourism market are very high

as there are significant technological, regulatory, market, and capital issues to

overcome. Before any reasonable firm would risk the vast amounts of resources

needed to serve this market, they need to be extremely confident that a viable

market truly exists.

The Research Questions

R01.

R02.

R03.

Which forecasting methods should be used for
forecasting consumer adoption of radical
technological innovations?

Which forecasting methods should be used for
forecasting consumer adoption of really new
technological innovations? The answer to this
question may be the same as RQ1, but this research
may show that radical and really new technological
innovations should use different forecasting
techniques.

Does an innovation ’3 price afiect which methods
should be used to forecast consumer adoption of
technology innovations? In other words, does price
affect forecasting accuracy for various methods? If
so, what forecasting methods should be used for low
and high priced innovations?

The Research Context
This study will evaluate the diffusion of the innovations shown in Figure 1.

That is, this research is looking at the diffusion of radical and really new

innovations intended for use in the home. The innovations will be classified as

either high priced or low priced.

Figure 1: Initial Classification of 8 Consumer Electronic Innovations

 

 

 

 

 

Innovations for Consumers
Price Level Radical Innovation Really New Innovation
PCs Camcorders
(1980 - 2000) (1985 — 2000)
High
Satellite Receivers Projection TVs
(1986 - 2000) (1984 - 2000)
VCR Cordless Phones
(1974 - 2000) (1980 -— 2000)
Low
CD Players Telephone Answering Device
(1983 - 2000) - (1982 - 2000)

 

 

 

 

 

To reduce confounds and to simplify the data-collection process, only the
US. market will be considered. Likewise, only consumer electronic innovations

will be studied in this research.

Data Sources
This study used secondary data for the eight data sets shown in Figure 1.

The overwhelming majority of the data was obtained from the Consumer
Electronics Association. The CEA, formerly the Consumer Electronic
Manufacturers Association, includes more than a thousand companies within the
US. consumer technology industry. They are the best possible single source for
industrial level US. sales of consumer electronics.

As shown in Figure 1, the eight data sets were initially selected to include

two samples in each cell of consumer electronic innovations. Only data sets with

a reasonable history were considered. Newer innovations were not feasible as
one would have to wait at least 10 years before comparing the results of the

various forecasts with actual results.

Greater detail about each data set is provided in Chapter 3.

Chapter 2

LITERATURE REVIEW

Forecasting: Techniques and Methods
Bright (1978) defined a forecast as "a statement about a condition in the

future, arrived at through a system of reasoning consciously applied by the
forecaster and exposed to the recipient." Jantsch (1969) first differentiated
between two general approaches to forecasting: exploratory and normative.
Exploratory forecasting utilizes relevant historical records to project parameters
and/or functional capabilities into the future. Normative forecasting starts with
future goals and works backwards to identify what barriers must be overcome in
order to obtain these goals. Armstrong (2001) considered normative forecasting
as synonymous with planning. Lenz (1971) noted that these distinctions are not
absolute. All forecasters bring some normative thinking into their forecasts
simply by what assumptions they make and what factors they select as
important. Conversely, all normative forecasts use exploratory techniques as the
starting points for their assumptions. Nevertheless, the distinction between
exploratory and normative forecasts is a useful one. All of the forecasts in this

study are exploratory forecasts.

Classification Schemes in the Literature
Brucks (1986) stated that a good typology should have three objectives:

1) The typology and coding scheme should be easy to

use and seem logical to people who are using the
coding scheme.

2) The typology should cover as many of the subjects'
statements as possible while remaining relatively
parsimonious.

3) The categories in the typology should be as distinct
from each other as possible.

In other words, a good classification system should be exhaustive,
exclusive, and concise. Exhaustive means that the classification system should
cover every potential option. Exclusive means that anything that belongs into
one category should clearly not belong in another category. These criteria will be
used to evaluate the various classification schemes that researchers have
created to compartmentalize technological forecasting methods.

There are many ways to classify forecasts, all of them at least somewhat
arbitrary. The ones more frequently used in the literature are discussed. The
classification systems are listed in chronological order as this approach allows
the reader to see how subsequent classifications built upon earlier classification

methods.

Cetron and Ralph, 1971 - summary
Cetron and Ralph grouped forecasting techniques into five categories:

intuitive methods, trend extrapolation, trend correlation, analogy, and dynamic
predictive models. This classification system appeared to have been largely

based upon the chapter headings of Lenz’s 1962 landmark work on technological

forecasting, but Cetron and Ralph did place some new methods within some of
the classifications.

Intuitive methods include: individual forecasting, polls, panels, and the
Delphi technique. Cetron and Ralph’s reasoning for grouping these methods
together was that all were based upon opinions. Ideally, these opinions were
well-educated estimates made by experts, but they were all based upon the
intuition of the forecaster.

Trend extrapolation is simply forecasting based upon the continuation of
existing trends. It includes: simple extrapolation, substitution, and modified
curve-fitting. Cetron and Ralph found that the general opinion in 1971 was that
trend extrapolation was widely used due to its ease-of-use rather than due to any
accuracy advantages (echoing an observation made a decade earlier by Lenz in
1962). The two key assumptions of trend extrapolation are:

1) the factors which caused the prior pattern of progress
will continue;

2) the combined effect of these factors will continue the
same pattern of progress.

In a substitution forecast, one measures the rate of substitution, with time,
of a new innovation over an older innovation. While the relative increase in
performance is presumably the reason for the substitution, this performance
increase is reflected in the rate of substitution. The key assumption of
substitution is that the process will continue until the new innovation has

completely replaced the older innovation if at all possible.

Since technological progress typically advances slowly, reaches a critical
mass, accelerates exponentially, and then slows as it reaches limitations, one
can expect a given innovation to fit a type of trend curve. Cetron and Ralph
distinguished between five types of trend curves: linear with flattening,
exponential with no flattening, s-shaped, double exponential, gradual-rapid-
subsequent flattening.

In trend correlation, the forecaster assumes that "one factor is the
primary causal influence in the advancement of the technological parameter of
interest." Trend correlation analysis is optimal for situations where the
development of a certain innovation lags the development of another innovation.

Analogy forecasting simply looks fer another pattern that should be
similar to the pattern to be forecast. These are typically classified as growth or
historical analogies. Forecasters have used growth formulas (e.g., the rate of
cell increase within a rat) and historical patterns (e.g., GE looked at fossil fuel
and hydroelectric power development to successfully forecast nuclear power
development).

Dynamic predictive models are based upon work initially done by
Forrester (1958), the chair of Lenz’s thesis. Lenz built upon Forrester's modeling
structure to simulate the impact of important causal factors. Over time, these
models became more sophisticated. Currently, these types of models are most

frequently referred to as structural models.

10

Cetron and Ralph, 1971 — strengths and weaknesses
Cetron and Ralph’s original contributions are largely in the area of intuitive

methods, in the addition of historical analogies to the analogy classification, and
in incorporating previous research into a formal classification system. Their
taxonomy is concise, but neither exhaustive nor exclusive. It is not exhaustive as
it does not consider techniques such as forecasting by role-playing. It is not
exclusive as their definition of trend correlation specifically incorporates causality.
Thus, one could reasonably say that trend correlation - as defined by Cetron and

Ralph - is a subset of their dynamic predictive model classification.

Martino, 1972 - summary
Martino discussed five types of forecasts: intuitive, consensus, analogy,

trend extrapolation, and structural models.

Intuitive forecasts are obtained by simply asking an expert. Martino
wryly noted that "even though an expert may be wrong, his intuitive forecast may
still be the best forecast available." He then cited Ralph C. Lenz’s quip that
intuitive forecasting’s real problem is it is "impossible to teach, expensive to
learn, and excludes any process of review."

Consensus methods obtain results by asking multiple experts. These
experts typically meet together, but this is not a requirement. The positive
aspects of this method are:

that any fact that is known to one expert becomes available to all;
multiple heads are less likely to overlook something;

chances are that biases will balance out;

opportunities for experts to see how others think and thus revise
estimates with new input.

11

The negative aspects of this method include:

c all the problems associated with group dynamics (the Delphi technique

is a consensus method that tries to eliminate/reduce these problems);

0 any misinformation known to one is known by all.

The forecasting analogy method compares a known event (historical
event, physical/biological process, etc.) with the event to be forecasted. Growth
curves are often used to predict the advance of some technology. The S-curve
has been found in many living species for both individual and population growth
curves. The adoption of many technological innovations follows a similar pattern
- starting slow, followed by a rapid rise, then a leveling off that leads to
obsolescence. "The major strength of this method is that it eliminates much of
the subjectivity of either intuitive or consensus methods of forecasting. Its major
weakness, however, is that the exact extent of the analogy between the model
and the thing to be forecast is often not evident until it is too late to do any good"
(Martino, 1972).

Trend extrapolation avoids the problem of estimating changes in specific
S-curves. Instead of focusing on a single device - or technology - trend
extrapolation considers a series of devices that perform the same function.
Successive devices usually have major differences in performance (on the order

of 100% or more), while improvements to a single device are usually on the order

of a few percent.

12

Structural models create an analytical model of the technology-
generation process. "A characteristic feature of such models is they tend to be
abstractions; certain elements are omitted because they are judged to be
irrelevant, and the resulting simplification in the description of the situation is

intended to be helpful in analyzing it and understanding it" (Martino, 1972).

Martino, 1972 - strengths and weaknesses
Martino’s classification system is concise and easily understood. His

lexicon is a bit confusing, as intuitive forecasts do not consist of all intuitive
forecasts, but merely those that are from the opinion of a single expert. He
reserves the classification consensus methods for the opinions of multiple
experts. As his boundaries are quite clear for all five categories, Martino’s
classifications are exclusive.

One might question the need for dividing subjective techniques into two
categories based upon whether a single or multiple number of experts
contributed toward it. This distinction does not seem useful and Martino is the
only one to have made such a division. Further, the preciseness with which
Martino defined his two expert classifications actually precluded both of these
categories from incorporating non-expert intuitive forecasting methods such as

role-playing. Thus, Martino’s taxonomy is not exhaustive.

13

Bright, 1978 - summary
Bright developed and used eight categories of forecasting: intuitive

forecasting, trend extrapolation, dynamic modeling, morphological analysis,
normative forecasting, monitoring, cross-impact analysis, and scenarios. As one
would expect from their names, Bright's intuitive forecasting, trend
extrapolation, and dynamic modeling categories are virtually identical to their
Cetron and Ralph (1971) counterparts: respectively, intuitive methods, trend
extrapolation, and dynamic predictive models.

Bright's classification of morphological analysis was for techniques that
created a matrix of all theoretically possible combinations of technological
approaches and configurations. He admitted that for morphological analysis to
be considered forecasting, "one must argue that morphological analysis identifies
known technology and predicts future technology by displaying possibilities that
are not yet in use or even explored." Bright stated that in 1942, Zwicky used
morphological analysis of the jet engine to conceptualize the terra-jet, the hydra-
jet, and the ram-jet.

However, granting Bright’s assumption that morphological analysis allows
one to identify future possibilities does not make morphological analysis a
forecasting technique. Since morphological analysis does not mention the timing
of a new innovation, but rather the potential for its existence, it falls short of
Bright's own criteria for a forecast. This is not to say morphological analysis has

no place, but rather, morphological analysis may help the forecaster conceive of

14

some new technology. Then the forecaster can determine the appropriate
method to forecast the adoption of this innovation.

Bright categorizes forecasts that assume new technology will materialize
to meet a specific need as normative forecasting. However, the distinction
between a normative forecast and an exploratory forecast does not change how
forecasts are done. Rather, it changes the rate-of-progress assumptions for the
forecast and normative forecasts should obviously show a faster rate-of-progress
than exploratory forecasts.‘ Thus, while it is important to understand the
distinction between normative and exploratory forecasting, normative forecasting
is a type of forecasting, not a method of forecasting.

Bright stated that monitoring is based upon assessing events in process

and included four activities:

1) Searching the environment for signals that may be the
forerunners of significant technological change;

2) Identifying possible alternative consequences if these signals are
not spurious and if the trends that they suggest continue;

3) Choosing those parameters, policies, events, and decisions that

should be followed in order to verify the true speed and direction
of technology and the effects of employing that technology;

4) Presenting the data from the first three steps in a timely and
appropriate manner for management's use in decisions about the
organization's reaction.

Bright (1978) believed the essence of monitoring is "evaluation and continuous
review." Like his mistake with normative forecasting, Bright is confusing a goal of
the forecast (monitoring) with the forecast itself. Monitoring is simply a way of

using forecasts, but is not a forecast in itself. Indeed, monitoring more accurately

 

1 An exception to this expectation would be in the theoretical case where the demand was to slow
down progress (e.g., Luddites making policy decisions).

15

describes a way in which one may wish to use forecasting techniques to
incorporate data as it becomes available.

Bright stated that cross-impact analysis “attempts to do in fact what is
implied in all forecasting - to provide a prediction of future conditions with
allowance for all the interacting forces that will shape that future." Cross-impact
analysis is a technique for building a matrix from the opinions of experts. It has
some similarities to the Delphi technique and Bright mentioned that cross-impact
analysis could complement the Delphi technique. So, cross-impact analysis
should be more properly considered as a technique within the intuitive
forecasting classification.

Bright (1978) uses the term scenario to describe a detailed description of
a possible future. “In effect, the planner concedes he cannot predict the 'real'
future, so he looks at several possible futures with the idea of being prepared for
any uncertainty (the usual military goal) or of coming up with a plan that best
accommodates the variety of uncertainties ahead (the usual industrial goal).”
This was indeed a new technique that does not readily fall into any of the
previously discussed classifications. One might force it to fit into a loose
definition of an intuitive forecast, but as Bright used them, scenarios were meant
to cover the entire range of foreseeable options with little thought given to which

scenario was most probable.

Bright, 1978 - strengths and weaknesses
Bright was a strong advocate of the use of scenarios in forecasting and

this was one of his main contributions to the field. He also distinguished between

16

forecasts, predictions, and speculations. Bright (1978) defined a forecast as "a
statement about a condition in the future, arrived at through a system of
reasoning consciously applied by the forecaster and exposed to the recipient."
He defined a prediction as "a statement about the future based on rationale, if
any, that the predictor has not made known." And Bright defined speculation as
"a statement about the future in which the predictor admits high uncertainty
and/or admits lack of a highly supportive rationale." By these definitions, one
cannot make an intuitive forecast, but merely an intuitive prediction or
speculation.

With eight classifications, Bright’s taxonomy is hardly concise. However,
three of Bright’s categories - morphological analysis, normative forecasting, and
monitoring are not actually forecasting classifications at all. In addition, the
cross-impact analysis is a subset of his intuitive forecasting classification, so his
classifications are not exclusive. His classification system is one of the more
exhaustive systems and it would not take much redefining to incorporate newer

techniques such as forecasting by role-playing into his scenario classification.

Armstrong, 1985 - summary
Armstrong (1985) said that research for analyzing data has historically

been organized along three continuums: subjective vs. objective, naive vs.
causal, and linear vs. classification methods. He then placed five forecasting
methods within these continuums to develop a methodology tree (Figure 2) that
also provided guidance as to when various methods should be used. The

heavier lines represent the key decisions that need to be made by the forecaster;

17

the decisions in turn will help determine which methods should be used.
Armstrong’s five classifications were: judgmental, bootstrapping, extrapolation,

econometric, and segmentation.

Figure 2: Forecasting Methodology Tree (1985)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Econometric Segmentation
T Linear Classification T
Extrapolation
A Naive Causal
Objective
Judgmental Bootstrapping
I Subjective Objective
Start with feet on ground (Armstrong, 1985)

The subjective methods are those using implicit (i.e., vague) processes for
data analysis. Naive methods only use data on the variable of interest; causal
models use additional variables. Causal models ask "why?” and use these
factors to make forecasts. “Linear” is used by Armstrong as meaning a formula.
Armstrong preferred linear models as they are both simpler and - in his
experience - more accurate than non-linear models. The other side of the linear

continuum is classification (segmentation).

18

Armstrong stated that there are three main decisions to be made when
making a forecast. The primary decision is to select intuitive or objective
methods. If objective methods are chosen, then Armstrong says another choice
must be made between naive and causal approaches. And if a causal approach
is selected, the forecaster must then decide between linear and classification
approaches.

The judgmental classification in Armstrong’s lexicon is synonymous with
his use of the term subjective. In his words, “These methods are also called
implicit, informal, clinical, experienced-based, intuitive methods, guestimates,
WAGs (wild-assed guesses), or gut feelings." This category may be considered
equivalent to Cetron and Ralph’s (1971) intuitive methods. Likewise,
Armstrong’s extrapolation classification is similar to Cetron and Ralph’s use of
trend extrapolation. The only difference of note is that Armstrong included
analogies within his extrapolation category.

Bootstrapping methods are ways of explicitly capturing the subjective
processes used by an intuitive forecaster. Direct bootstrapping involves input
from a forecaster on how an intuitive forecast was made. In many cases, the
predictor is unable to produce an algorithm for producing his forecast. Indirect
bootstrapping is used to reverse engineer the rules the forecaster is intuitively
using, thus making these rules explicit.

All of the previous classifications schemes placed all explicit models into

one category. Armstrong divided his into two categories: econometric and

19

segmentation. The econometric classification is used for linear2 representations
of causal models that summarize existing knowledge within the models
themselves. The segmentation methodology "attempts to find behavioral units
that respond in the same way to the causal variables and to group these units.”
For example, a very basic forecast about the initial acceptance of a new
innovation may use a gender segmentation scheme and assume that five
percent of males and three percent of females will adopt the innovation in the first

yeah

Armstrong, 1985 - strengths and weaknesses
' Armstrong’s Forecasting Methodology Tree provided guidance that better

enabled a forecaster to understand what elements went into determining which
forecasting method(s) to use. Armstrong’s suggestion and use of the
naive/causal continuum was also quite useful and built upon the traditional
subjective/objective distinction. However, his linear/classification distinction
seems questionable. Not only does this distinction include a bias against non-
linear methods, it seems to serve little purpose.

For example, the resulting classifications — econometric and segmentation
- are not exclusive (e.g., econometric models can easily incorporate multiple
segments with their models). One might even say that segmentation is not a
forecasting method per se; rather, segmentation techniques may be used to
complement most forecasting methods. Forecasters may create forecasts from

aggregate data or they may first segment the data, create individual forecasts for

 

2 As discussed earlier, Armstrong saw little point in non-linear econometric models and his
nomenclature reinforced his bias. .

20

its! -.Ialllllilt It

each segment, and then sum these forecasts. Table 1 shows some of the

empirical results from using segmentation.

Table 1: Segmentation’s Effectiveness In Forecasting

 

Source F inding(s)

 

When comparing forecasts of gasoline sales, a regression
2:32;?91 3;: technique had a 58% error rate. By using segmentation, a
’ forecast was created with only a 41% error rate.

 

Dunn, William, Found that additive decomposition forecasts (i.e., summing

 

 

and Spiney, segments) were superior to a top-down approach for
1971 forecasting demand for telephones.

Found that additive decomposition forecasts (i.e., summing
Dangerfield products) were superior to a top-down approach for forecasting
and Morris, demand for a product class (used over 15,000 aggregate
1992 series created by combining individual series from the M-

 

competition database).

 

In addition, the models that result from bootstrapping might be viewed as
econometric and/or segmentation models. Armstrong’s (1985) classification

scheme is concise, but is neither exhaustive nor exclusive.

Armstrong, 2001 — summary
Fortunately for the progress of forecasting, Armstrong did not stop with his

initial Forecasting Methodology Tree. Armstrong’s (2001) Methodology Tree is a
much revised version of his earlier classification scheme. It also provides

guidance to which method(s) should be used in a given situation.

21

 

Figure 3: Armstrong’s Methodology Tree (2001)

   

Knowledge
Source

 
   

judgmental statistical

 

        
  

univariate multivariate

 
    

self others

       

 
  
 

 

 

 

 

 

 

 
   
    

 

 

 

 
    

 

 

 

 
 
  

 

 

 

role no role theory—based data-based
7
Role Intentions Expert Extrapolation Multivariate
Pla in_ Opinions, Models Models
Analogies
Conjoint J udgmental Rule—Based
Analysis Bootstrapping Forecastin
"""""""""""""""""""""""" ‘v
I_ _______________________________ Expert Econometric
Systems Models

 

 

 

n

 

Dashed lines represent possible relationships.
Armstrong (2001) believed there are eleven types of forecasting methods:

role playing, intentions, conjoint analysis, expert opinions, judgmental
bootstrapping, analogies, extrapolation methods, rule-based forecasting, expert
systems, econometric models, and multivariate models. Armstrong placed these
eleven categories into a Methodology Tree (see Figure 3) where the first branch
separates judgmental methods from statistical methods. Judgmental methods
are then subdivided into those that predict one's own behavior (self) and those
where experts predict how others will behave (others). The self methods are
further subdivided into roleplaying (where people are placed in a role and asked
to act accordingly) and intentions (where people predict their own behavior in
various scenarios). Conjoint analysis examines how different scenarios affect

intentions. Along the "others" branch, expert opinions are used to make

22

forecasts. Judgmental bootstrapping uses regression analysis to infer experts'
rules for forecasting based upon the information that the experts use to make
forecasts. Analogies are typically used when few, or no, observations are
available (e.g., the introduction of a completely new innovation like holographic
television).

The statistical side of the methodology tree first splits into univariate and
multivariate branches. The univariate branch is also known as “extrapolation
methods” since it uses values of a series to predict other values. Rule-based
forecasting is a type of expert system that integrates forecasting methodology
with domain knowledge. Expert systems represent rules that the experts use.
The multivariate branch subdivides into theory-based (econometric) and data-

based (multivariate) models.

Armstrong, 2001 - strengths and weaknesses
Armstrong’s scheme is more useful than the older schemes as it provides

guidance as to when to use various techniques. However, it is also a very flawed
classification system. It is neither exhaustive, exclusive, nor concise. It is not
exhaustive because certain classifications are not listed (e.g., where do non-
expert opinions about the behavior of others 90?). It is not exclusive since he
has a classification for extrapolation models, yet all forecasts are extrapolations
in one sense or another and some of his classifications are really subsets of a
more general classification that he also listed. For instance, he stated that

judgmental bootstrapping and rule-based forecasting were expert systems, yet

23

he listed these as unique types along with expert systems. And with eleven non-

exhaustive classifications, his system was hardly concise.

A Forecasting Typology is Proposed
The existing classification schemes have made great contributions to the

development of forecasting, especially technological forecasting. The earlier

typologies (Cetron and Ralph 1971; Martino, 1972) were most useful in

determining what was — and was not - forecasting. The later ideas (Armstrong,

1985, 2001) took a step fonNard by also providing guidance as to when certain

classifications should be used. Unfortunately, these taxonomies were neither

exhaustive, exclusive, nor concise (Table 2).

Table 2: Summary of Forecasting Classification Schemes

 

 

 

 

 

 

Source Classifications Strength(s) Weakness(es)
Cetron and intuitive methods, trend concise neither
Ralph, extrapolation, trend exhaustive nor
1971 correlation, analogy, and exclusive
dynamic predictive
models
Martino, intuitive, consensus, concise and not exhaustive
1972 analogy, trend exclusive
extrapolation, and
structural models
Bright, intuitive forecasting, added concept neither
1978 trend extrapolation, of scenarios, exclusive nor
dynamic modeling, could be concise; also
morphological analysis, considered included some
normative forecasting, exhaustive with categories that
monitoring, cross-impact a liberal were
analysis, and scenarios interpretation inappropriate
Armstrong, judgmental, concise, added neither
1985 bootstrapping, naive/causal exclusive nor
extrapolation, continuum, exhaustive
econometric, and provided
segmentation guidance to

 

 

 

which forecast
should be used

 

 

24

 

 

Source Classifications Strengfi(s) Weakness(es)

 

 

 

 

 

Armstrong, 11 role playing, intentions, provides flawed

2001 conjoint analysis, expert guidance to classification
opinions, judgmental which forecast system (neither
bootstrapping, analogies, should be used exclusive,
extrapolation methods, exhaustive, nor
rule-based forecasting, concise).
expert systems,
econometric models, and
multivariate models

 

 

As per Korchia (1999), "If a typology does not satisfy any of Brucks’ three
criteria (1986), it must be modified and improved." Therefore a simpler
forecasting typology is proposed. As it only has four classifications, it is
unquestionably the most concise scheme yet discussed. Thus it should be
evaluated to see if it is more exhaustive and exclusive than the other
classifications. Figure 4 shows the Forecasting Classification Grid (hereafter,
simply the “‘Grid”). Like all the other classification schemes, it recognizes the
importance of distinguishing between opinion and ideas that can be empirically
evaluated. It also includes Armstrong’s naive/causal distinction. This typology
assumes that these two continuums are independent. Given this assumption,
four exclusive categories logically follow: predictions, scripts, correlations, and

models.

Predictions are defined as explicit forecasts that are based upon opinions
whose assumptions have not been made explicit. Scripts are defined as made
up scenarios in which a potential future is described and causal assumptions are
made. Correlations are defined as forecasts based upon the performance of
another factor without any causal assumptions. Models are defined as any

forecast with explicit causal assumptions that may be mathematically stated.

25

 

Figure 4: Forecasting Classification Grid

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Empirical
Correlations Models
Naive Causal
Predictions Scripts
Opinion

One of the attractions of the Forecasting Classification Grid is its simplicity
relative to the other ways of classifying forecasts. However, even if the grid is
concise, exclusive, and exhaustive, it needs to also fit well with the existing
forecasting techniques. Figure 5 shows how the existing techniques fit within the
proposed classification scheme. The various techniques and their applicability to
forecasting as noted in the literature are discussed using the Grid classifications

(predictions, scripts, correlations, and models).

26

Figure 5: Existing Forecasting Techniques and the Grid

Empirical .
Econometric

Trend Extrapolation segmentation SEM
Neural Networks

 

 

 

 

Correlations Models

 

 

 

 

Combinations
Hybrids

Historical Analogies

Biological Analogies
Bootstrapping
Naive Causal

 

Delphll ROle Playing

 

 

 

 

 

Predictions Scripts

 

 

 

Conjoint Analysis Scenarios
Intent

, , Novels/Short Stories
Expert Opinion (i.e., science fiction)

Opinion

 

Predictions
By definition, predictions are opinion-based speculation with no explicit

causal assumptions. Techniques in this classification include methods such as
intentions, conjoint analysis, and expert opinion practices (e.g., Delphi).
Intentions

Since intentions have been shown to influence behavior (Fishbein and
Ajzen, 1975; Ajzen, 1991), polling purchase intentions of potential consumers is
used by many firms to develop market forecasts. Jamieson and Bass (1989)
found that 70% to 90% of market-research clients use purchase intentions data
on a regular basis. Table 3 summarizes the major empirical finding on using

purchase-intentions data for forecasting.

27

Table 3: Summary of Intentions Findings

 

 

 

 

 

Source F inding(s)
Found that purchase intentions data for durable goods

Juster 1966 underestimates actual purchasing

. Found that purchase intentions data for durable goods
MCNe" 1974 underestimates actual purchasing
Theil and Found that purchase intentions data for durable goods
Kosobud, 1968 underestimates actual purchasing
3:353; Found that purchase intentions data for nondurable goods
1966 g, overestimates actual purchasing

 

Morrison, 1979

Concluded that intentions are imperfect measures of behavior
and that intention-based predictions should be adjusted

 

Morwitz and
Schmittlein,
1992

Found that by segmenting households before creating
intention-based predictions, they were able to reduce
forecasting error by more than 25% compared to comparable
aggregate forecasts. This was only true for segmentation
methods that distinguished between dependent and
independent variables — that is, methods using discriminant
analysis or CART (Classification And Regression Trees).

 

Bemmaor, 1995

Created a model that used intentions to bound forecasts that
was accurate for existing consumer products, but not new
products.

 

Lee, Elango,
and Schnaars,
1997

Found that extrapolation of past sales provided more accurate
forecasts than intention-based forecasts

 

 

 

 

 

323$"; d Found that extrapolation of past sales provided less accurate
K ’ forecasts than intention-based forecasts
umar, 2000

Showed how to use historical intention and behavior data to
adjust for bias in future predictions. Using Theil and

Morwitz, 2001 Kosobod’s (1968) data, her method reduced the absolute
percent error of intention-based predictions from 17.2% to
9.7%.

Conjoint Analysis

In a search of literally hundreds of conjoint analysis articles, only a single

peer-reviewed article could be found where conjoint analysis was used to

forecast the acceptance of a really new innovation. Vavra, Green, and Krieger

(1999) describe how conjoint analysis was used to help determine commuter

demand for the EZPass system throughout the Northeast corridor. Even in this

28

 

instance, similar systems had been available in other states for years. There are
innumerable articles on how conjoint analysis was used to forecast the
acceptance of new products, but the “new” products were invariably incremental
innovations (e.g., faster cars in Steckel, DeSarbo, and Mahajan, 1991). One of
the few times conjoint analysis was used to evaluate a really new innovation
(e.g., on-line shopping in Talaga and Tucci, 2001), the researcher used the
technique to determine what features are important to the consumer after the
consumer has already adopted the innovation.

After discussing the theory and history of conjoint analysis, Wittink and
Trond (2001) concluded that conjoint analysis should not be used for
discontinuous innovations. If a forecaster strongly desired to use conjoint
analysis to make a forecast about "new-to-the-world types of products", Wittink
and Trond recommended first educating respondents about the category. Even
then, they had limited hope for the accuracy of such a forecast. This author’s
own experience with professional market-research firms’ attempts to forecast
consumer demand for radical and really new products in the consumer electronic
and PC industry supports their recommendation and conclusion.
Expert Opinion

Table 4 summarizes some of the empirical findings on how expert

opinions are used in forecasting.

29

Table 4: Summary of Expert Opinion Findings

 

Source

I Finding(s)

 

Use of information

 

Ebbesen and
Konecni, 1975

Experts (judges) did not base their judgments on all the
available relevant information.

 

Gaeth and
Shanteau, 1984

Agricultural experts were influenced by irrelevant factors
when making soil quality'Ludgments.

 

Brockhoff, 1984

Additional information did not increase the accuracy of
experts forecastflg interest rates.

 

Lusk and
Hammond, 1991

 

Additional information did not increase the accuracy of
meteorologists forecastingmicrobursts.

 

Overconfidence Bias

 

Lawrence and
Makridakis, 1989

When forecasters were asked to place 95% confidence
intervals around their forecast ranges, the ranges were
about 10% narrower than they should have been.

 

O’Conner and
Lawrence, 1989

 

When forecasters were asked to set 50% and 75%
confidence intervals around their own forecasts, only 37.3%
and 63.3% of outcomes fell within the respective intervals.

 

Delphi Technique

 

Brockhoff, 1975

Found no significant difference in accuracy between panels
with five, seven, nine, and eleven panelists.

 

Boje and
Murnighan, 1982

Found no significant difference in accuracy between panels
with three, seven, and eleven panelists.

 

Brockhoff, 1975

Accuracy of Delphi results increased for first three rounds
with a loss of accuracy for additional rounds.

 

 

Erffmeyer,
Erffmeyer, and
Lane,1986

 

Accuracy of Delphi results increased for first four rounds
with no benefit for additional rounds.

 

Harvey (2001) recommended that experts use a checklist when making

their forecast in order to minimize the problems with judgments (i.e., experts not

using information that they should use while using information that they should

not). Given the evidence that expert forecasters are overconfident, Harvey found

it reasonable to allow for an overconfidence bias of approximately 10 to 14

percent.

30

 

Scripts

Scripts are opinion-based speculation with detailed causal assumptions

described in writing. Techniques in this classification include role-playing,

scenarios, and the traditional writings of many hard science fiction3 authors and

futurists.

Role Playing

In role playing, subjects are asked to take on roles and act accordingly.

Researchers use their decisions as forecasts.

Table 5: Summary of Role Playing Findings

 

Source

Finding(s)

 

Cyert, March,
and Starbuck,
1961

Subjects made significantly different forecasts depending upon
the role they were given (cost analyst vs. market analyst).

 

 

Statman and . .
Tyebjee, 1985 Repllcated findlngs of Cyert, March, and Starbuck (1961)
Mandel, 1977 Concluded that researchers would obtain Similar results usnng

experts or students as subjects

 

Babcock et al,
1995

Found significantly different outcomes depending upon
instructions given to subjects: “Ask the role players to act as
they themselves would act given the role and the situation, or
ask them to act as they believe the persons they represent
would act."4

 

 

Armstrong,
2001

 

In reviewing the role playing literature, “role playing was
effective in matching results for seven of eight experiments”
and in “five actual situations, role playing was correct for 56 of
143 predictions while unaided expert opinions were correct for
16 percent of 172 predictions.”

 

Armstrong (2001) concluded, “Experts are probably better at identifying

what should happen than what will happen. Role playing should be more

accurate as to what will happen.”

 

3 Hard science fiction is the subset of the genre that limits itself to known facts and possibilities.
‘ There does not yet appear to be any strong evidence to show which question leads to more

accurate results.

31

 

Scenarios

Schnaar (1989) noted that Herman Kahn popularized the scenario

technique in the 1950s when he worked at the Rand Corporation. Bright (1978)

advocated the use of scenarios, but sometimes referred to them as an anti-

forecast. In his thinking, scenarios were important tools for contingency

planning; but the probabilities of each scenario were of little import. Bright’s

focus was on the benefits of planning for all reasonable outcomes.

Table 6: Summary of Scenario Findings

 

 

Source Finding(s)
Found that scenarios only increased expectancies of the
Carroll 1978 described event when the subject did not have a

preconceived preference for an alternative forecast in an
election context.

 

Gregory, Cialdini,
and Carpenter,
1982

Found that scenarios influenced behavior — 47% of
subjects exposed to scenarios about subscribing to cable
TV subscribed shortly thereafter, compared to 20% of the
control group.

 

Schoemaker, 1991

Advocated scenarios for contingency planning (“bounding
the uncertainity”)

 

Goodwin and

Recommend using scenarios for contingency planning.

 

 

 

 

Wt, 1997
In their review of the scenario literature, Gregory and Duran
Gregory and concluded that every use of scenarios “enhance a person’s
Duran, 2001 expectancies of the likelihood of the event depicted in the
imaged scenario."
Correlations

Correlations are defined as forecasts based upon the performance of

another factor without any causal assumptions. Techniques in this classification

include methods such as extrapolation, analogies, and neural networks.

32

 

Extrapolation
In his review of the literature, Armstrong (2001) found that the

appropriateness of the data source used for extrapolation depended upon the

goals of the forecasters (see Table 7).

Table 7: Ranking of Data Sources for Extrapolation by Intended Use (Armstrong, 2001)

 

 

 

 

 

 

 

 

Intent
(1 = most appropriate or most favorable, 4 = least appropriate or least favorable.)
To control To To
for effects To forecast forecast
To reduce of estimate effects of effects of
Data cost of researcher’s current small large
Source forecasts bias status charges charges
Historical 1 1 1 1 4
A.”a"’.g°“s 2 2 2 4 3
srtuatlon
Laboratory 3 4 4 3 2
experiment
Field
experiment 4 3 3 2 1

 

 

 

 

 

Armstrong concluded that there were five conditions that favored the use of

extrapolation.

1) when a large number of forecasts is needed;

2) when the forecaster is ignorant about the situation;

3) when the situation is stable;

4) when other methods would be subject to forecaster bias; and/or

5) as a benchmark in assessing the effects of policy changes.
Table 8 summarizes some of the major empirical findings on using extrapolation
for forecasting. Findings suggest that simpler extrapolation methods are more
accurate than complex extrapolations and that the Box-Jenkins method of

extrapolation - which uses autoregressive integrated moving averages to provide

time-series forecasts — should be avoided, as better methods are available.

33

 

Table 8: Summary of Extrapolation Findings

 

Source I Finding(s)

 

Srm Ie Extrapolation vs. Complex Extrapolations

 

Found that simple extrapolations were more accurate than

 

 

 

Dorn, 1950 complex extrapolations.

Makridakis et al. Found that simple extrapolations were generally as or more
1982 accurate than complex extrapolations.

Makridakis et al. Found that simple extrapolations were generally as or more
1993 accurate than complex extrapolations.

Makridakis and Found that simple extrapolations were generally as or more
Hibon, 2000 accurate than complex extrapolations.

 

Use of Box-Jenkins

 

In reviewing 14 studies, Box-Jenkins was less accurate

Armstrong, 1985 than other extrapolation methods 71% of the time.

 

 

 

 

Makridakis et al. Found that Box-Jenkins was one of the least-accurate
1993 methods.
Analogies

Analogies were originally simply used as patterns for growth models. No
causal reasoning was desired; forecasters simply selected a pattern that they
thought — or hoped — would be appropriate (Cetron and Ralph, 1971; Martino,
1972). Forecasters sometimes used biological analogies for growth models —
Cetron and Ralph even discussed how one firm created forecasts based upon
the growth rate of a rat’s cell. As can be seen in Tables 9 and 10, Lentz (1962)
developed an extensive set of biological analogies to facilitate the use of

biological growth formulas.

 

Table 9: Cellular Analogy (Lenz, 1962)

 

 

 

BIOLOGICAL GROWTH TECHNICAL IMPROVEMENT
Initial Cell Initial Idea or Invention
Cell Division Inventive Process

 

Second Generation
Cell

“New” Idea or Invention

 

Cell Division Period

Time Required for Initial Invention to Initiate “New”
Invenfion

 

 

 

 

Nutrient Media Economic Support for Invention
Cell Lifetime Useful Life of Invention

Cell Death, Normal Obsolescence of Invention

Cell Mass Technical Area or Machine Class

 

Volume Limit of Cell
Mass

Limits of Economic Demand for Invention in Given
Technical Area

 

Size of Cell Mass

Total of Existing, Non-Obsolescent Inventions in
Technical Area

 

 

 

Strength of Cell Mass

Performance Capability

 

Table 10: Bisexual Reproduction Analogy (Lenz, 1962)

 

BIOLOGICAL GROWTH

TECHNICAL IMPROVEMENT

 

Male Parent, or Parent Cell

Existing Invention or Discovery

 

Female Parent

Inventor

 

Opportunifl for Fertilization

Communication of Knowledge

 

 

 

 

 

 

 

 

Conception Origination of Idea

Embryo Evidence of Growth of Idea

Gestation Period Period Required for Invention

Birth Disclosure of Invention

Nutrition Economic Support

Maturation Period Reduction to Practice

Maturity Operational Use of Invention

Lifetime Period from Disclosure to Obsolescence

 

Death, Normal

Obsolescence

 

Total Male Population

Total Inventions Disclosed Minus Obsolete
Invenfions

 

Total Work Force

Total Operational Inventions

 

 

Total Strength of Work
Force

 

Performance Capability

 

 

 

The main problem with forecasting by analogy is that the proper analogy is
usually not known until after the new opportunity unfolds - at which point the

researcher is using hindsight (Martino, 1971). Naive analogies are rarely seen in

35

the current literature. This may be due to the academic bias toward theory-

based solutions.

This is not to say analogies are no longer used. However, researchers
now pick an analogy and use the parameters in explicit growth curve models.
These hybrids are explicit models, not analogies or correlations, and give the
appearance of being more scientific. However, the historical problems related to
analogies still apply to these models. For example, the author of the most widely
used forecasting model, the Bass Model, still struggles with the same problems
the perplexed users of analogies: "Choosing the appropriate analogy of
previously introduced new products is important for the Bass model. However,
little is known about the best way to guess by analogy other to say that it
depends on judgment” (Bass et al, 2001). Armstrong (2001) also found it
“surprising that little research has been done on such topics as how to select
analogies...and how much gain one might achieve by pooling data from
analogies.”

Neural networks

Forecasts produced by neural networks are commonly perceived as a
“black box” production - examining the model parameters does not indicate why
the model makes good predictions (Remus and O’Conner, 2001). Given this lack
of explicit causal assumption, neural network forecasting is classified as a
correlation method. However, any neural network forecasts that explicitly
documents its causal assumption should be considered a model, not a

correlation. If causal assumptions are someday routinely included in neural

36

network forecasts, then the method should be reclassified as a model at that

time.

Remus and O’Conner (2001) recommended using traditional models if the

data fit the assumptions for those models. In theory, the neural network forecast

should be as accurate as the traditional models. In practice, Remus and

O’Conner concluded that the traditional model was much easier to develop and

use in these circumstances. Table 11 summarizes some of the major empirical

findings on forecasting with neural networks.

Table 11: Summary of Neural Network Findings

 

 

 

 

 

 

Source F inding(s)
Sharda and .
Patil, 1990 Found neural networks were as accurate as Box-Jenkins.
223:; and Found neural networks comparable to traditional methods on
U 39 a r, 1992 quarterly data, less accurate on annual data.
Found neural networks to be superior to Box-Jenkins (Autobox)
Kan 1991 when data included trend and seasonal patterns. Othenrvise,
9’ Kang found Box-Jenkins to be same or better than neural
networks.
In their comprehensive evaluation study, they found that neural
Hill, networks were more accurate than any other tested method
O’Connor, when using quarterly and monthly data. Other methods were
and Remus, more accurate when using annual data; however, neural
1996 networks were more accurate than Box-Jenkins even with

 

annual data.

 

37

 

Models
Models are defined as forecasts with explicit causal assumptions that may

be mathematically stated. These models could also be known as rule-based
forecasting, but at least one forecasting expert (Armstrong, 2001) reserved this
term for forecasts of time series data. Techniques in the “model” classification
include expert systems, econometric models, and structural models (e.g., the
Bass 1969 model).
Expert Systems

Armstrong (2001) sometimes distinguished between judgmental
bootstrapping and expert systems, but was inconsistent in his descriptions (e.g.,
on page 188 he stated bootstrapping is a “type of expert system,” but on page
283 he introduced an article on expert systems by contrasting bootstrapping
methods with expert systems). In this document, expert systems are systems
that use a model of how an expert would act in making a forecast. Judgmental
bootstrapping is a subset of expert systems that infers the rules an expert uses
by reverse engineering these rules from the results. Forecasters who desire to
create expert systems that directly ask experts how they make their forecasts
should ensure the availability of experts with a lot of time (Collopy, Adya, and
Armstrong, 2001).

In theory, expert systems should be most useful when experts are making
repetitive forecasts (e.g., analyzing traffic patterns to determine where to put a

fast-food restaurant) and when problems are semi-structured.5 After reviewing

 

5 Use econometric techniques for very structured problems and judgmental techniques for
unstructured problems.

38

the expert system literature between 1977 and 1993, Wong and Monaco (1995)
found that prediction was only the fifth most common use of expert systems
(behind planning, monitoring, design, and implementation) and that there were
not many research articles about the accuracy of expert systems in a forecasting
context. When using expert systems as a replacement for judgmental forecasts,
Collopy, Adya, and Armstrong (2001) recommended using a Turing test to check
face validity. The following tables summarize some of the empirical findings on

how expert systems compare to other forecasting methods.

39

Table 12: Summary of Expert Systems vs. Judgmental Forecasts

 

Source

Finding(s)

 

Yntema and
Torgerson, 1961

Found that bootstrapping resulted in an accuracy of .89 while
the accuracy of judges was .84 in a simple evaluation of
ggmetric shapes (180 juggments by 6 judges).

 

Kleinmuntz, 1967

Found expert systems to be more accurate than expert
judgments in a counseling setting (the expert system was
wrong 28.8% of the time vs. the judgmental error rate of
34.4%).

 

Goldberg, 1970

Developed bootstrapping models more accurate than 79
percent of the clinicians in a mental health context (123
casesL

 

Found that bootstrapping predictions for the performance of

 

 

 

Dawes, 1971 incoming doctoral students was more accurate than the
admission’s committee predictions (19 students).
Found that 100% of the derived bootstrapping models were
Wiggins and more accurate than the judgments of 98 experts in
Kohen, 1971 forecasting the GPA of incoming graduate students (110
judgments).
Developed an expert System that was better than the expert
Michael, 1971 in forecasting catalog sales in terms of both unit sales and
dollar sales.
Concluded that experts were more accurate than
Libby, 1976 bootstrapping in predicting whether or not a large corporation

would declare bankruptcy (60 companies).

 

Goldberg, 1976

Used Libby’s (1976) data to show that Libby’s results were
due to severe skewness in data. By correcting for this
skewness, the revised bootstrapping model was more
accurate than the experts 72% of the time (vs. the previous
23%).

 

Roose and
Doherty, 1976

Despite some questionable methodology that violated
accepted bootstrapping principles (i.e., they used stepwise
regression), they found that bootstrapping was slightly more
accurate in forecasting the success of life insurance agents
than forecasts made by managers (200 juggments).

 

Ebert and Kruse,
1978

In forecasting future returns of securities, bootstrapping
models were more accurate than financial analysts for 72% of
the comparisons (15 new securities were evaluated by 5
analysts).

Note: they also used stepwise rgLression.

 

 

Abdel-Khalik,
Rashad and El-
Sheshai, 1980

 

Bootstrapping models and lending officers were equally
accurate in prediction loan defaults (28 loan officers).

 

40

 

 

Source

Finding(s)

 

Camerer, 1981

After reviewing the bootstrapping literature, Camereer
concluded that that the empirical evidence clearly showed
that bootstrapping should improve expert judgments.

 

Dougherty,
Ebert, and
Callender, 1986

Developed bootstrapping models for three expert interviewers
and predicted the future job performance of applicants. The
bootstrapping models were much better than two of the
experts and tied the third (120 taped interviews).

 

Stewart et al,
1 989

Found mixed results in comparing an expert system with
seven meteorologists. The human judgments were slightly
better at forecasting hail and the expert system was slightly
better at forecasting severe hail.6

 

Silverrnan, 1992

Developed an expert system that helped military planners
spot biases in their own forecasts. When using expert
system, new forecasts did not contain these biases (and will
presumably be found to be more accurate).

 

Ashton, Ashton,
and Davis, 1994

In an artificial advertising context, experts were required to
forecast annual sales. Use of a bootstrapping model resulted
in 6.4% less errors than the expert judgments (13 judges).

 

Reagan-
Cirincione, 1994

Found expert systems to be much more accurate than
judgments in two experiments (forecasting teachers’ salaries
and baseball team records).

 

Leonard, 1995

Developed an expert system for detecting bank fraud. The
judges were better than this expert system (80% detection of
actual frauds vs. 71 %).

 

Smith et al, 1996

Found that an expert system used by British Gas was more
accurate than human experts at forecasting short-term gas
demand.

 

 

Ganzach,
Kluger, and
Klayman, 2000

 

Global judgments of military conscripts” probability of success
were made by experts and bootstrapping. Experts were
slightly more accurate than bootstrapping (116 interviews).
Note: success was judged by absence of failure.

 

 

6 In reviewing the literature on expert systems, there seems to be a tendency for expert systems
to improve their accuracy on the more extreme forecasts (e.g., severe hail vs. hall).

41

 

Table 13: Summary of Expert Systems vs. Econometric Forecasts

 

 

 

 

 

 

 

Source Finding(s)

Stewart et Found mixed results in comparing an expert system with

al, 1989 econometric methods for forecasting hall. The econometric
forecasts were slightly better at forecasting hall and the expert
system was better at forecasting severe hail.

Moninger et Found mixed results in comparing several expert systems with

al, 1991 several econometric models in a meteorological context.

Leonard Found that an expert system for detecting fraud was more

1995 ’ accurate than an econometric model (71 % of actual frauds
detected vs. 66%).

Econometric Forecasts

The distinction between econometric models and structural models is

vague. Technically, it is difficult to create a definition that would differentiate the

two techniques — which is one of the reasons against using the term

econometrics as one of the four proposed forecasting classifications. In practice,

econometrics usually refers to the use of regression analysis. As such,

econometrics is a forecasting technique within the proposed model classification.

Table 14: Summary of Econometric Findings

 

 

 

 

 

 

Source Finding(s)
Lutkepohl, Said the maximum number of variables should not be greater than
1991 the cube root of total observations.
Neter et al, “A general rule of thumb states that there should be at least 6 to
1996 10 cases for every variable in the pool.”
Grove and Given a good measure of success and ample historical data,
M e ehl 1996 econometric approaches are Vlrtually always more accurate than
’ judgmental forecasts.
After reviewing the literature - over 30 comparisons of judgmental
Allen and and econometric forecasts — Allen and Fildes concluded that
Fild es, 2001 econometric models “appear to be galnlng over extrapolatlve or

 

judgmental methods, even for short-term forecast, though much
more slowly than their proponents had hoped.”

 

42

 

 

Structural Models

Researchers have concluded that little empirical research has been done

to investigate the comparative forecasting performance of demand forecasting in

various settings (Armstrong, Brodie, and McIntyre, 1987; Meade and Islam,

2001). The following table lists various models that have been used to predict

the adoption of an innovation.

Table 15: List of Growth Curve Models7

 

 

 

 

 

 

 

 

 

Source Model

Gregg, Hassel, and Richards, 1964 Modified Exponential
Gregg, Hassel, and Richards, 1964 Logarithmic Parabola
Gregg, Hassel, and Richards, 1964 Simple Logistic
Gregg, Hassel, and Richards, 1964 Gompertz

Rogers, 1962 Cumulative Normal
Bain, 1963 Cumulative ngnormal
Bass, 1969 Bass Model

Bass, 1969 Extended Logistic

 

Bass, Krishnan, and Jain, 1994

Generalized Bass Model

 

Tanner, 1978

Logiogistic

 

Easingwood, Mahajan, and Muller,
1981

Nonsymmetric Responding Model

 

Bewly and Fiebig, 1988

The F lexible-Logistic (FLOG) Model:
Inverse Power Transfer (IPT)

 

Bewly and Fiebig, 1988

The flexible-logistic (F LOG) Model:
Exponential (ELOG)

 

Bewly and Fiebig, 1988

The Flexible-Logistic (F LOG) Model: Box
and Cox

 

Meade, 1985

Observation-Based Modified Exponential
(Local Logistic)

 

 

Mar-Molinro, 1980

 

Auto-Regressive Error Term

 

 

7 Many of growth models in this list were first tabulated by Meade and Islam (2001).

43

 

Summary of Literature Review

The review of the literature led to three main points of interest to this
research. First, the consensus of forecasting experts was that no single
forecasting method can obtain both accurate and valid forecasts over various
conditions. In other words, various forecasting methods have unique strengths

and weaknesses in the context of different conditions.

Second, an enduring research question has been asked for decades:
How can we demonstrate (empirically) some guidelines for the selection of
forecasting approaches under different environmental conditions? This research
addresses this question for pre-launch forecasts (i.e., forecasts made without the
benefit of market data obtained from actually seeing the innovation in the market)

for various innovation and price level contexts as described in Chapter 3.

Third, a systematic way to organize the literature is proposed. The
forecasting classification grid is based upon the work of earlier forecasters
(largely Armstrong, 1985). The difference in approach may be due to the

differing purpose of this research from that of earlier classification proposals.

44

Chapter 3
METHOD

This research determined which forecasting methods are most appropriate
for forecasting consumer adoption of radical and really new technological
innovations. This research also investigated the impact of pricing on these
determinations. While the questions are general, this research focused on
consumer electronic innovations and evaluated five well-established models of
innovation diffusion. Two model variants were also evaluated.

In this research, it was useful to visualize a quadrant consisting of two
continuums — the level of innovation (radical vs. really new) and the price
level.(high vs. low). The terms same, horizontal, vertical, and opposite were
used to describe how similar or different one innovation was from another. If an
innovation was from the same quadrant, this meant that the innovations shared
both the same level of innovation and the same price level. If an innovation was
said to be from a horizontal quadrant, then it belonged to a different innovation
classification, but stayed within the same price level. Likewise, if an innovation
was said to belong to a vertical quadrant, it had the same innovation
classification, but had a different price level. Finally, if an innovation was in an
opposite quadrant, then both the innovation and price levels were different.
Figure 6 shows how these terms are used in reference to the Personal Computer

(radical, high-price) innovation.

45

Figure 6: How Descriptive Terms (Same, Horizontal, Vertical, 8: Opposite) Are Used

 

 

Example: Forecasting PCs

 

Price Level

Radical Innovation

Really New Innovation

 

 

 

 

 

PCs
. Camcorders,
ngh Projection TVs
Satellite Receivers (horizontal quadrant)
(same quadrant)
VCR,
LOW Cordless Phones,
CD Players Telephone Answering Devices
(vertical quad rant) (opposite quadrant)

 

These descriptive terms are used to separate innovations into four

analogous groups. An analogous group is a collection of innovations that share

both the same price level and innovation level. For example, VCRs, Cordless

Phones, and Telephone Answering Devices belong to the same analogous

group.

Hypotheses

While this research was largely exploratory research aimed at providing

guidance for the three general research questions discussed in Chapter 1, some

specific hypotheses were developed. These hypotheses were created to either

provide confirmatory support or falsify assumptions behind the research

questions.

46

 

Hypothesis 1.

Hypothesis 2.

Hypothesis 3.

Forecasts using parameters from the same quadrant
for a dataset will be more accurate than forecasts
using parameters from other quadrants.

a. Forecasts using parameters from the same
quadrant will be significantly more accurate (have
less error) than forecasts using parameters from
the opposite quadrant.

b. Forecasts using parameters from the same
quadrant will be significantly more accurate than
forecasts using parameters from horizontal
quadrants.

c. Forecasts using parameters from the same
quadrant will be significantly more accurate than
forecasts using parameters from vertical
quadrants.

d. This will be most apparent in comparison to
forecasts using parameters from opposite
quadrants.

l- ZHIa > zHIb
ii. ZH1a > zH1c

Forecasts using parameters from adjacent (horizontal
and vertical) quadrants for a dataset will be more
accurate than forecasts using parameters from
opposite quadrants.

a. Forecasts using parameters from a vertical
quadrant will be significantly more accurate than
forecasts using parameters from the opposite
quadrant.

b. Forecasts using parameters from a horizontal
quadrant will be significantly more accurate than
forecasts using parameters from the opposite
quadrant.

The level of innovation will have a greater impact on
the accuracy of a forecast than the price level. (i.e.,
forecasts using parameters from a vertical quadrant
will be significantly more accurate than forecasts
using parameters from horizontal quadrants.)

47

Data Sources
In many cases, when an innovation was first made available is largely a

matter of interpretation. For the purposes of this diffusion research, an
innovation was considered to be first available when it met the following
conditions.

1) The innovation had to be available to consumers nationwide.

2) The innovation should be available as a complete product — not merely
plans or parts to be assembled by a skilled hobbyist.

3) The innovation had to free of burdensome regulations that would inhibit
adoption of the innovation.

With the exception of the CD Player dataset, the CEA data started several
years after the introduction of the product- Other sources were obtained to fill in
the missing data wherever possible. In some cases, the missing data had to be

partially extrapolated. These extrapolations are described for each innovation.

Personal Computers (PCs)
One could argue that the 1949 Simon was the first personal computer,

although it was never sold as a product and thus fails to meet the criteria used in
this research. Rather the plans to the Simon were sold to hobbyists who built
their own computer. The 1955 GENIAC was the first pre-assembled computer
sold to consumers. It was followed by the Heathkit EC-1 (1959), the Honeywell
Kitchen Computer8 (1966), the DEC PDP-8 desktop model (1968), the Arkay CT-

650 (1969), the Imlac PDS-‘l (1970), the Kenbak-1 (1972), the HP 9830 (1972),

 

8 The Honeywell Kitchen Computer even included a cutting board.

48

the French Micral (1973)9, the Scelbi-8H (1973), the Mark-8 (1974), the Altair
(1975), the IBM 5100 (1975), the Pro Tech SOL Computer (1977), the
Commodore PET (1977), the Apple ll1°(1977), the Radio Shack TRS—80 (1977)
and the 1981 introduction of the IBM PC. Several sources were used to compile
this list, but the Blinkenlights (2002) timeline was especially useful.

In 1977 several new computers were made available to the public. Not
only did these computers meet the innovation criteria used in this research, but
all of them included a keyboard and output to a video display (e.g., a monitor or
television). Thus 1977 was selected as the starting point for the diffusion of the
personal computer. Personal computers being defined as programmable
devices complete with a keyboard for input and a video port for output.

The CEA dataset started in 1980, the data from 1977-1979 were created
by a combination of extrapolation, various references, and judgment.
Specifically, an average price of $1,000 was used for these three years based
upon known prices for personal computers in 1977 and the CEA average price of
$1,000 for 1980. While the CEA’s data started in 1980, it did not show a
penetration of 1% until 1981. Since the data was rounded, a zero % penetration
rate in 1980 meant that the consumer penetration was actually between 0% and
.49%. Given that 500,000 units were sold in 1980 to businesses and

households, a consumer household penetration rate of .4% was estimated for

 

9 The Xerox Alto was also created in 1973, yet it cannot be considered as a personal computer
for this research since Xerox made their infamous decision not to market it.

1° The Apple I (1976) was sold as a motherboard only and may be considered a prototype since
only about 200 were made.

49

1980. This number was repeatedly halved for 1979 (.2%), 1978 (.1%), and for
1 977 (05%).
DBS Satellite Receivers

According to the Satellite Broadcasting & Communications Association
(SBCA), the first Direct Broadcast Satellite receiver was built by Taylor Howard in
1976 after the FCC declared smaller, personal satellite receivers would be
allowed. In 1978, Howard published a manual to enable hobbyists to build their
own systems. In 1979, manufacturers first sold complete systems to consumers,
5,000 units were shipped including a $36,000 version by Scientific Atlanta that
made the cover of the Nieman Marcus catalog.

The CEA dataset started in 1986. The SBCA was able to provide
information from 1979-1986, so there was perfect overlap between the two
datasets. Both datasets included quantities for 1986 and the data matched
perfectly. While the price points and unit penetration were available from SBCA,
the consumer home penetration had to be derived from SBCA data. This was
done by dividing unit sales by the number of households for all years except
1984 and 1985. Since the CEA consumer penetration started in 1986 at 1%, the
penetration for earlier years were capped below 1%. .8% was used for 1984 and

.9% was used for 1985.

50

CD Players
Philips invented the Compact Disc and teamed with Sony to bring it to

market. Since both firms are important members of the Consumer Electronic
Association, the CEA dataset tracked the diffusion of CD players since its US
introduction in 1983. During the first year of US sales, 30,000 CD players were

sold along with 800,000 005 — almost 27 CDs sold for every player.

Camcorders
A camcorder is defined as an integrated camera that records video into a

video cassette. According to the CEA, the first camcorder hit stores in May,
1983. Interestingly enough, it was a Beta camcorder.

The CEA dataset starts with 1985. The data for years 1983-84 were
created by a combination of extrapolation, various references, and judgment.
Specifically, the average prices of $2,950 (1983) and $2,000 (1984) were chosen
by looking at press releases, consumer reviews, and advertisements from 1983
and 1984. The consumer penetration data was derived by repeatedly halving the
CEA consumer penetration data. Since the CEA showed that 1% of consumer
households owned a camcorder in 1985, 0.5% household penetration was used

for 1984 and 0.25% household penetration was used for 1983.

51

Projection Televisions (PTVs)
According to the CEA, the first rear projection television (PTV) was sold in

1982 and this date is used for the diffusion study.11 The CEA dataset starts with
1984. The data for years 1982-83 were created by a combination of
extrapolation, various references, and judgment. Specifically, the average prices
of $2,177 (1982) and $2,073 (1983) were obtained using the consumer electronic
industry rule of thumb of assuming an annual 5% price reduction and working
backwards from the CEA average price of $1,974 in 198412. The consumer
penetration data was derived by repeatedly halving the CEA consumer
penetration data. Since the CEA showed that 1% of consumer households
owned a projection television in 1984, 0.5% household penetration was used for

1983 and 0.25% household penetration was used for 1982.

VCRs
The first video cassette recorder for the home market was the 1972 AVCO

Cartrivision System.13 To reinforce the cliche that those who forget history are
doomed to repeat it, their business model was later reinvented by DIVX. Two
types of cassettes were available. Black ones for recording — that could be
reused — and red ones that could be rented. The red cassettes could only be
viewed once and could only be rewound by a special machine owned by the

company that offered rentals. By the time the Betamax product was released in

 

‘1 In point of fact, the first rear projection set was introduced by RCA in 1947 - the 648PTK.
However, it suffered from a dim image and was a market failure. Rear projection televisions were
not available for another 35 years.

12 The average PTV price was derived by multiplying the following year's price by 1.05. So the
actual decrease was .0476, not .05.

52

1975, AVCO was no longer manufacturing units. The first stand-alone VHS VCR
in the US was available in 1977.

The CEA dataset starts in 1974. The data for years 1972-73 were created
by a combination of extrapolation, various references, and judgment.
Specifically, the average prices of $1,600 (1972) and $1,000 (1973) were chosen
by looking at press releases, consumer reviews, and advertisements from 1972
and 1973. Zero percent consumer penetration was assumed for 1972-1973 as

the CEA data showed zero percent consumer penetration from 1974-1978.

Cordless Phones and Telephone Answering Device (TADs)
In 1976, the Federal Courts agreed with the FCC and permanently halted

the practice of requiring consumers to inSert special “safety” devices between
telephones (and telephone devices such as answering machines and modems)
and the phone lines so long as these devices met FCC regulations. This
decision put a stop to burdensome regulations that were dissuading consumers
from connecting telephony innovations to their lines. While both cordless phones
and telephone answering devices (T ADs) predate 1976, their home penetration
was insignificant (less than .5% of households). Thus, for the purposes of this
research, 1976 was selected as the start of the diffusion process for these

innovafions.

 

‘3 The Sony U-matic (1970) was actually the first VCR and was initially intended for the home
market. However, its costs were too great so Sony decided to market it to corporations instead.

53

The CEA datasets start with 1980 for cordless phones and 1982 for the
TADs. The information from 1976 until the CEA data started was created by a
combination of extrapolation, various references, and judgment. Specifically, the
average prices of were obtained using the same methods employed to
extrapolate the missing PTV prices. The consumer penetration data was derived
by repeatedly halving the CEA consumer penetration data which measured
consumer household penetration of cordless phones at 0% in 1980“ and

consumer household penetration of TADs at 1% in 1982.

Revised Classification of Innovations
While reading sources to aid in the extrapolation of the two years of data

for the VCR case not included in the CEA dataset, the author discovered a
consumer electronic innovation that is no longer in use. Video Tape Recorders
(VT Rs) were available to consumers in the sixties and some were specifically
aimed at home consumers. The existence of these products falsified the
assumption that the VCR was the first innovation that consumers could purchase
to record television shows. Thus, VCRs were a really new innovation, not a

radical innovation.

 

1‘ Similar to the extrapolation used for the PC data, a household penetration of 0.4% was used for
1980.

54

Figure 7: Revised Classification of 8 Consumer Electronic Innovations

 

 

Innovations for Consumers

 

Price Level

Radical Innovation

Really New Innovation

 

 

 

 

(1983 - 2000)

 

PCs Camcorders
(1977 — 2000) (1983 - 2000)
High
Satellite Receivers Projection TVs
(1979 — 2000) (1982 - 2000)
VCR
(1972 - 2000)
L CD Players Cordless Phones
CW

(1976 — 2000)

Telephone Answering Device
(1976 — 2000)

 

Figure 7 shows the revised classification of the innovations in this

research. The reclassification of the VCR provided a third innovation for low-

priced, really new innovations. However, this resulted in only one low-priced,

radical innovation being used in this research.

Models

Many diffusion models have been used in various contexts. Throughout

the forecasting literature, one common refrain was repeatedly stressed — no

single forecasting method was appropriate for every situation (Cetron and Ralph,

1971; Armstrong, 2001). While there were many well-known models from which

to choose, the following seemed most represented in the literature (Table 16).

55

 

Table 16: Diffusion Models Initially Considered

Logarithmic Parabola (Gregg, Hossel, & Richardson, 1964)
Modified Exponential (Gregg, Hossel, & Richardson, 1964)
Observation-Based Modified Exponential (Meade, 1985)
Bass model (Bass, 1969)

Generalized Bass model (Bass, Krishnan, and Jain, 1994)
Simple Logistic (Gregg, Hossel, & Richardson, 1964)
Gompertz (Gregg, Hossel, & Richardson, 1964)

Extended Logistic (Bass, 1969)

Log-logistic (Tanner, 1978)

Flexible Logistic (FLOG) — Inverse Power Transform (Bewley & Fiebig,
1988)

FLOG — Box & Cox (Bewley & Fiebig, 1988)

FLOG — Exponential (Bewley & Fiebig, 1988)

From these models, it was desired to select a manageable number of
diffusion models for the purposes of this research. Meade and Islam (2001)
strongly recommended that, “A reasonable initial set of models should include
the [simple] logistic, Gompertz, and Bass models.” Given the interest in price,
the Generalized Bass model (price only) was appropriate. Some exploratory
research was done with all of the models and the F LOG Box & Cox seemed
more robust within the consumer electronic context than the other models
(APPENDIX A).

In the process of setting up all the models, the author became intrigued by
Bass assumption that m should remain constant. In the market of interest, the
number of US households is continually expanding. Therefore two variant
models, a Bass variant and a Generalized Bass (Price) variant, were also

developed.

56

Table 17: Diffusion Models used In Research

Bass model (B)

Generalized Bass model - Price (GB)

Bass model variant (Bv)

Generalized Bass model (Price) variant (GBv)
Simple Logistic model (SL)

Gompertz model (G)

F LOG — Box & Cox model (BnC)

While supported by the literature and some exploratory research, the
decision of which models to select for the research was based upon the author's
judgment. As a check on this selection, two forecasting experts were

consulted.” After review, both experts concurred with the decision.

Bass Model (B) .
The Bass 1969 model has been stated in many forms. This research used the

Lilien, Rangaswamy, and Van Den Bulte’s (2000) transfiguration of Bass

X(r-l)
m

 

x(r) = [ p + q( )][m — X (r _ 1)] as it is common in the literature and since Lilien

et al. also provided a large list of Bass parameters.

Bass Model Variants
The Generalized Bass model (Bass, Krishnan, and Jain, 1994) was

developed to consider the impact of price and advertising in forecasts. Since the
datasets provided by the CEA were industry data, information on average pricing
was available, but individual firms did not share their related advertising

expenditures. Thus a Price-only variant of the Generalized Bass model was

 

‘5 Professors Roger Calantone and Jon Bohlmann.

57

 

 

used. This equation x(r)=[p+q(X('_l))][m—X(r—l)ll + B( ”cliff-0)] is a
m r-I

subset of the complete Generalized Bass model (GB).

Both the Bass model and the Generalized Bass model constrain m to be
constant. However, it is common for the actual m to change over the period to
be forecast. Therefore a changing m variant was created by the author for both

the Bass model and Generalized (Price) Bass model. The equation for the Bass

X(r - I)
m(t)

 

model variant (Bv) used is x(r) = [ p + q( )][m(t) — X (r - 1)] and the equation

for the Generalized Bass (Price) model variant (GBv) is

 

 

x(r) =[p+q(Xng'(t’)'))][m(r)—X(r-011 + B( PK'I),;((1:()'"))].

The author investigated changing m variants for the other models, but
given how the other three models were structured, allowing m to change with I
had zero impact on the results.
Simple Logistic (SL) & Gompertz (G)

The Simple Logistic and Gompertz models (Gregg, Hossel & Richardson,
1964) are some of the earliest and simplest diffusion models. Meade & Islam’s
(2001) transfigurations were used. The equation for the Simple Logistic is

__ m
1 + c exp(—bt)

 

X (r) and the equation for the Gompertz is

X (r) = m exp(—c (exp(—bt))) .

58

Flexible logistic (FLOG) - Box and Cox (BnC)
Bewley and Fiebig (1988) developed several flexible logistic models that

used the base equation Xi = m . Multiple variants use different

I + c exp— (B(t))

 

(1+r)"—1

formulas for B(t). The Box and Cox model uses B(r) = (b ).

The Box and Cox model has a tendency for one of its variables (c) to tend
to infinity in some cases. Since using such extreme values would cause the
parameters to give poor results for other cases, a cap of 100,000 was placed on
the 0 variable in this research. This value allowed the BnC model to be viable

with all the datasets.

Selected Models and Proposed Forecasting Classification Grid
Using the proposed classification grid, all seven forecasting methods are

models (Figure 8). Most of the models barely meet the minimum definition of a
model, but all of these forecasting methods explicitly express their causal
assumptions mathematically. Since the Bass Models also provide a deeper
theoretical reasoning as to why they work, these models are farther to the right

on the Naive/Causal continuum.

59

Figure 8: Classification of Research Models

Empirical

 

Models

 

Simple Logistic,

Gompertz, &
.Box & Cox eBass Models

Models

 

 

Naive Causal

 

Opinion

Verification of Models
Once the Lilien, Rangaswamy, and Van Den Bulte’s (2000) Bass model

was working, an attempt was made to verify it by comparing it to Meade and
Islam’s (2001) transfigured Bass formula: x(.) = pm + (qp)X(r _ I) -%[X(r _ l)2 ]. The
results did not match. A third Bass model was created, based upon the original
article (Bass, 1969) with the equation x(.) = pm + (q — pm, - r) ——%[X(, - 02]. The

results from this model perfectly matched that of the Lilien et al. transfiguration,
validating both models and served as an indication that there was a problem with

the Meade and Islam variant that turned out to be a typographical mistake.16

 

‘6 There should be a minus sign between the q and p in the Islam and Meade paper.

60

 

Since the Bass model was going to serve as the benchmark for the other
models, additional testing was done to ensure the Bass models were working as
expected. The innovations listed by Lilien et al. (2000) overlapped with four of
the datasets being used in this study. All data sets used penetration data for
tracking diffusion. By reducing the CEA datasets to the same periods covered by
the Lilien et al. datasets, it was possible to compare the Bass parameters listed
by Lilien et al. to those obtained by this research. As shown in Table 18, the

parameters obtained by this method differed from those described by Lilien et all.

Table 18: Minding p's and q's

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Lilien et al. (2000) Gentry (2003)
Product Years p g m p q m
Camcorders 1986-96 0.044 0.304 30.5 0.022 0.035 100
CD Player 1986-96 0.055 0.378 29.6 0.034 0.246 100
Cordless TeleLhone 1984-96 0.004 0.338 67.6 0.034 0.136 100
VCR 1981-94 0.025 0.603 76.3 0.029 0.299 100

 

 

 

 

 

It would be understandable for some of the parameters to differ since the
data came from different sources. However it seemed unlikely that all four
datasets would significantly differ. After analyzing the Bass model itself, the
conundrum was resolved. Changing the size of m within the Bass formula, when
using discrete time notation, does not directly affect the percentage of those who
adopt so long as m remains constant as specified. It plays a significant role
when one is interested in the amount of units to be purchased, but has no impact
on the percentage of adopters. If one multiplies the percentage of adopters
obtained by the Lilien et al. parameters by the m given by Lilien et al, the results

approached those obtained by the Gentry parameters in two of the four cases.

61

 

Table 19: Camcorder Diffusion with Lilien Adjustment

 

 

 

 

 

 

 

 

 

 

 

 

Year Actual Lilien et aI Gentry Lilien Adjusted
1986 2% 4% 2% 1%
1987 4% 10% 4% 3%
1988 5% 17% 7% 5%
1989 8% 24% 9% 7%
1990 11% 33% 11% 10%
1991 15% 43% 14% 13%
1992 18% 53% 16% 16%
1993 19% 63% 18% 19%
1994 21% 71 % 21% 22%
1995 22% 79% 23% 24%
1996 25% 85% 25% 26%

 

 

 

 

 

 

 

When using both the Lilien et al. coefficients and adjusting for m leads to
very similar results compared to the Gentry parameters for both the Camcorder

and VCR products.

Figure 9: VCR Diffusion with Lilien Adjustment

   
 

 

VCR Diffusion
100%
90%7
80%
70% 7
60% a
50% { i—x—Lilien Adjustedl
40% -°- Gentw_cM__3Jl
30% 1-
20% 4
10% . ,
0% - .4 ., - , w
‘— N ('0 V I!) (D N 00 O) O ‘— N 00 V
ssssssesssssss

62

Even with the adjustments, the Bass parameters obtained with the Gentry
datasets were significantly different that those obtained by the Lilien et al.
datasets for cordless phones and CD players. However, Figure 10 clearly
demonstrates that is due to differences in the data as the Lilien et al. curves
greatly differ from the actual data provided by the Consumer Electronics
Association. Thus, it appears that the Bass models are valid in all cases and any
true discrepancies between the Lilien results and the results of this research are

due to differences in the data.
Figure 10: Cordless Phone Diffusion

Cordless Phone Diffusion

70% a

60%l «Liens. ____ i
50% ‘—A—Lilien l
40% _' _—>::Lilien Adjusteg
30% ~'
20% -
10% ’
0%

     
  

 

1984
1985
1986
1989 1
1990 e
1991 ~
1992 «
1993
1994 a
1995
1996

The other models used in this research were basic implementations of
standard formulas. Perhaps because they were not as famous as the Bass
model, it was not necessary to choose from many variants. After reviewing to

ensure that these additional models were working as expected, their results were

63

compared to the Bass model. As expected, all models gave results similar to the

Bass model. No additional validation procedures were performed.

Process

Curve Fitting
In order to calculate which seven diffusion models had the potential to

work best, all seven models were run with the eight innovation datasets provided
by the CEA. Only the CEA datasets were used as they contained perfect (non-
extrapolated) information for these fifty-six models.

The curve fitting exercise was then duplicated with the extended datasets.

The extended datasets cover the time period of interest for the forecasting.

Forecasting
The model parameters obtained through extended curve-fitting procedures

were used to create the forecasts. The parameters from each of the 8
innovations were used to forecast the diffusion of the other 7 innovations. This
was done for each of the seven models. Thus, a total of 392 forecasts were
created. As part of the forecasting analysis, it was clear that the Generalized
Bass models were not as well suited for diffusion forecasts as the other models

(see APPENDIX B), so the GB models were not used for the quadrant analysis.

Hypotheses Testing (Quadrant Analysis)
Using the squared sum of errors obtained by the forecasting models, the

results for each forecast were used to compare the relative importance of price
level and innovation type. This was done in two ways. First, each forecasting
method was reviewed as a whole and segmented by the two price levels and two
innovation levels.17 Then the specific hypotheses were tested by seeing how
many results predicted by the hypotheses were actually correct. This provided
two distinct methods of looking at the price levels, innovation levels, and forecast
method.

While analyzing this information, it became clear that forecasts based
upon the PC parameters did not work as‘well as the parameters from other
innovations. A posteriori, this may be because PCs may have been purchased
for reasons other than home entertainment. Many may have been purchased for
home offices. The PC may be used for educational purposes as well as
entertainment. The home office purchases and educational consideration may
explain why the PC diffusion differed than that of the other innovations. Given
the unique characteristics of the personal computer diffusion curve, the quadrant

analyses were repeated without using the PC dataset.

 

‘7 It may prove helpful to have Figure 6: How Descriptive Terms (Same, Horizontal, Vertical, 8
Opposite) Are Used (page 46) at hand.

65

Chapter 4

RESULTS

Table 20: Model Abbreviations

 

 

 

 

 

 

 

 

B Bass model

Bv Bass model variant

GB Generalized Bass model (Price)

GBv Generalized Bass model (Price) variant
SL Simple Logistic model

G Gompertz model

BnC Box and Cox model

 

 

 

Potential Fit of Models
After determining and using the optimal parameters for seven models, the

sum of the squared errors (SSE) were obtained by subtracting the curve-fitting
results from the actual results in order to ”show how well each model did in
comparison to one another for each innovation. One can make a case for
measuring the best and worse models by either the total SSE (Table 21) or by

their cumulative placement rankings (Table 20).

Table 21: Curve Fitting Results

 

e2 of e2 of e2 of e2 of e2 of e2 of e2 of
Innovation (data starts) B Bv GB GBv SL G BnC
PCS (1980) 0.011 0.012 0.007 0.007 0.016 0.015 0.013
Sat. Receivers (1986) 0.001 0.001 0.001 0.001 0.001 0.001 0.001
VCRS (1974) 0.074 0.063 0.036 0.029 0.055 0.017 0.027
CD Players (1983) 0.038 0.033 0.035 0.031 0.047 0.016 0.008
Camcorders (1985) 0.002 0.002 0.002 0.002 0.007 0.004 0.003
PTVS (1984) 0.000 0.000 0.000 0.000 0.001 0.000 0.001
Cordless Phones (1980) 0.005 0.005 0.005 0.005 0.007 0.012 0.005
TADS (1982) 0.021 0.018 0.011 0.011 0.042 0.012 0.006
Total: 0.153 0.135 0.097 0.087 0.177 0.077 0.064

66

Table 22: Curve Fitting - Comparative Placement

 

Innovation (data starts) B Bv GB GBv SL G BnC
PCs (1980) 3 4 1 2 7 6 5
Sat. Receivers (1986) 4 5 2 3 1 6 7
VCRs (1974) 7 6 4 3 5 1 2
CD Players (1983) 6 4 5 3 7 2 1
Camcorders (1985) 3 4 1 2 7 6 5
PWS (1984) 5 4 3 2 7 1 6
Cordless Phones (1980) 4 2 3 1 6 7 5
TADs (1982) 6 5 2 3 7 4 1
Total: 38 34 21 19 47 33 32

Judging by total SSE, the Box and Cox model is the best potential model
(.064) given perfect information. However, if one uses the comparative
placement method, the Generalized Bass variant is the best potential model. In
either case, the Simple Logistic model is clearly the worse potential model.
However, it is important to note that even the Simple Logistic model only had a
total SSE of 0.177 for all eight innovations. Since this was a curve-fitting
exercise, not a forecast, the accuracy of the various diffusion models is not
surprising. At the .05 level of testing, there were no significant differences

between any of the seven models.

67

Optimal Parameters

The curve fitting exercise was duplicated with the extended datasets to

determine the optimal parameters for each model.

Table 23: Curve Fitting - Optimized Parameters for 8 Model

 

Innovation p q

PCs (1977-2000) 0.0076 0.1267
Satellite Receivers (1979-2000) 0.0003 0.2604
VCRs (1972—2000) 0.0014 0.3554
CD Players (1983-2000) 0.0170 0.2230
Camcorders (1983-2000) 0.0088 0.1329
PTVs (1982-2000) 0.0054 0.0515
Cordless Phones (1976-2000) 0.0039 0.2313
Telephone Answering Devices (1976-2000) 0.0049 0.2175

Table 24: Curve Fitting - Optimized Parameters for Bv Model

 

Innovation p q

PCs (1977-2000) 0.0076 0.1453
Satellite Receivers (1979-2000) 0.0003 0.2771
VCRs (1972-—2000) 0.0013 0.3871
CD Players (1983-2000) 0.0164 0.2494
Camcorders (1983-2000) 0.0087 0.1499
PTVs (1982-2000) 0.0054 0.0651
Cordless Phones (1976-2000) 0.0038 0.2552
Telephone Answering Devices (1976-2000) 0.0048 0.2418

Table 25: Curve Fitting - Optimized Parameters for GB Model

 

Innovation p q B

PCs (1977-2000) 0.0075 0.1401 -1 .5073
Satellite Receivers (1979-2000) 0.0005 0.2586 1.0531
VC Rs (1972-—2000) 0.0017 0.2243 -8.5919
CD Players (1983-2000) 0.0160 0.2603 1 .5604
Camcorders (1983-2000) 0.0023 0.1 195 -8.9563
PTVs (1982-2000) 0.0060 0.0547 4.2393
Cordless Phones (1976-2000) 0.0041 0.2360 0.7047
Telephone Answering Devices (1976-2000) 0.0053 0.2188 0.4371

68

Table 26: Curve Fitting - Optimized Parameters for GBv Model

 

 

Innovation p q B
PCs (1977-2000) 0.0074 0.1604 -1.5360
Satellite Receivers (1979-2000) 0.0005 0.2747 1.0545
VCRs (1972-2000) 0.0017 0.2530 -7.7575
CD Players (1983-2000) 0.0154 0.2889 1.5009
Camcorders (1983-2000) 0.0022 0.1319 -9.1342
PTVs (1982-2000) 0.0059 0.0691 3.5670
Cordless Phones (1976-2000) 0.0039 0.2607 0.7328
Telephone Answering Devices (1976-2000) 0.0036 0.2352 -1.6927
Table 27: Curve Fitting - Optimized Parameters for SL Model
Innovation b c
PCs (1977-2000) 0.1599 35.2554
Satellite Receivers (1979-2000) ‘ 0.2403 1016.7619
VCRs (1972-2000) 0.3705 632.6383
CD Players (1983-2000) 0.2839 30.4163
Camcorders (1983-2000) 0.1828 38.4293
PTVs (1982-2000) 0.1236 54.1284
Cordless Phones (1976-2000) 0.2431 95.7757
Telephone Answering Devices (1976-2000) 0.2377 78.5701

Table 28: Curve Fitting - Optimized Parameters for G Model

 

Innovation b c

PCs (1977-2000) 0.0865 4.9556
Satellite Receivers (1979-2000) 0.0856 12.1903
VCRs (1972-—2000) 0.2566 55.7292
CD Players (1983-2000) 0.1877 6.2126
Camcorders (1983-2000) 0.0898 4.6937
PTVs (1982-2000) 0.0458 4.4081
Cordless Phones (1976-2000) 0.1530 1 1 .5618
Telephone Answering Devices (1976-2000) 0.1543 1 1.0536

69

Table 29: Curve Fitting - Optimized Parameters for BnC Model

 

Innovation b c18 k

PCs (1977-2000) 0.8919 224.3901 0.3748
Satellite Receivers (1979-2000) 1.2582 26500.0001 0.4417
VC Rs (1972—2000) 2.2013 100000.0000 0.3718
CD Players (1983-2000) 6.3438 100000.0000 -0.2766
Camcorders (1983-2000) 2.7401 2118.1201 -0.0818
PTVs (1982-2000) 2.4619 1560.3284 -0.1931
Cordless Phones (1976-2000) 0.7533 534.4088 0.6042
Telephone Answering Devices (1 976—2000) 3.8056 100000.0000 0.0193

Actual Fit of Models (Forecasting)

For the purposes of forecasting the consumer adoption of innovations, the

Generalized Bass models were not as reliable as the other five diffusion models

(APPENDIX 8). Therefore, only the results of the other five models were

presented here. For each of the eight innovations, forecasts were created by

using the optimal parameters of the other seven innovations. The results for the

five diffusion models still of interest were tabulated by both sum of the squared

errors and by the comparative placement method (Tables 30 to 45 and Tables

56-64).

 

‘8 As discussed in Chapter 3, an upper limit of 100,000 was used for variable c.

70

Table 30: Personal Computer Forecasting Results

PC Forecasts

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
VC Rs (1 972—2000)

Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Cordless Phones (1976-2000)
Using coefficients optimized for
Telephone Answering Devices
(1 976-2000)

Total

Ranking of PC Forecasts

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
VCRs (1 972—2000)

Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Cordless Phones (1976-2000)
Using coefficients optimized for
Telephone Answering Devices
(1976-2000)

Total

e2 of
3
0.983
0.803
2.770
0.051
0.674
0.262

0.309

e2 of
Bv
0.993
0.869
2.625
0.042
0.686
0.272

0.323

e2 of
SL
0.983
0.834
2.889
0.100
0.581
0.271

0.328

5.865 5.822 6.007
Table 31: PC Forecasts - Comparative Results

B
1

1

15

23

v
3

5

SL
2

3

21

e2 of
6
1.023
0.849
2.620
0.039
0.635
0.282

0.346

5.809

25

G
5
4
2
2
2

e2 of
BnC
1.000
0.804
2.369
0.028
0.716
0.273

0.338

5.543

BnC

21

The Box and Cox Model performed the best overall for forecasting PC

71

diffusion with a SSE of 5.543 and tying for second in the comparative results.

Table 32: D88 Satellite Receiver Forecasting Results

 

Satellite Receiver Forecasts 62 of 62 of e2 of 62 of e2 of
B Bv SL G BnC

Using coefficients optimized for 0.773 0.792 0.749 0.792 0.788

PCs (1977-2000)

Using coefficients optimized for 2.205 2.386 2.240 2.246 2.230

VC Rs (1972-2000)

Using coefficients optimized for 5.885 5.773 6.043 5.724 5.432

CD Players (1983-2000)

Using coefficients optimized for 1.102 1.080 1.208 1.059 0.976

Camcorders (1 983-2000)

Using coefficients optimized for 0.062 0.061 0.067 0.064 0.061

PTVs (1 982-2000)

Using coefficients optimized for 1.470 1.529 1.476 1.540 1.503

Cordless Phones (1976-2000)

Using coefficients optimized for 1.647 1.717 1.656 1.724 1.735

Telephone Answering Devices
(1 976-2000)

Total 13.145 13.338 13.440 13.150 12.726
Table 33: DBS Satellite Receiver Forecasts - Comparative Results

Ranking of Satellite Receiver

 

Forecasts B Bv SL G BnC
Using coefficients optimized for 2 4 1 5 3
PCs (1 977-2000)

Using coefficients optimized for 1 5 3 4 2
VC Rs (1 972-2000)

Using coefficients optimized for 4 3 5 2 1
CD Players (1983-2000)

Using coefficients optimized for 4 3 5 2 1
Camcorders (1 983-2000)

Using coefficients optimized for 3 2 5 4 1
PTVs (1982-2000)

Using coefficients optimized for 1 4 2 5 3
Cordless Phones (1976-2000)

Using coefficients optimized for 1 3 2 4 5
Telephone Answering Devices

(1 976-2000)

Total 16 24 23 26 16

The Box and Cox Model performed the best overall for forecasting the
diffusion of satellite receivers with a SSE of 12.726 and tying for first in the

comparative results.

72

 

Table 34: CD Player Forecasting Results

 

CD Player Forecasts e2 of e2 of e2 of 62 of 92 of
B Bv SL G BnC

Using coefficients optimized for 1.505 1.476 1.578 1.478 1.485

PCs (1977-2000)

Using coefficients optimized for 3.407 3.405 3.406 3.426 3.420

Satellite Receivers (1979-2000)

Using coefficients optimized for 0.076 0.091 0.099 0.177 0.122

VC Rs (1 972-—2000)

Using coefficients optimized for 1.233 1.232 1.260 1.228 1.215

Camcorders (1983-2000)

Using coefficients optimized for 2.636 2.634 2.674 2.653 2.625

PTVs (1 982-2000)

Using coefficients optimized for 1.309 1.269 1.332 1.311 1.321

Cordless Phones (1976-2000)

Using coefficients optimized for 1.141 1.096 1.182 1.175 1.141

Telephone Answering Devices
(1 976-2000)

 

Total 11.345 11.235 11.578 11.464 11.337
Table 35: CD Player ForeCasts - Comparative Results

Ranking of CD Player

Forecasts B Bv SL G BnC

Using coefficients optimized for 4 5 2 3

PCs (1977-2000)

Using coefficients optimized for 3 2 5 4

Satellite Receivers (1979-2000)

Using coefficients optimized for 2 3 5 4

VC Rs (1 972-2000)

Using coefficients optimized for 4 3 5 2

Camcorders (1983-2000)

Using coefficients optimized for 3 2 5 4

PTVs (1 982-2000)

Using coefficients optimized for 2 5 3 4

Cordless Phones (1976-2000)

Using coefficients optimized for 3 5 4 2

Telephone Answering Devices
(1 976-2000)

Total 20 1 1 30 25 19

The Bass Model variant performed the best overall for forecasting the
diffusion of CD players with a SSE of 11.235 and placing first in the comparative

results.

73

Table 36: Camcorder Forecasting Results

Camcorder Forecasts

e2 of
B

e2 of

Bv

e2 of
SL

e2 of
G

e2 of
BnC

 

Using coefficients optimized for
PCs (1977-2000)

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
VC Rs (1972—2000)

Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Cordless Phones (1976-2000)
Using coefficients optimized for
Telephone Answering Devices
(1 976-2000)

Total

0.018
0.564
0.076
1.241
0.284
0.020

0.021

2.229

0.015
0.564
0.091
1.244
0.283
0.022
0.026

2.249

0.030
0.564
0.099
1.286
0.295
0.023
0.024

2.329

0.016
0.571
0.177
1.241
0.288
0.054
0.058

2.409

Table 37: Camcorder ForeCasts - Comparative Results

Ranking of Camcorder

0.016
0.569
0.122
1.218
0.281
0.032
0.053

2.294

BnC

 

Forecasts 3 EV SL G
Using coefficients optimized for 4
PCs (1 977-2000)

Using coefficients optimized for 3 1 2 5 4
Satellite Receivers (1979-2000)

Using coefficients optimized for 1 2 3 5 4
VC Rs (1972-—2000)

Using coefficients optimized for 3 4 5 2 1
CD Players (1983-2000)

Using coefficients optimized for 3 2 5 4 1
PTVs (1 982—2000)

Using coefficients optimized for 1 2 3 5 4
Cordless Phones (1976-2000)

Using coefficients optimized for 1 3 2 5 4
Telephone Answering Devices

(1 976-2000)

Total 16 15 25 28 21

The Bass Model and the Bass variant performed the best overall for
forecasting the diffusion of camcorders with respective SSEs of 2.229/2.249 and

placements of second/first in the comparative results.

74

Table 38: Projection Television Forecasting Results

 

 

PTV Forecasts 92 of 92 of 92 of 92 of 02 of
8 EV SL G BnC

Using coefficients optimized for 0.219 0.230 0.200 0.234 0.230

PCs (1977-2000)

Using coefficients optimized for 0.057 0.057 0.057 0.060 0.059

Satellite Receivers (1979-2000)

Using coefficients optimized for 0.618 0.709 0.644 0.721 0.682

VC Rs (1972—2000)

Using coefficients optimized for 3.186 3.168 3.276 3.155 3.067

CD Players (1983-2000)

Using coefficients optimized for 0.360 0.357 0.375 0.357 0.345

Camcorders (1 983-2000)

Using coefficients optimized for 0.423 0.454 0.422 0.496 0.449

Cordless Phones (1976-2000)

Using coefficients optimized for 0.518 0.557 0.511 0.586 0.593

Telephone Answering Devices

(1 976-2000)

Total 5.382 5.531 5.486 5.610 5.426

Table 39: PTV Forecasts - Comparative Results

Ranking of PTV Forecasts B Bv SL 6 BnC

Using coefficients optimized for 2 4 1 5 3

PCs (1977-2000)

Using coefficients optimized for 3 2 1 5 4

Satellite Receivers (1979-2000)

Using coefficients optimized for 1 4 2 5 3

VCRs (1972--2000)

Using coefficients optimized for 4 3 5 2 1

CD Players (1983-2000)

Using coefficients optimized for 4 2 5 3 1

Camcorders (1 983-2000)

Using coefficients optimized for 2 4 1 5 3

Cordless Phones (1976-2000)

Using coefficients optimized for 2 3 1 4 5

Telephone Answering Devices

(1 976-2000)

Total 18 22 16 29 20

The Bass model performed the best overall for forecasting the diffusion of
projection televisions with a SSE of 5.382 and placing second in the comparative

results.

75

Table 40: Video Cassette Recorder Forecasting Results

VCR Forecasts

Using coefficients optimized for
PCs (1977-2000)

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Cordless Phones (1976-2000)
Using coefficients optimized for
Telephone Answering Devices
(1 976-2000)

Total

Ranking of VCR Forecasts

Using coefficients optimized for
PCs (1977—2000)

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1 983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Cordless Phones (1976-2000)
Using coefficients optimized for
Telephone Answering Devices
(1 976-2000)

s2 of
3
1.176
4.450
1.653
0.798
4.908
0.232

0.224

B
2

1

e2 of

Bv
1.268
4.601
1.470
0.928
5.027
0.252

0.237

Bv
5

3

e2 of
SL
1.107
4.492
1.688
0.556
4.124
0.224

0.202

SL

1

2

e2 of
G
1.266
5.081
1.624
0.994
4.634
0.229

0.196

13.518 13.848 12.449 14.041
Table 41: VCR Forecasts - Comparative Results

G
4

5

N-kw

e2 of
BnC
1.255
4.744
1.586
1.376
5.250
0.219

0.216

14.658

BnC

3

4

Total 20 26 14 22 23

The Simple Logistic model performed the best overall for forecasting the
diffusion of VCRs with a SSE of 12.449 and placing first in the comparative

results.

76

Table 42: Cordless Phone Forecasting Results

Cordless Phone Forecasts

Using coefficients optimized for
PCs (1977-2000)

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
VCRs (1 972-2000)

Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Telephone Answering Devices
(1 9762000)

Total

92 of

B
0.305
2.330
0.174
1.784
0.150
2.007

0.015

6.773

e2 of

Bv
0.313
2.358
0.195
1.656
0.175
2.034

0.014

6.751

e2 of
SL
0.297
2.333
0.184
1.860
0.079
1.770

0.015

6.546

e2 of
G
0.316
2.438
0.189
1.699
0.203
1.911

0.019

6.787

Table 43: Cordless Phone Ferecasts - Comparative Results

Ranking of Cordless Phone
Forecasts

G

e2 of
BnC
0.315
2.377
0.165
1.562
0.319
2.107

0.019

6.868

 

Using coefficients optimized for
PCs (1977-2000)

Using coefficients optimized for
Satellite Receivers (1979-2000)
Using coefficients optimized for
VCRs (1 972--2000)

Using coefficients optimized for
CD Players (1983-2000)

Using coefficients optimized for
Camcorders (1983-2000)

Using coefficients optimized for
PTVs (1 982-2000)

Using coefficients optimized for
Telephone Answering Devices
(1 976-2000)

NW

Total 16 21 16 27 25

The Simple Logistic model performed the best overall for forecasting the
diffusion of cordless phones with a SSE of 6.546 and tying for first in the

comparative results.

77

Table 44: Telephone Answering Device Forecasting Results

 

 

TAD Forecasts e2 of 02 of 92 of 02 of 82 of
8 EV SL G BnC

Using coefficients optimized for 0.378 0.384 0.381 0.376 0.377

PCs (1 977-2000)

Using coefficients optimized for 2.511 2.540 2.514 2.609 2.553

Satellite Receivers (1979-2000)

Using coefficients optimized for 0.195 0.204 0.196 0.170 0.160

VC Rs (1 972--2000)

Using coefficients optimized for 1.622 1.494 1.681 1.536 1.406

CD Players (1983-2000)

Using coefficients optimized for 0.203 0.228 0.135 0.246 0.356

Camcorders (1983-2000)

Using coefficients optimized for 2.136 2.164 1.909 2.041 2.232

PTVs (1 982-2000)

Using coefficients optimized for 0.055 0.051 , 0.055 0.019 0.037

Cordless Phones (1976-2000)

Total 7.147 7.106 6.919 7.010 7.126

Table 45: TAD Forecasts — Comparative Results

Rankimf TAD Forecasts 8 EV SL G BnC

Using coefficients optimized for 3 5 4 1 2

PCs (1977-2000)

Using coefficients optimized for 1 3 2 5 4

Satellite Receivers (1979-2000)

Using coefficients optimized for 3 5 4 2 1

VC Rs (1 972—2000)

Using coefficients optimized for 4 2 5 3 1

CD Players (1983-2000)

Using coefficients optimized for 2 3 1 4 5

Camcorders (1983-2000)

Using coefficients optimized for 3 4 1 2 5

PTVs (1 982-2000)

Using coefficients optimized for 4 3 5 1 2

Cordless Phones (1976-2000)

Total 20 25 22 1 8 20

The Gompertz model performed the best overall for forecasting the

diffusion of telephone answering devices with a SSE of 7.010 (second best) and

placing first in the comparative results.

78

Hypotheses Testing (Quadrant Analysis)
The primary purpose of this research is to provide guidance on which

diffusion models should be used in various conditions. While the previous set of
tables looked at the forecasts for each innovation, the following set of tables

looks at of the forecasts as a whole and then as segments.

Table 46: All Eight Innovations - Comparative Results
62 of e2 of e2 of e2 of e2 of
B Bv SL G BnC

 

Sum of e2 85.4 85.9 64.8 66.3 88.0
Total finish score (lower is better) 141 167 167 200 165
Rankings by e2 sums 2 3 1 5 4
Rankings by finish position 1 3 3 5 2

The Bass model performed the best overall for forecasting the diffusion of
all innovations with a SSE of 65.4 (second best) and placing first in the

comparative results. However, the results are not statistically significant.

Table 47: Radical Innovations - Comparative Results
Personal Computers, Satellite e2 of e2 of e2 of e2 of e2 of

 

Receivers, CD Players B Bv SL G BnC
Sum of e2 30.4 30.4 31.0 30.4 29.8
Total finish score (lower is better) 51 58 74 76 56
Rankings by e2 sums 2 3 5 4 1
Rankings by finish position 1 3 4 5 2

The Bass model and the Box and Cox model performed the best overall
for forecasting the diffusion of radical innovations with respective SSEs of

30.4/29.6 and placements of first/second in the comparative results.

Table 48: RadicaIIHigh Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

PCs, Satellite Receivers B Bv SL G BnC
Sum of e2 19.0 19.2 19.4 19.0 18.3
Total finish score (lower is better) 31 47 44 51 37
Rankings by e2 sums 3 4 5 2 1
Rankings by finish position 1 4 3 5 2

79

The Box and Cox model performed the best overall for forecasting the
diffusion of radical, high-priced innovations with a SSE of 18.3 and placing

second in the comparative results.

Table 49: RadicaIILow Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

CD Players 8 Bv SL G BnC
Sumofe2 11.3 11.2 11.6 11.5 11.3
Total finish score (lower is better) 20 11 30 25 19
Rankings by e2 sums 3 1 5 4 2
Rankings by finish position 3 1 5 4 2

The Bass model variant performed the best overall for forecasting the

diffusion of radical, low-priced innovations with a SSE of 11.2 and placing first in
the comparative results.

Table 50: Really New Innovations - Comparative Results

 

Camcorders, PTVs, VCRs, e2 of e2 of e2 of e2 of e2 of
Cordless Phones, TADs B Bv SL G BnC
Sum of e2 35.0 35.5 33.7 35.9 36.4
Total finish score (lower is better) 90 109 93 124 109
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 3 2 5 3

The Bass model and the Simple Logistic model performed the best overall
for forecasting the diffusion of really new innovations with respective SSEs of

35.0/33.7 and placements of first/second in the comparative results.

Table 51: Really NewIHigh Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

Camcorders, PTVs B Bv SL G BnC
Sum of e2 7.8 7.8 7.8 8.0 7.7
Total finish score (lower is better) 34 37 41 57 41
Rankings by e2 sums 1 3 4 5 2
Rankings by finish position 1 2 3 5 3

80

The Bass model performed the best overall for forecasting the diffusion of
really new, high-priced innovations with a SSE of 7.6 and placing first in the

comparative results.

Table 52: Really NewILow Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of
VCRs, Cordless Phones, TADs B Bv SL G BnC

 

Sum of e2 27.4 27.7 25.9 27.8 28.7
Total finish score (lower is better) 90 109 93 124 109
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 3 2 5 3

The Bass model and the Simple Logistic model performed the best overall
for forecasting the diffusion of really new, low-priced innovations with respective

SSEs of 27.4/25.9 and placements of first/second in the comparative results.

Table 53: High Priced Innovations - Comparative Results

 

PCs, Satellite Receivers, e2 of e2 of e2 of e2 of e2 of
Camcorders, PTVs 8 EV SL G BnC
Sum of e2 28.8 28.9 27.3 27.0 28.0
Total finish score (lower is better) 65 84 85 108 78
Rankings by e2 sums 2 3 5 4 1
Rankings by finish position 1 3 4 5 2

The Bass model and the Box and Cox model performed the best overall
for forecasting the diffusion of high-priced innovations with respective SSEs of

266/260 and placements of first/second in the comparative results.

Table 54: Low Priced Innovations - Comparative Results

 

CD Players, VCRs, Cordless e2 of e2 of e2 of e2 of e2 of
Phones, TADs 3 EV SL G BnC
Sum of e2 38.8 38.9 37.5 39.3 40.0
Total finish score (lower is better) 76 83 82 92 87
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 3 2 5 4

81

The Bass model and the Simple Logistic model performed the best overall
for forecasting the diffusion of low-priced innovations with respective SSEs of

38.8/37.5 and placements of first/second in the comparative results.

Cell Testing (Hypotheses Testing)
The specific hypotheses discussed earlier (page 46) were tested by

measuring the differences between the sum of squared errors for forecasts using
parameters from various quadrants. Since the hypotheses made specific
predictions about the accuracy of various comparisons, the total number of
successful predictions were simply counted to compute the binomial distribution

(Berry and Lindgren, 1996).

Table 55: Results of Cell Comparisons

number percent
n correct correct zscore

 

H1 270 206 76.3% 8.6"
H1a (opp) 100 85 85.0% 70”
H1 b (hz) 70 40 57.1% 1.2
H1c (vt) 100 81 81.0% 6.2“

H2 280 173 61.8% 3.9**
H2a (vt vs. op) 140 73 52.1% 0.5
H2b (hz vs. op) 140 100 71.4% 51*“

H3 140 33 23.6% -6.3**

**P < 0.01
Strong support for the first two hypotheses was found, although the results
for hypotheses H1b and H2a were not significant. Support for H1d (not shown
on Table 55) was also found as Zma > (Zmb; ZH1c). Not only was support lacking

for the third hypothesis, but it was clearly refuted.

82

Quadrant Analysis without PCs
As discussed in Chapter 3, it became clear that the diffusion of PCs

followed a pattern that differed from the other consumer electronic innovations.

Therefore the quadrant analysis was repeated without using this dataset.

Table 56: All Seven Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of
B Bv SL G BnC

 

Sum of e2 55.0 55.4 54.2 55.9 55.9
Total finish score (lower is better) 95 108 117 121 99
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 3 4 5 2

The Bass model performed the best overall for forecasting the diffusion of
all innovations with a SSE of 55.0 (second best) and placing first in the
comparative results.

Table 57: Radical Innovations — Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

Satellite Receivers, CD Players B Bv SL G BnC
Sum of e2 22.2 22.3 22.8 22.3 21.8
Total finish score (lower is better) 27 29 45 39 25
Rankings by e2 sums 2 3 5 4 1
Rankings by finish position 2 3 5 4

The Box and Cox model performed the best overall for forecasting the

diffusion of radical innovations with a SSE of 21.8 and placing first in the

comparative results.

83

Table 58: Radical/High Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

Satellite Receivers B Bv SL G BnC
Sum of e2 12.4 12.5 12.7 12.4 11.9
Total finish score (lower is better) 14 20 22 21 13
Rankings by e2 sums 3 4 5 2 1

Rankings by finish position 2 3 5 4
The Box and Cox model performed the best overall for forecasting the

diffusion of radical, high-priced innovations with a SSE of 11.9 and placing first in
the comparative results.

Table 59: Radical/Low Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

CD Players B Bv SL G BnC
Sum 8er _ 9.8 9.7 10.0 10.0 9.8
Total finish score (lower is better) 13 9 23 18 12
Rankings by e2 sums 2 1 4 5 3
Rankings by finish position 3 1 5 4 2

The Bass model variant performed the best overall for forecasting the

diffusion of radical, low-priced innovations with a SSE of 9.7 and placing first in
the comparative results.

Table 60: Really New Innovations - Comparative Results

 

Camcorders, PTVs, VCRs, e2 of e2 of e2 of e2 of e2 of
Cordless Phones, TADs B Bv SL G BnC
Sum of e?- . 32.8 33.2 31.6 33.8 34.2
Total finish score (lower is better) 68 79 72 82 74
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 4 2 5 3

The Bass model and the Simple Logistic model performed the best overall
for forecasting the diffusion of really new innovations with respective SSEs of

328/316 and placements of first/second in the comparative results.

Table 61: Really New/High Priced Innovations — Comparative Results
e2 of e‘2 of e2 of e2 of e2 of

 

Camcorders, PTVs B Bv SL G BnC
Sum of e2 7.4 7.5 7.6 7.8 7.5
Total finish score (lower is better) 22 29 32 40 27
Rankings by e2 sums 1 3 4 5 2
Rankings by finish position 1 3 4 5 2

The Bass model performed the best overall for forecasting the diffusion of

really new, high-priced innovations with a SSE of 7.4 and placing first in the
comparative results.

Table 62: Really NewILow Priced Innovations - Comparative Results
e2 of e2 of e2 of e2 of e2 of

 

VCRs, Cordless Phones, TADs B Bv SL G BnC
Sum of e2 25.4 25.8 24.0 25.8 26.7
Total finish score (lower is better) ~ 46 50 40 42 47
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 3 5 1 2 4

The Simple Logistic model performed the best overall for forecasting the

diffusion of really new, low-priced innovations with a SSE of 24.0 and placing first
in the comparative results.

Table 63: High Priced Innovations - Comparative Results
Satellite receivers, Camcorders, e2 of e2 of e‘2 of e2 of e2 of

 

PTVs B Bv SL G BnC
Sum of e2 19.7 20.1 20.3 20.1 19.4
Total finish score (lower is better) 36 49 54 61 40
Rankings by e2 sums 2 3 5 4 1
Rankings by finish position 1 3 4 5 2

The Bass model and the Box and Cox model performed the best overall
for forecasting the diffusion of high-priced innovations with respective SSEs of

19.7/19.4 and placements of first/second in the comparative results.

85

Table 64: Low Priced Innovations — Comparative Results

 

CD Players, VCRs, Cordless e2 of e2 of e2 of e2 of e2 of
Phones, TADs B Bv SL G BnC
Sum of e2 35.3 35.4 34.0 35.8 38.5
Total finish score (lower is better) 59 59 63 60 59
Rankings by e2 sums 2 3 1 4 5
Rankings by finish position 1 1 5 4 1

The Bass model performed the best overall for forecasting the diffusion of
low-priced innovations with a SSE of 35.3 (second) and placing first in the

comparative results.

Cell Testing (Hypotheses Testing) without PCs
Table 65: Results of Cell Comparisons

number percent
It correct correct 2 score

H1 170 146 85.9% 9.4"
H1 a (opp) 40 40 100.0% 6.3"
H1 b (hz) 40 35 87.5% 4.7**
H18 (vt) 90 71 78.9% 5.5"
H2 170 132 77.6% 7.2**
H2a (vt vs. op) 85 57 67.1% 3.1 **
H2b (hz vs. op) 85 75 88.2% 7.1 **
H3 85 31 36.5% -2.5**
**P < 0.01

Strong support for the first two hypotheses was found, the results for all
sub-hypotheses were significant. Support for H1d (not shown on Table 65) was
also found as 2H1, > (Zmb; ZHrc). Not only was support lacking for the third

hypothesis, but it was clearly refuted.

86

Chapter 5
DISCUSSION OF RESULTS

It is important to differentiate between forecasts that are created before an
innovation is easily available and forecasts that are created after years of history
in the marketplace. The conclusions drawn from this research are appropriate
for creating forecasts before the innovation is marketed. This research used
datasets from the United States consumer electronic market. The conclusions
drawn from this research may be applicable to other industries and other
countries, but further research will be needed to determine if generalizations are

valid.

Answering the Research Questions
The research questions asked which forecasting method(s) should be

used under various innovation levels (radical and really new) and price levels
(high and low). The results of the research provided specific answers to these
questions. When forecasting the diffusion of a radical high-priced innovation,
one should use the Box & Cox model. It is recommended that one also generate
a Bass model forecast if a second opinion is desired. When forecasting the
diffusion of really new high-priced innovation, one should use the Bass model
with the Box & Cox model serving as a backup. The Bass variant model should
be used when forecasting the diffusion of low-priced radical innovations, with
either the Bass model or the Box & Cox model providing a second opinion.
When forecasting the diffusion of low-priced really new innovations, the Simple

Logistic model should be used. The robust Bass model may also be used if

87

multiple models are desired. Figure 11 summarizes when various models should

 

 

 

 

 

be used.
Figure 1 1: Recommended Models by Context
Consumers
Price Level Radical Innovation Really New Innovation
High Box & Cox Bass
Bass Box & Cox
Bass variant Simple Logistic

Low

Bass / Box & Cox Bass

 

 

 

 

 

Lessons From the Hypotheses
Hypotheses 1 and 2 stated that the various combinations of innovation

levels (radical and really new) and price levels (high and low) would result in four
populations that were significantly different from one another. The research
supported these claims. As theorized, parameters from populations that were
different in terms of both innovation level and price level did less well than

parameters from more similar populations.

88

Hypothesis 3 presumed that the level of innovation would have a greater
impact on the accuracy of a forecast than the price level. This presumption was
clearly wrong. Not only did the research falsify it, it did so in such a manner that
the opposite statement appears to be true. The price level of an innovation

actually has more impact on the accuracy of a forecast than the innovation level.

Models
As discussed in Chapter 4, the Box and Cox and Generalized Bass

models were the best models when it came to curve-fitting while the Simple
Logistic model did the poorest. Curve-fitting is a very useful tool and may be
useful for forecasts when an innovation has already been available in the
marketplace. However, the results of the research showed that a curve-fitting
advantage did not translate into a forecasting advantage when creating a

forecast for an innovation without a market history.

Bass Models
The popularity of the Bass model derives from two unique factors. As this

research has reinforced, the Bass model is very robust — working well in all
tested contexts. In addition, the Bass model’s two coefficients have a theoretical
foundation. However, the coefficients of innovation and imitation are only
theoretically sound if the model starts from the initial diffusion of the innovation.
Otherwise, the model assumes that the innovation first appeared later than it
actually did. As shown in Table 66, this false assumption artificially inflates the
role of p (the coefficient of innovation) and artificially deflates the role of q (the

coefficient of imitation).

89

Table 66: Watching p's and q's

Description Bp Bq BSSE GBp GBq GBB GB SSE
VCR (1974-2000) 0.003 0.349 0.074 0.010 0.177 -5.000 0.091
VCR (1975-2000) 0.004 0.344 0.073 0.009 0.179 -10.775 0.037
VCR (1976-2000) 0.005 0.337 0.070 0.010 0.180 -10.460 0.036
VCR (1977-2000) 0.008 0.328 0.067 0.014 0.188 -8.197 0.034
VCR (1978-2000) 0.011 0.317 0.063 0.003 0.140 -20.793 0.035
VCR (1979-2000) 0.016 0.301 0.058 0.004 0.145 -18.892 0.034
VCR (1980-2000) 0.023 0.279 0.051 0.007 0.154 -15.614 0.033
VCR (1981-2000) 0.034 0.250 0.043 0.007 0.163 —13.813 0.033
VCR (1982-2000) 0.050 0.211 0.033 0.023 0.177 -6.601 0.028
VCR (1983-2000) 0.075 0.159 0.021 0.056 0.152 -2.670 0.020
VCR (1984-2000) 0.114 0.086 0.011 0.113 0.087 -0.044 0.011
VCR (1985-2000) 0.168 0 0.005 0.171 0 0.201 0.005
VCR (1986-2000) 0.202 0 0.024 0.235 0 2.673 0.022
VCR (1987-2000) 0.245 0 0.065 0.311 0 5.681 0.049
VCR (1988-2000) 0.304 0 0.114 0.356 0 7.382 0.066
VCR (1989-2000) 0.381 0 0.147 0.486 0 6.846 0.117
VCR (1990-2000) 0.465 0 0.137 0.481 0 7.431 0.111
VCR (1991-2000) 0.558 0 0.120 0.488 0 6.848 0.097
VCR (1992-2000) 0.637 0 0.096 0.671 0 7.172 0.038
VCR (1993-2000) 0.694 0 0.068 0.719 0 6.434 0.020
VCR (1994-2000) 0.748 0 0.044 0.778 0 5.621 0.006
VCR (1995-2000) 0.828 0 0.034 0.845 0 5.173 0.003
VCR (1996-2000) 0.850 0 0.022 0.866 0 4.617 0.001

This does not mean that the Bass models cannot be useful if one’s data
starts after the initial diffusion. On the contrary, the Bass models may still be
used for forecasting just as any other model. Rather, this caution is meant for
how one interprets the coefficients of innovation and imitation.

Despite the flexibility given by Bass, Krishnan, and Jain (1994) in allowing
the sign of the price coefficient (8) to fluctuate, researchers who conduct similar
experiments are advised to constrain the price variable to be negative. While this
will result in sub-optimal curve-fitting, the loss in accuracy should be relatively
minor. Conversely, forecasts of other innovations using only negative price

variables should see gains in their accuracy. It is expected that research done

90

with the negative constraint on the price coefficient should allow direct
comparisons between the Generalized Bass models and the other diffusion
models.

The Bass model variants created for this research deliberately violated the
assumption of a constant m. This resulted in a model (Bv) that outperformed any
of the others in the radical low-priced innovation context. Unfortunately, there
was just one innovation in this context — additional research is recommended to

test the viability of this variation with more datasets in various contexts.

Simple Logistic and Gompertz
The Simple Logistic model is one of the oldest diffusion models known.

True to its name, it is a very basic model. However, it clearly outperformed the
other models in the context of really new low-priced innovations.

The Gompertz model has also been used for quite a while. Based upon
this research, it is not recommended for forecasting the diffusion of really new or
radical innovations before the launch of an innovation. However, the Gompertz
model may be very well suited for forecasts generated well after the launch of an
innovation. While this was not the focus of this research, it was observed that
the diffusion of the Projection Television innovation follows a perfect Gompertz

curve.

91

Box and Cox
As discussed in Chapter 3, the Flexible Logistic Box and Cox model has a

problem where the 0 variable tends to run to infinity in some scenarios. This was
addressed by capping the upper limit of c to 100,000. Despite (or because of)
this fix, the author must admit to being skeptical as to how well the Box and Cox
model would do in comparison to the other models. As it turned out, the Box and
Cox was second only to the Bass model in terms of robustness. The Box and

Cox was also the best model in the context of radical high-priced innovations.

Contributions
This research has provided the following contributions:

Support for the use of multiple forecasting methods
Guidance for when various models should be used
Guidance for when various models should not be used
Criteria for when an innovation is released

Definition of an Analogous Innovation

Evidence that Analogous Groups Matter

Superior method for extrapolation

Evidence that price levels matter more than innovation levels
A forecasting classification grid was created and proposed

This research has provided additional support for the traditional view that
no single forecasting method is best for every situation, although the Bass model
comes pretty close. The unique contribution of this forecasting research was in
providing guidance for selecting forecasting models in various price and
innovations contexts.

This research also provided the first empirical study that suggests the

Gompertz Model is not a preferred model for use in pre-Iaunch conditions. While

92

this finding still needs to be verified in other studies, this finding could help
forecasters improve their accuracy by guiding them to more appropriate models.

Three specific criteria were proposed as necessary before first counting
when an innovation became available. The use of this criteria should allow for
researchers to compare forecasting model parameters from one innovation with
the same parameters from another innovation.

A definition of an analogous innovation was proposed. This definition was
used as the basis for research that provided evidence that analogous innovation
groups make an important difference in determining which methods should be
used for pre-launch forecasting. It appears likely that the definition may also
need to include the industry (e.g., reallynew innovation, low price level,
consumer electronic industry), but this is currently speculation and needs to be
tested.

This research provided evidence that the discrete time notation of the
Bass Model used by this author was superior for extrapolation than the method
employed by Lilien et al. Both methods work approximately the same (see
Figure 12) for a given period of time, although the method used here had a

slightly lower sum of squared errors.

93

Figure 12: Comparison of Gentry and LIIIen et al. Diffusion Forecasts for VCRs

VCR Diffusion

100% a
80% l
60% .
40% -
20% —
0%

81 82
H-EL,, l l . - .
+Actual _ l 2% l 4% 8% 19%-??? 30% 40%P2% 84% 89% 74% 713% 80% 81%[

—a— Lilien etai l 3% 8% 12% 21% 33%l48% 84%l79% 90%4‘95%_ 98% 99% 100 199i

._ __ _. _ _. ..____,

—x—_Ad_justed Lilieni 2% 5% 9% 18% 25%l37% 49% 80% 88% 73% 75% 78%l 78% 76%|

4 —— .___,_2__.

2_G_emy (B)_,_ 3%, 6% 11% 15% 23%j3_0%i 39% 48%l57% 65% 73%1800/ojgflj/1. 8_9%,l

p q m SSE
Lilien etal. 0.025 0.603 76.3% 0.521
Adjusted Lilien n/a n/a n/a 0.038
Gentry (B) 0.029 0.299 100% 0.029

 

 

8384 85 88 87l88 89790 9192 93 94.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

However, when the forecast was extended, using the same parameters, the

superiority of the method used in this research becomes apparent (Figure 13).

94

Figure 13: Extended Comparison of Gentry and Lilien et al. Diffusion Forecasts for VCRs

 

 

VCRDiffusion

100% — ‘-—‘-—

80%

60%

40% l

20% i

0% " V/ i T ATV—k * ““”—'—‘~'T /T_ 7

‘- 0') In N O) ‘- 0') L0 N O)
00 CD 00 (I) (I) O) O) O) O) O)
93 93 9 93 93 93 93 93 93 92

 

 

§+Actual + unenetaifiéé-Adiusted Lilien — Gentry (B) '

 

 

 

p q m SSE
Lilien et al. 0.025 0.603 76.3% 0.578
Adjusted Lilien n/a n/a n/a 0.167
Gentry (B) 0.029 0.299 100% 0.049

 

A forecasting classification grid was also proposed to simply the
classification of various forecast models. By revisiting the 1985 findings of
Armstrong, the forecasting classification grid provides an exhaustive, exclusive,

and concise method for classifying forecasts.

95

APPENDICES

96

APPENDIX A

SELECTING DIFFUSION MODELS

Table 16: Diffusion Models Initially Considered

Logarithmic Parabola (Gregg, Hossel, & Richardson, 1964)
Modified Exponential (Gregg, Hossel, & Richardson, 1964)
Observation-Based Modified Exponential (Meade, 1985)
Bass model (Bass, 1969)

Generalized Bass model (Bass, Krishnan, and Jain, 1994)
Simple Logistic (Gregg, Hossel, & Richardson, 1964)
Gompertz (Gregg, Hossel, & Richardson, 1964)

Extended Logistic (Bass, 1969)

Log-logistic (Tanner, 1978)

Flexible Logistic (FLOG) - Inverse Power Transform (Bewley & Fiebig,
1988)

F LOG — Box & Cox (Bewley & Fiebig, 1988)

FLOG — Exponential (Bewley & Fiebig, 1988)

As discussed in Chapter 3, the Bass model, the Generalized Bass model,
the Simple Logistic model, and the Gompertz model were selected on the basis
of the research and the literature. As both a check on the literature and an
opportunity to see how each model worked, each model was created and plotted
against the actual VCR diffusion.

A quick review of the following figures (starting on the next page) revealed
that Meade and Islam’s recommendation was wise: The parameters of the
Simple Logistic, Gompertz, and Bass models were easily adjusted to a shape
similar to the actual VCR diffusion curve. The Generalized Bass model was
likewise appropriate. This graphical review supported the initial decision to use
these four models.

The other models were also reviewed. The Logarithmic Parabola,

Modified Exponential, Observation-Based Modified Exponential, and Log-

97

Logistics models did not lend themselves to a close approximation of the actual
VCR diffusion. Thus, these models were removed from consideration. The
Extended Logistic model and all three Flexible Logistic models were able to
approximate the actual VCR diffusion and all were judged appropriate for use.
Given the amount of modeling required for this research, it was decided to
add just one of these four models to those already selected. Since the Extended
Logistic model was a variant of the Bass model — which was already selected for
the research along with several variants — it was decided to use one of the
Flexible Logistic models instead. While all three FLOG models were suitable, it
was judged that the Box and Cox model was slightly more appropriate for the

VCR diffusion and it was selected for the research.

Figure 14: Initial Look at Logarithmic Parabola Model

VCR Diffusion - Logarithmic Parabola

100% —
90% 7
80% «j
70%
60%
50%
40% ~,
30% E
20% 1
10% i

0%

1' “_._' A8031

' +Logan'thmic I
Parabola ‘

 

 

1 974
1 977
1 980
3

86

1 989
1 992

98

1

Figure 15: Initial Look at Modified Exponential Model

00% .

90%
80%

70%.*

60%

50%,«
40%>:
30%.1
20%i4
10%.1

0%

1 974

 

VCR Diffusion - Modified Exponential

—4»—Amn0ai' *

l
. + Modified
1 _ Exponential.

1977
1980
1983v~
1988
1989 E
1992
1995
1998—<

Figure 16: Initial Look at Observation-Based Modified Exponential Model

100%

90% t

80%

70% 1
60% .

50%
40%
30%

20%.,

1 0%
0%

VCR Diffusion - Observation-Based Modified Exponential

1 976
1 978

 

f:;;_iuauai

+ Modified
Exponential -
observed '

1990 4
1992
1994
1996 ‘
1998
2000

1980
1982
1984'
1988
1988-1

99

120% -—

100% ‘
80% .

60%
40%
20%

0%

Figure 17: Initial Look at Bass Model

1 980

VCR Diffusion - Bass Model

 

1995 7

1998 7

[ __._____._ ....

; 49:-Actual
+ Bass Model

Figure 18: Initial Look at Generalized Bass Model

120% --

100% «
80% -
60% ~
40% '
20% ‘

0%

1 974
1 976
1 978

VCR Diffusion - Generalized Bass Model (Price)

100

 

...—C 8 Actual—‘8 8
+68 Model

 

Figure 19: Initial Look at Simple Loglstlc Model

120%
100% ,
80% -
+Actual
60% a-
. —I—Simple
40% “ LEE”?
20%
00/0 ' ’T ‘ flrT ' 7'“ T ' ’
V N O (‘0 (D O) N In 00
ix N 00 Q 00 00 O) O)
93 93 92 93 93 93 93 S’.’ 5’3
Figure 20: Initial Look at Gompertz Model
VCR Diffusion - Gonpertz
120% -
100% f
80% .
+Gomperlz
40% , ""'77‘*————‘—
20% ,
0% Y*——r*r_"—* —
.2 r: 8 8 8 8 8 8 8
93 93 9’. 93 93 93 93 93 93

 

VCR Diffusion - Simple Loglstlc Model

 

 

101

Figure 21: Initial Look at Extended Logistic Model

VCR Diffusion - Extended Logistic

120%
100% -
8096
6096
40%:«
2095.
0%:

6+ 8’ Actual 8

+ Extended I
Logistic

 

1974
1977
1980
1983
1986
1989

Figure 22: Initial Look at Log-Logistic Model

VCR Diffusion - Log-Logistic

,—§— Actual

.' + Log J;
Logistic

 

 

1974
1977
1980
1983 i
1986 ‘
1989 «

Figure 23: Initial Look at the Flexible Logistic Inverse Power Transform Model

 

VCR Diffusion - FLOG IPT
120%-
100%;
80%4
80% f—o—AEmY—SI“
40% +FLOGIPT
20%‘
0% 4 . -.
VCOQONV‘IOQONgCDwO
N N N 6 Q Q w 03 O) O) O) 0
99229292222298

102

Figure 24: Initial Look at the Flexible Logistic Box and Cox Model

VCR Diffusion - FLOG Box and Cox

120%
100% -
80% <

i +Actua| N i
+ F LOG BnC

60% .
40% .

20%

 

0%

2000

1974
1978
1978
1980
1982
1984
1988 I
1988 A
1990
1992
1994
1998
1998‘

Figure 25: Initial Look at the Flexible Logistic Exponential Model

VCR Diffusion - FLOG ELOG
120% ,,
100% ,

80% .

  

I + Actual
—I— FLOG ELOG‘

8088 i
4098
2088

0%

1974
1978
1978
1980
1982
1984
1988
1988 l
1990 A
1992
1994
1998
1998 i
2000

103

APPENDIX B
DIFFUSION AND THE GENERALIZED BASS MODEL

Bass, Krishnan, and Jain (1994) created the Generalized Bass model in
response to criticism that the Bass model did “not combine contagion effects with
traditional economic variables such as price.” They expected the price coefficient
(8) to be negative, but did not constrain the coefficient. As can be seen in Table
25, three of the price coefficients had negative values when the parameters were

optimized for curve-fitting.

Table 25: Curve Fitting - Optimized Parameters for GB Model

 

Innovation p (L 8

PCs (1977-2000) 0.0075 0.1401 -1 .5073
Satellite Receivers (1979-2000) 0.0005 0.2586 1.0531
VCRs (1972-2000) 0.0017 0.2243 -8.5919
CD Players (1983-2000) 0.0160 0.2603 1 .5604
Camcorders (1983-2000) 0.0023 0.1 195 89563
PTVs (1982-2000) 0.0060 0.0547 4.2393
Cordless Phones (1976-2000) 0.0041 0.2360 0.7047
Telephone Answering Devices (1976-2000) 0.0053 0.2188 0.4371

Ceteris paribus, a negative price coefficient increases diffusion while a

positive price coefficient retards diffusion. In five of the studied innovations, a

positive price coefficient was found to provide optimal results for curve-fitting.

These optimal parameters were used in accordance with the freedom Bass,

Krishnan, and Jain (1994) established for the price variable. This did not appear

to be a problem when the hundreds of models were generated.

However, during the analysis portion of the research, it became clear that

using a mixture of positive and negative price variables was problematic. The

104

Generalized Bass models (and GB variants) were significantly different from the
other models when parameters from an innovation with a positive price
coefficient were used with innovations that had an optimized negative price
coefficient. These differences resulted in poor showing (Table 67) by the two
models that used the price variable (the Generalized Bass model and the GB

vananfl.

Table 67: Sum of Squared Errors for All Forecasts

B BV GB GBV SL G BnC
65.2 65.7 74.9 75.4 64.6 66.2 65.9

 

Based upon these results, the Generalized Bass model and the GB
variant were not analyzed further since they were significantly less
accurate than the other models by over three standard deviations. Reliable
conclusions about the comparison of the Generalized Bass model with the other
five models should not be drawn from this research.

Researchers who conduct similar experiments are advised to constrain
the price variable to be negative. While this will result in sub-optimal curve-fitting,
the loss in accuracy would be relatively minor. Conversely, forecasts of other
innovations using only negative price variables should see gains in their
accuracy. It is expected that research done with the negative constraint on the
price coefficient would allow direct comparisons between the Generalized Bass

models and the other diffusion models.

105

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