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This is to certify that the

dissertation entitled

SPATIAL MODELING OF SEASONAL HOMES
IN THE UPPER GREAT LAKES STATES

presented by

Bradley Aric Shellito

has been accepted towards fulﬁllment
of the requirements for

 

 

 

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Major professor

 

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6/01 c:/ClFIC/DateDue.p65—p.15

 

SPATIAL MODELING OF SEASONAL HOMES IN THE UPPER GREAT LAKES
STATES

By

Bradley Aric Shellito

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
For the degree of

DOCTOR OF PHILOSOPHY

Department of Geography

2001

ABSTRACT

Seasonal home location is inﬂuenced by a variety of factors, including many
related to land use. Water bodies, natural areas, agriculture, and distance from cities are
some of the qualities that affect the location and distribution of seasonal homes. This
research examines the 1990 seasonal home distribution for the Upper Great Lakes States
of Michigan, Wisconsin, and Minnesota at a minor civil division (MCD) level.
Geographic Information Systems are used to construct independent variables over the
three state level. Modeling techniques, including the application of logit regression and
artificial neural networks, are used to examine this distribution. These models are used to
determine the principal predictors of seasonal home distribution in the region. The
research also serves as a test of the applicability of combining these modeling approaches
with GIS and recreational tourism related theory. Conclusions are drawn about the
principal predictors of seasonal home distribution as well as a comparison of modeling

approaches. Finally, future directions and expansions of this research are discussed.

For my parents, David and Elizabeth

ACKNOWLEDGEMENTS

I would like to extend my deepest thanks to the professors who have helped guide
me through this process. Grateful appreciation and thanks goes out to Dr. Bryan
Pijanowski for all of his help with the research and data involved with this project and for
all of his assistance and guidance over the last few years. Very special thanks also goes
to Dr. David Lusch for all of his help, direction and assistance, along with serving as
committee chair. Thanks also go out to Dr. Jon Burley, Dr. David Campbell, and Dr.
Daniel Stynes for invaluable assistance, advice, and patience in completing this research.

I would also like to thank Dr. Daniel Brown for all of his help and guidance
during my ﬁrst few years at MSU and the formative stages of this dissertation. Also,
thanks go to Dr. Michael Chubb for his help as well. Special thanks go to Mr. James
Biles for his endless patience as well as suggestions and advice regarding the statistics
and modeling approaches used in this project. Thanks for statistical help must also go out
to Dr. Bruce Pigozzi and Dr. Ashton Shortridge. Thanks also to Mr. Gaurav Manik and
Mr. Snehal Pithadia for their assistance with the neural networks used here.

Thanks also go out the people and agencies whose contributions to the data
sources made this project possible: Dr. Mike Vasievich of the US Forest Service and the
Great Lakes Ecological Assessment Project; Dr. Stuart Gage, Director of the
Computational Ecology and Visualization Laboratory; the Michigan and Minnesota
branches of RESAC; the Michigan and Wisconsin Departments of Natural Resources; the
MDEQ; and the NASA LULCC project.

Finally, I’d like to say thank you to Dr. Ron Shaklee, for starting me down this

road in the ﬁrst place.

iv

TABLE OF CONTENTS

LIST OF TABLES ............................................ vii

LIST OF FIGURES ........................................... viii

CHAPTER 1

INTRODUCTION ............................................ 1
Research Questions and Objectives ......................... 1
Deﬁnitions ............................................ 2
Format of the Dissertation ................................ 4

CHAPTER 2

LITERATURE REVIEW .............................................. 6
Introduction ........................................... 6
Theory in Geography .................................... 7
Land Use and Landscape Ecology .......................... 10
Seasonal Homes and Land Use ............................ 11
Seasonal Homes and Public Lands .......................... 16
Seasonal Home Development .............................. 18
Seasonal Homes’ Link to Recreation and Tourism ............. 21
Tourism Development and Land Use ........................ 22
Modeling Recreation and Tourism Issues .................... 23
Geographic Information Science ........................... 25
GIS and Recreational Tourism ............................. 26
GIS, Seasonal Homes, and Real Estate ...................... 27
Conclusion ............................................ 27

CHAPTER 3

STUDY AREA ............................................... 29
The Upper Great Lakes States and Seasonal Homes ............ 29
Spatial Distribution of Seasonal Homes ...................... 32
Conclusion ............................................ 35

CHAPTER 4

METHODS .................................................. 37
Introduction ........................................... 37
Modeling Framework .................................... 37
Unit of Analysis ........................................ 39
Dependent Variable ..................................... 40
Spatial Autocorrelation ................................... 40
Independent Variables ................................... 41
Development of Independent Variables ...................... 43
Correlation of Dependent and Independent Variables ........... 51
Principal Components Analysis ............................ 51
Logistic Regression and the Logit Model ..................... 53
The Artiﬁcial Neural Network Model ........................ 54

Conclusion ............................................ 57

CHAPTER 5

MODEL RESULTS ........................................... 58
Introduction ........................................... 58
Spatial Autocorrelation ................................... 58
PCA Results ........................................... 60
Logit Model Results ..................................... 63
Neural Network Model Results ............................ 64
Examination of Independent Variables ....................... 64
Logit Model ............................................ 65
Neural Network Model ................................... 65
The Principal Predictors .................................. 67
Spatial Distribution of Seasonal Homes ...................... 67
Model Comparison ...................................... 69
The Spatial Error Signal and Residual Analysis ............... 71
Logit Estimates vs. Neural Network Estimates ................ 77
Conclusion ............................................. 77

CHAPTER 6

DISCUSSION ................................................ 79
Introduction ........................................... 79
Dependent Variable ..................................... 79
Independent Variables ................................... 82
Bias in the System ..................................... 84
Methods and Model Building .............................. 89
The Science Under the System ............................. 91
Implications for Land Use and Potential Land Use Change ...... 93
Conclusion ............................................ 98

CHAPTER 7

FUTURE DIRECTIONS ....................................... 99
A Baseline Approach .................................... 99
Regionalization ......................................... 101
Temporal Modeling ..................................... 102
Adapting for Land Use Change ............................ 105
Other Applications of the Framework ....................... 108
Methodological Exploration ............................... 109
Spatial Statistics Approaches .............................. 1 1 1
Conclusion ............................................ 1 12

BIBLIOGRAPHY ............................................ 113

APPENDIX A: Independent Variable Maps ........................ 126

vi

Table 3.1:
Table 3.2:
Table 4.1:
Table 5.1:
Table 5.2:
Table 5.3:
Table 5.4:
Table 5.5:
Table 5.6:
Table 7.1:

LIST OF TABLES

Metro MCDs and their numbers of seasonal homes, 1990 ..... 34
Types of MCDs and the average % seasonal they contain ..... 35
Bivariate Correlations ................................. 52
Initial Eigenvalues .................................... 6O
PCA Rotated Component Matrix ........................ 61
Initial beta values and solved values ...................... 63
Reduced variable runs of neural network .................. 66
Comparison of model rankings of principal predictors ........ 67
Mean Absolute Deviation of the modeling approaches ....... 71
US Housing and Seasonal Homes by year ................. 103

vii

LIST OF FIGURES

Figure 3.1: # of seasonal homes in the Upper Great Lakes States, 1970-1990. 31

Figure 3.2: Percentage of the total housing stock that is seasonal .......... 33
Figure 4.1: Basic Architecture of a MLP Neural Network ................ 55
Figure 5.1: Variograrn of the dependent variable (distance in meters) ....... 59
Figure 5.2: Variogram of the residuals of the dependent variable (in meters). 59
Figure 5.3: Logit and Neural Network Residuals ....................... 72
Figure 5.4: Logit Residuals with Public Land Boundaries Overlayed ....... 73
Figure 5.5: Selected Residuals ..................................... 74

Figure 7.1: # of seasonal homes in the United States, 1940-1990 .......... 104

viii

Chapter 1: Introduction

Research Questions and Objectives

The notion of having a second residence, one that is only used part-time, is
extremely attractive to many people. This concept of a part-time residence encompasses
a spectrum of housing types, ranging from a lakefront house, to a time-share
condominium, to a simple hunting cabin. These second (or seasonal) homes are
frequently used as vacation homes, perhaps for weekend getaways or longer trips.
Seasonal homes are also used as a base from which to enjoy amenities (such as hunting,
ﬁshing, or boating) or a place to store materials to be used at another time (such as a
snowmobile or a boat). Seasonal homes also have the potential to transition to a new
permanent home for retirees.

Numerous factors play into the location of seasonal homes. Some of these depend
on the personal needs, wants, and desires of the person buying the seasonal home,
including income level, land price, and reasons for why this second home is desired.
However, several other destination—based factors play a role in the location of seasonal
homes, involving landscape features and land use characteristics. For instance, the
growth of urban land use may be seen as a “push” factor for people to leave a highly
populated urban area for more rural settings. Likewise, land cover features such as
forests, water bodies, and more natural environments may be seen as “pull” factors to
bring seasonal homes into these areas.

This dissertation research will bring these concepts of seasonal home location

together with land use in a geographic context. This will aid in answering the questions

of (1) what are the principal predictors of seasonal home location and (2) can this link
between the pattern of land use and landscape features and the process of seasonal home
distribution be modeled in a spatial GIS-based framework?
There are several objectives to this project:
1. To describe the spatial distribution of seasonal homes within the Upper Great Lakes
States region of Michigan, Wisconsin, and Minnesota.
2. To identify the principal predictors of seasonal home distribution in this region.
3. To test a GIS-based modeling framework and various modeling approaches in
examining the relationship between the patterns on the landscape and seasonal home

distribution.

Deﬁnitions

In the 1990 census, second homes are labeled as homes kept for “seasonal,
recreational, or occasional use.” This is deﬁned as: “vacant units used or intended for use
only in certain seasons or for weekend or other occasional use throughout the year.
Seasonal units include those used for summer or winter sports recreation, such as beach
cottages or hunting cabins. Seasonal units may also include quarters for herders or
loggers. Internal ownership units, sometimes called shared ownership or time-share
condominiums, also are included here” (Census 1990). (The Census Bureau seems to
label these factors as “vacation homes” in the current analysis (Census Bureau 2000)).
Other categories not included under this deﬁnition are housing units classiﬁed as: rent,

for sale, rental or sold — not occupied, migrant workers, and other vacant (Census 1990).

There are several concerns in deﬁning secondary and seasonal homes including:
(1) determining the difference between rental properties and permanently owned ones;
(2) distinguishing between recreational homes and migrant housing; and (3) conversions
of second homes to permanent ones. The third situation is one of individual choice and
can change over the course of time. The temporal or psychological factors involved with
this change are outside the scope of this project (see Stewart 1994). To adequately
address the problems of the ﬁrst and second situations, as well as to provide a clearer
deﬁnition of second homes for this project, the deﬁnitions and framework used by Spotts
(1991) will be used here. The US Census Bureau contains two labels for housing units in
its 1980 census: (1) “vacant seasonal and migratory” and (2) “vacant year round — held
for occasional use.” Spotts (1991) combines the counts from these two categories (which
includes recreational cabins, cottages, condominiums for rent, migratory worker housing,
time-share condos, shared-ownership condos). The Census Bureau also notes that
seasonal homes may fall into either category, thus the numbers from both must be used.
Of these, only migratory housing is not needed in the analysis. However, as Spotts
(1991) notes, there are so few of these type of housing units that their inclusion in a
statistical analysis is inconsequential. For instance, in the 1970 census, migrant housing
made up only 3% of all secondary homes in the entire US. However, this issue of
migratory housing in the seasonal home deﬁnition was excluded in the 1990 Census.

For the purposes of this dissertation, the term “seasonal homes” will be used to
refer to the object of study, and can be considered interchangeable with “second home“

and “vacation home.”

Format of the Dissertation:

The chapters of this dissertation are organized as follows:

Chapter 2 discusses where this literature that this project draws ﬁ'om. First, it
examines the role of how this research ﬁts in the overall geographic theory and literature.
It then examines the development of seasonal homes in the context of the literature.
Several other branches of literature pertaining to seasonal home development are touched
on as well, including amenity migration, real estate, and public lands. The role of land
use and land cover in the seasonal home development process is examined as well. The
linkage between seasonal homes and areas of recreation and tourism is examined as well.

In addition, further literature describing recreational tourism as a land use and the
associated connections between tourism development and land use is examined, as well
as a brief look at human / environmental interaction based on the paradigms of landscape
ecology and its relationship to this project is also reviewed. The role of Geographic
Information Systems as well as its connection to seasonal homes and tourism modeling
issues is also examined.

Chapter 3 discusses the study area of the Lake States of Michigan, Wisconsin, and
Minnesota in terms of their potential for seasonal home and recreational tourism
development. The development of seasonal homes over time in these states is examined,
as well as the geographic and land use factors, in these states which contribute to the
process.

Chapter 4 discusses the methodology and approach to the problem, in terms of the

development of variables and models. The GIS framework used in this project is

examined, along with descriptions of the variables and their construction, along with
examination of the modeling approaches.

Chapter 5 looks at the results of the models and what these results mean in terms
of the objectives stated above.

Chapter 6 provides a discussion that places this study back within the literature
and gives further insight into the process of seasonal home location. The role of this
project in the greater body of theory is examined, as well as the importance of this project
in practical application. In addition, the broader implications of this project in terms of
concepts of development and land use change are examined. The modeling approaches
are examined and conclusions drawn about them. Some limitations of the project are also
discussed.

Finally, Chapter 7 details future directions that can be developed from this

research.

Chapter 2: Literature Review

Introduction

This project employs many concepts from the discipline of geography, but is
grounded within three bodies of literature and theory: landscape ecology, tourism
development, and geographic information science. Each of these broad areas of
knowledge are not easily deﬁned or bounded, leading to considerable overlap between
ﬁelds. The object of this review is not to provide an in-depth look at all literature
available on these areas, but to examine the research in them pertinent to this project.

Tourism development literature encompasses a wide variety of topics and ﬁelds.
Seasonal home literature is primarily included under this umbrella, yet there are other
branches of literature pertinent to the seasonal home process, including amenity
migration.

Likewise, landscape ecology is a wide ﬁeld with a multitude of deﬁnitions, which
represents the study of human / environment interactions. The focus here is to touch on
some of the relevant theory of this ﬁeld and how it applies to the problem at hand in
terms of analyzing pattern and process.

Finally, geographic information science encompasses a wide variety of ﬁelds as
well. The aim of this section is to examine the nature of the “science” and the “system”
of GIS, as well as its applicability to problems of spatial distribution, tourism, and

seasonal home questions.

Theory in Geography

This project has connections to geographic theory as well as several broader
implications and links to other branches of theory. In Explangtion in Geography, David
Harvey (1969) examines Haggett’s (1965) groupings of the ﬁve major themes in
geographic theory. These are: areal differentiation, the landscape, man-environment,
spatial distribution, and the “geometric” theme. As Harvey (1969) notes, the ﬁve themes
are “not mutually exclusive or entirely inclusive” of all branches and studies of
geography, but provide some operational parameters and deﬁnitions from which to form
concepts. The spatial distribution theme can be seen to encompass areas of locational
analysis and providing a description and explanation of the distribution of a phenomenon.
In other words, this theme may be seen as trying to describe and explain why things are
located where they are.

Of these broad areas, this study ﬁts best within the “spatial distribution” theme. It
focuses on the concepts of where seasonal homes are located (or not located) and why
they are where they are. However, this project has relations to the “man-environment”
theme of the literature, typiﬁed as a view of geography as human ecology. Harvey
(1969) notes that this may be the true overriding theme that lies at the heart of geography.
However, Harvey does recognize the need for interdisciplinary research in the overall
advancement of knowledge. The link between humans and the land is often associated
with the locations of man in relation to land use.

Early work in linking location and land use came from David Ricardo’s theories
of land rent (referenced in Barlowe 1986). Here, the concept of rent referred to a surplus

gained from a factor of production that is a result of a locational advantage. Ricardo

attributed land rent to issues of the fertility of the land — in which only the most fertile
lands would be used and rent would arise on these fertile lands only when increases in
demand lead to the use of less fertile lands (referenced in Barlowe 1986).

This connection between theories of land use and location continued in the work
of Von Thunen (von Thunen 1826, referenced in Haggett et al. 1977). Von Thunen’s
model of rural land use examined the city in terms of an “isolated state” with no outside
inﬂuences (a pre-industn'alization notion). The model shows concentric rings emanating
outward from the monocentn'c city to denote distinctive “zones” of land use (including
dairying and farming, forest, ﬁeld crops, and ranching). This model assumes that the
farmers surrounding the market will produce crops with the highest value (or the highest
“land rent”). Though outdated today, the Von Thunen model was an early theoretical
model of the location of the city and the role of the area surrounding that location.

This location theory was followed by Weber (1909, referenced in Haggett et a1.
1977). Weber’s theory focuses on locating industrial sites to minimize distance and
unnecessary movement. This theory showed that industrial sites will be located nearest
the centers for raw materials, thus reducing cost and movement for industrial
development.

Location theory and analysis was furthered by the work of Walter Christaller
(1933) who developed Central Place Theory. This concept was used to explain the size
and location of cities that specialize in selling goods and services. As cities would be
centrally located, they are assumed to be “central places.” He introduced two concepts:

threshold (the minimum size market needed to keep a city in business) and range (the

maximum distance people will travel to purchase goods). Once a threshold size is
established, the central place will try to expand out to the limit of the range.

Christaller also makes the distinction between “higher order” central places (those
areas which provide more goods and services than other areas) and “lower order” central
places (which provide less goods and services, but whose goods and services are
consumed more frequently). He posits that higher order places are more widely
distributed and fewer in number than lower order locations.

Losch (1940) built off of Christaller’s work by examining areas as a continuous
series of centers rather than steps in a hierarchy. It is noted (Haggett et al. 1977) that
Losch’s model produces patterns more like what exists in reality than Christaller’s.
Likewise, Pred (1966) extended Christaller’s theory by examining the movement of
goods and services between the ranks of cities rather than between cities themselves.

Another major contribution to location theory came from William Alonso (1964)
with his theories of land rent. Alonso’s theory postulated that each of three types of land
use (commercial, industrial, and housing) have a certain yield of rent for any given
location, and that these three land uses are in competition for one another. The theory
shows that commercial and industrial land uses will often be closer to the central city,
along with lower-income housing. More expensive housing, which does not need a
strong connection to the central city, will be found on the outskirts of the city where the
cheaper land may be found. Thus, a segregated land use system will be created.

All of these theories relate land use and location in some way. According to
theory, where certain types of areas (i.e. residential or industrial) are found are reliant

about the locations of surrounding patterns of land use. Degrees of urbanization and

varying types of urban development rely on spatial patterns and usually a link to the
landscape. It is this basic theory of spatial distribution, location theory, and its relation to
land use that this project draws upon. The historical work in geography provided studies
of “idealized” environments to draw conclusions about linkages between land use and
location. However, this work has been expanded on by more recent theorists to
encompass “real world” concepts and ideas into the theory. It is this linkage between the
location of places and their relationship with elements of the landscape or land use that is
part of the theoretical background of this project. In this fashion, this dissertation is set
within the context of geography as a project to explain why things are where they are.
This over-arching umbrella of location can be seen as one of the core tenets of geography

(i.e. Harvey 1969, Haggett et al. 1977).

Land Use and Landscape Ecology

The study of land use in geography often falls under the umbrella of landscape
ecology. The term “Landscape Ecology” was ﬁrst coined by Carl Troll (1939) in his
paper examining landscapes of Africa through aerial photography. He described it as
"...the study of the entire complex cause-effect network between the living communities
and their environmental conditions which prevails in a speciﬁc section of the landscape...
and becomes apparent in a speciﬁc landscape pattern.” (Troll 1939, quoted in Thomas
2000). Zonneveld (1995) notes that this was an attempt by Troll to create “a marriage
between biology and geography.” Later works would further embellish Troll’s basic
deﬁnition and aims. Vink (1983) describes landscape ecology as “the study of

relationships between phenomena and processes in the landscape or geosphere including

10

the communities of plants, animals, and man.” Forrnan and Godron (1986) deﬁne
landscape ecology as “a study of the structure, function, and change in a heterogeneous
land area composed of interacting ecosystems.” Naveh and Lieberman (1984) describe
landscape ecology as “the recognition of the dynamic role of man in the landscape and
the quest for the systematic and unbiased study of its ecological implications.” Likewise,
Sanderson and Harris (2000) note that “it (landscape ecology) deals withthem (humans)
explicitly as entities and forcing functions on the landscape.” From these deﬁnitions,
landscape ecology theory can be broadly interpreted as a study of the interaction between
humans and the environment.

By combining the science and theory of these two broad ﬁelds, landscape ecology
seeks to deﬁne the spatial patterns of the landscape and to also explain the processes
behind these patterns, as well as the interactions resulting from them. The “ecology” in
the ﬁeld comes from the study of “the house of the Earth” (Zonneveld 1995). As Urban
et al. (1987) note, “pattern is the hallmark of the landscape.” As Davis (1976) notes,
geography remains a strong force in controlling land development and use. This project

focuses on the issues of spatial distribution of land use and seasonal homes.

Seasonal Homes and Land Use

A wide variety of landscape features contribute to the location of seasonal homes.
Coppock (1977) notes that, across the world, the main controlling factors of seasonal
home distribution appear to be: the distance from major population centers; the quality
and character of the landscape; the presence of sea, rivers, or lakes; the presence of other

recreational resources; the availability of land; and the climates of importing or exporting

ll

regions. Spotts (1991) notes that seasonal homes are concentrated in areas with lakes,
rivers, forests, and other natural resources.

Water bodies provide access for a wide variety of outdoor recreational activities
such as ﬁshing, boating, and swimming. Lakes are a strong factor in seasonal home
development (Coppock 1977, Stynes et al. 1995). Chubb and Chubb (1981) note that the
availability of sites along water-oriented areas in the United States and Canada such as
lakes, rivers, or the Great Lakes has resulted in the development of seasonal homes at
these locations. In a study of Michigan seasonal home owners, Tombaugh (1970) found
that 55% owned a seasonal home on an inland lake, 24% on the Great Lakes, and 10% on
a river or stream. In a study of three counties in the northern Lower Peninsula of
Michigan, Gartner (1987) found that 57% of seasonal homeowners have their homes
located on a water resource. Also, the Great Lakes provide a wide range of recreational
opportunities (Chubb 1989), while lakes with houses built around them may have private
boat docks or public launching facilities. Stynes and Safronoff (1982) found that 30% of
Michigan boat owners and 80% of those from outside the state owned seasonal homes
within Michigan.

Second homes are found primarily in areas away from the “big cities” and heavily
populated / dense urban areas (Coppock 1977). Coppock (1977) notes that the majority
of seasonal homes appear to be 100 to 150 miles away from population centers. In
Michigan, Tombaugh (1970) found that 70% of a sample of seasonal homes were within
200 miles of the owner’s ﬁrst home. Thus, seasonal homes are often found outside the

more urban areas in places of low population, i.e. rural or forested areas (Coppock

12

1977). The remoteness of these rural areas (Keller 2000) provides part of the draw of the
area.

Previous models of second and seasonal home use in Canada (Lundgren 1974)
identify seasonal home developments appearing away from an urban center and slowly
being subsumed by growing urban development over time. Seasonal homes are often
developed at areas away from crowded or overly developed urban areas (Lundgren
1974). Thus, the surrounding few miles is rural, but modern amenities are within a short
drive. This boundary between urban and rural areas is referred to as “living space”
around the cities (Cracknell 1967) or “recreation hinterlands” (Mercer 1970) for
enjoyment of non-urban recreation. These more rural communities feature low
population but still have some amenities and services on hand that residents of an area
would require — i.e. grocery stores, gas stations, garages, bars, small restaurants, or local
stores (Hart 1998). Neamess to medical treatment (i.e. health care facilities such as
hospitals) plays a part in seasonal home development, particularly in retirement home
communities (Hart 1998). An overabundance of “commercial tourism” sites (i.e. hotels,
theme parks, or prime commercial tourist attractions) may be a detriment to seasonal
home development (Hart 1998). It is also noted that few seasonal home developments are
occurring in primarily agricultural regions (Chubb and Chubb 1981).

Travel to and from seasonal homes also plays a part in the location of seasonal
homes. Coppock (1977) notes that accessibility depends on the quality and density of the
road network. The use of major highways reﬂects the movement of a large number of
people on direct routes (Wilder 1985). This could also be seen as reﬂective of the access

needed to areas or a “distance to markets” function, allowing second home owners the

13

privacy of their seasonal home while still maintaining access to nearby roads or health-
related facilities. “Easy travel” was rated the most important of the variables in the
selection process by seasonal home buyers (Coppock 1977). Travel to and from seasonal
homes can generate frequent trips, leading to a necessity for hi gh-volume travel
accessibility (Page and Getz 1997).

Seasonal homes are used in conjunction with winter sports, including
snowmobiling, cross country skiing, downhill skiing, sledding, tobogganing, and ice
skating. This has led owners of seasonal homes to keep their homes open and available
well into the winter months to use as a place to stay while snowmobiling or skiing (Hart
1998)

Natural settings play a role in seasonal home location. Forested areas provide a
great deal of outdoor recreation opportunities, and proximity to them is part of seasonal
home development (Stynes et al. 1995). There are numerous forest-oriented seasonal
homes within the United States (Chubb and Chubb 1981) providing homeowners with a
variety of recreational or relaxation opportunities. Many people look to nature and
outdoor recreation for peace of mind and a return to health (McHarg 1969). Factors such
as these are difﬁcult to quantify as landscape variables, but simulations of this aesthetic
quality can be created. For instance, Loomis and Walsh (1997) note that size of an area
(such as forests) is a good measure of its attractiveness. Similarly, forested areas provide
a great deal of outdoor recreation opportunities, and proximity to them is part of seasonal
home development (Stynes et al. 1995). Higher elevations (Chubb and Chubb 1981) and
the variability of the landscape are factors in inﬂuencing the choice of location of

seasonal homes. This desire for aesthetically pleasing landscapes may be linked to

14

seasonal home purchasers seeking a feel for a rural lifestyle or an alternative to an urban
one (Page and Getz 1997).

Several studies have examined the attributes that contribute to an aesthetically
pleasing landscape. Shafer et al. (1969) note the importance of vegetation within a view
along with water being important factors. These two factors were also prominent in the
Landscape Preference Model (Shafer and Tooby 1973) that identiﬁed the quantitative
variables in a natural landscape that were signiﬁcantly related to public preferences for
that landscape. In a study of Lake Michigan beaches, Peterson and Neumann (1969)
identiﬁed scenic natural beaches and the presence of trees and natural grth as factors
contributing to the aesthetic quality of an area.

More recent studies in attempting to quantitatively model the landscape factors
contributing to an aesthetically pleasing scene have incorporated GIS techniques. Bishop
and Hulse (1994) present predictive equations of an area’s aesthetic quality based on
GIS-derived variables. Among the factors they designate as aesthetically pleasing are:
rivers, amount of high slope, orchards, amount of forest, and range of relief. Similar
factors were found by Crawford (1994) through the use of remote sensing techniques:
rugged terrain, heavy tree cover, natural activities, outlook, diversity of landscape
features, and orderly arrangement of these factors. In the visual preference model
(Steinitz 1990) it was found that coastal development with a “historical character,” water
bodies, long distance views, a folded landscape (such as mountains or islands) and a
diverse and well maintained vegetation distribution were all factors contributing to
aesthetically pleasing landscapes. Also, Steinitz (1990) notes the sense of “mystery”

being of great importance in a pleasing scene. This “mystery” feature was later mapped

15

(Bishop and Hulse 1994) and found to be made up of “locations on roads or trails with
curvature and the edge zones between forest and the open land or water.”

Many factors have been identiﬁed that are associated with negative impressions
of the aesthetic quality of an area. Large industrial structures and areas of industrial or
commercial development (Crawford 1994) have been cited as being unpleasing to view in
a natural environment. Likewise, Steinitz (1990) notes that people do not wish to see a
developed or urbanized landscape, evidence of crowded use, or tourist—oriented
commercial development. Burley (1997) found that an abundance of humans, vehicles,

buildings, and polluted and eroded land were considered undesirable factors.

Seasonal Homes and Public Lands

The amount of public land (inferring related outdoor recreation amenities such as
hunting, ﬁshing, hiking, etc.) available is a factor in seasonal home location (Coppock
1977). These lands are classiﬁed as National Parks, National Forests, National
Lakeshores, State Parks, State Wildlife areas, and County parks. However, development
of urban land use occurs within these areas — in fact, whole sections of the Huron
National Forest contain towns, restaurants, bars, homes, farms, etc. Public lands provide
a host of opportunities including hiking, hunting, boating, ﬁshing, and camping.

There are several considerations to account for when dealing with public lands.
First, urban and commercial development is often allowed on public lands. Thus, public
lands cannot be excluded from consideration for seasonal home locations. For instance,
the National Forests Ownership Adjustment Program (USDA 1986) was created to

rearrange the ownership pattern of privately held lands within national forest boundaries

l6

into more cost-effective and useable forms. The program seeks to take areas that are
“low-priority” (i.e. not semiprimitive wilderness, recreational areas, or wildlife habitats)
and exchange them for privately held lands that meet these criteria (USDA 1986). These
non-priority lands are then used to facilitate community expansion, commercial,
industrial, and residential purposes (USDA 1975). Thus, active building will be
occurring in certain sites within public land boundaries.

Second, there may be some question as to the actual location of public land
boundaries. Lands within the Lake States were originally surveyed by the General Land
Ofﬁce more than 120 years ago. However, due to natural decay, ﬁres, and human
destruction, many of the originally surveyed corner monuments have been lost (USDA
1975). With the questionable or unknown locations of legal markers, as well as the errors
that may have been produced with the original surveying methods, a degree of
uncertainty exists as to the true boundaries of public lands.

Lastly, public lands contain seasonal homes and thus must be included in any
analysis of the subject. Seasonal homes within public land boundaries are ofﬁcially
classiﬁed as “recreation residence sites” (USDA 1986). Permits are annually issued (and
re-issued) for existing summer home tracts (USDA 1975). In fact, there are speciﬁc
regulations concerning how far recreational amenities (such as snowmobile or ATV
trails) may be constructed from seasonal residences (USDA 1986).

However, there are strict controls on the amount of land that can be developed
within public land boundaries. Also, one of the goals of the National Forests
Landownership Adjustment Program is not only to acquire priority lands, but to acquire

contiguous areas of 2500 acres or more WSDA 1986). Thus, while development is

17

allowed (for instance, towns containing schools, fast food restaurants, and other
commercial developments exist in the heart of the Huron National Forest), it is limited to

certain areas.

Seasonal Home Development

The notion of owning such things as a summer cottage, time—share condo, hunting
cabin, or a part-time residence in another location away from home is a driving force in
new development (Coppock 197 7). These properties can also be referred to as “temporal
residences” (Ragatz 1969). Assuch, seasonal homes need to be taken into account when
dealing with issues of tourism development. Stynes et al. (1995) cite Waters’ (1990)
ﬁndings that a failure to account for seasonal homes in recreational tourism studies may
omit as much as 50% of domestic tourist activity.

Qualities such as market factors, supply and demand (Loomis and Walsh 1997),
land valuation, and housing prices are all part of the decision making process of selecting
a seasonal home. However, many of these choices are subjective and speciﬁc to the
individual buyer. As Stewart (1994) notes, “real estate developers may aggressively
market certain developments as ‘seasonal home areas,’ but a decision maker’s
preferences for natural and social settings, recreational activities, their willingness to
travel, and their ﬁnancial resources have more to do with determining what is and what is
not a seasonal home area.” While these type of variables are certainly part of the
decision making process, their effect is a highly individual one — for instance, a wealthy
person looking to purchase a seasonal home will not be constrained by land price or

market ﬂuctuations.

l8

Manson and Groop (2000) have noted that migration patterns in the United States
are of people moving out from the cities. They ﬁrst move from the cities to the suburbs
and then to rural (or exurban) areas. Likewise, Stewart (2000) notes a high rate of net in-
migration to rural parts of the United States containing scenic or recreational amenities.
This form of amenity migration is restructuring part of the rural landscape in the United
States. No single factor can be distinguished as spurring amenity migration, but these
include individual decisions (Williams and McIntyre 2000), choices made by the elderly
or retired (Longino 2001), or tourism and seasonal home purposes (Stewart 2000).

Development of seasonal homes may be traced back to the construction of
primitive hunting cabins or lodges (Hart 1998). These were places for hunting, ﬁshing,
and “getting awayf’ from the busy lifestyle of civilization. As owners aged, these seasonal
retreats were often winterized and turned into permanent residences for retirement (Hart
1998). Retireesihave seen seasonal homes turning into their permanent homes and have
sometimes purchased their second home with this purpose in mind (Stewart 1994).
Similarly, seasonal homes can be seen as a shelter for access to nearby amenities or the
home can be the actual focus of the recreational activity (Coppock 1977). In a classic
feedback loop, some areas may have developed in response to seasonal homes, or some
areas may have seen increased seasonal home development as a result of increasing
development and popularity of a site.

Purchasing a seasonal home brings with it a number of changes, not only to a
destination, but also to a person. For instance, the purchase of a seasonal home will
likely inﬂuence the travel plans of a family (Stewart 2000). With the median price of a

seasonal home (in 1999) being $127,800 (NAR 2000) this represents a signiﬁcant

19

investment for the buyer, beyond the other costs of property taxes and maintenance. The
very nature of a seasonal home indicates that it will only be used for part of the year,
adding on ﬁrrther costs for upkeep and security for the property during the times of the
year that it stands vacant. Thus, the purchase of a seasonal home is not a lightly-made
investment, and will probably become the vacation destination of choice for the
purchaser for some time to come. This would cause a multitude of vacation trips to and
from the seasonal home, or the use of the seasonal home for an extended period of time
throughout the year.

The National Association of Realtors categorizes seasonal home buyers in 1999
as (NAR 2000): having a median income of $68,000 and a median age of 43. Of these,
79% were married couples. From purchases made by the “baby boom generation”, an
estimated 100,000 to 150,000 seasonal homes will be added each year.

As the number of seasonal homes in an area increases, there is an increase in
population, and thus an increase of growth and development of the area. For example, in
1990 there were estimated to be more than 223,000 seasonal homes in the state of
Michigan (Stynes et al. 1995), approximating 6% of all housing units in the state. Stynes
et al. (1995) estimate that the economic impact related to these seasonal homes is
between $60 to $75 million per year. In part, this may be due to seasonal homes
facilitating longer stays in regions (Page and Getz 1997). Wisconsin seasonal home
residents spent an estimated $2500 - $3500 per homeowner annually (beyond property
taxes) in the area surrounding their seasonal home (F edgazette 1997).

Seasonal home development brings with it a variety of impacts. Rural forest land

is being consumed to make way for new seasonal homes (V asievich 1999). Seasonal

20

homes built on a lakefront are contributing to problems including erosion, destruction of
shoreline vegetation, and loss of wildlife habitat (Gartner 1987). Seasonal homes in the
form of large recreational subdivisions cause strains on an area’s water supply and the

creation of extended road networks (Stroud 1983).

Seasonal Homes’ Link To Recreation and Tourism

As Stewart (2000) notes, seasonal home ownership is a step between tourism and
migration. To utilize seasonal homes, people are migrating from their permanent
residence to a secondary one for a certain amount of time. This could be for a day trip, a
weekend, a longer vacation, or for entire seasons (i.e. spending the winter in a warmer
climate or the summer in a cooler one). Travel is involved with this temporary migration,
which creates a link to tourism. As Chadwick (1994) notes, travel and tourism are words
to describe “1) the movement of people, 2) a sector of the economy of an industry, and 3)
a broad system of interacting relationships of people, their needs to travel outside their
communities, and services that attempt to respond to these needs by supplying products.”

This broad concept is broken down further with several deﬁnitions of what really
constitutes “tourism.” The World Tourism Organization (WTO) deﬁnes tourism as “the
activities of a person travelling outside his or her usual environment for less than a
speciﬁed period of time and whose main purpose... excludes only migration for
temporary wor ” (Chadwick 1994). The National Tourism Resources Review
Commission deﬁnes a tourist as a person who travels away from home at least 50 miles

(referenced in Chadwick 1994). Similarly, the United States Travel Data Center uses 100

21

miles as the cut-off for travel and requires at least one night’s stay in a destination to be
considered a tourist (Chadwick 1994).

While these deﬁnitions have different demands on factors such as the distance
traveled and the time spent at a destination, they all agree that tourism involves a
movement (or migration) of people outside their usual territory for short-term (or non-
permanent) travel. Thus, as seasonal homes constitute a temporary migration away from
one’s permanent residence (generally for purposes of recreation), seasonal home owners
can be classiﬁed as tourists. Issues of tourism location and development are related to

those of seasonal homes.

Tourism Development and Land Use

Recreational tourism-based activities can be seen as a speciﬁc type of land use.
However, the use of land for recreation or tourism purposes can sometimes be in conﬂict
with other needs or requirements for the land. McKercher (1992) describes the
competition for land use between logging companies and wilderness outﬁtting industries.
He notes that unlike harvesting operations that may only have a short term impact on land
use, ”once a wilderness area is accessed, it is accessed forever” (McKercher 1992).
Roehl and F esenmaier (1987) also point to land use conﬂicts occurring between areas of
designated wilderness and tourist-based land uses. Construction of structures requires a
permanency of land utilization (McKay 1987) that is often irreversible. Davis (1976)
notes that land uses such as urbanization, draining of coastal areas or inland lakes, and

mining and extractive practices carry an irreversible consequence for the environment.

22

Butler (1980) notes that recreation and tourism areas tend to follow a life-cycle
which begins with initial interest and usually ends with the stagnation and decline of the
area. Tourist destinations advance through this life-cycle as time progresses. Thus,
initially, there tends to be an increase in the usage of land for recreational tourism
purposes over time. At a certain point of development, some areas stagnate to the point
of decline due to the overdevelopment of the area (Wheatcrot’t 1991). Many areas face
the degradation of the resource that was the original initial attraction. In some ways, this
eventual decline can be seen as “self destructive” (Holder 1988): as tourists came to the
area the growing development in response to tourism brought the area to the “decline”
stage of the life-cycle. Damage to these resources can threaten the economic viability of
tourism in an area (Butler 1991). However, the stagnation of an area can often lead to
redoubled efforts to try and attract new tourists (Cooper and Jackson 1989) by

reinventing the area as a new concept.

Modeling Recreation and Tourism Issues

Frameworks have been constructed to model the changes that areas undergo in
response to tourism development, but the spatial land use component is not present. The
Destination Life Cycle Model (Butler 1980) uses the concept of product life cycle to
reﬂect the changes that a tourist destination goes through ﬁom its inception to the ‘end’
of its ‘lifespan.’ The Destination Life Cycle is conﬁgured as a plot with time on the x-
axis and number of tourists on the y-axis, with the plotted line reﬂecting the many stages
a destination passes through: from exploration through consolidation and ﬁnally to

eventual decline or rejuvenation.

23

Similarly, Miossec’s (1976, referenced in Pearce (1989)) model of development
reﬂects the changes to a destination, but focuses on the result of tourism development.
By taking into account factors such as the number of facilities, their transportation
infrastructure, the behavior of tourists, and the attitudes of decision makers, Miossec was
able to provide a model of the changes that a destination will go through over a series of
stages. Thurot’s (1973, referenced in Pearce (1989)) process is similar; it typiﬁes the
phases a destination undergoes from the discovery of the area through its saturation.
Gormsen (1981, referenced in Pearce (1989)) developed a representation of the increase
in the number and type of accommodations in international seaside areas. Plog (1973)
conceived a typology of tourists ranging from allocentrics (explorer types) on one end of
the continuum to psychocentrics (stereotypical mass tourists) on the other end. In this
way, the grth and development of an area is typiﬁed by the personality type of tourists
it attracts. Also, the Community Options model (Talhelm et al. 1991) uses the STELLA
modeling software to predict changes to a community based on possible recreation or
tourism-related developments over a set time span (30 years). However, the Community
Options model (and STELLA itself) are non-spatial in nature. None of these models deal
speciﬁcally with spatial relationships in the areas under development pressure.

Beyond tourism-speciﬁc models of development, several other applications of
statistical techniques to travel-based models exist. Wilkinson (197 3) lists several
distance-based economic and transportation based models (including time series
projection and gravity models) and their relevance to tourism modeling. Similarly, Wolfe
(1972) describes a variation on the gravity model called the inertia model, but notes it is

only useﬁrl within a narrow range of distances. The gravity model was also applied to

24

describing and predicting intraurban recreational travel (McAllister 1977). Modeling of
the spatial nature of recreation and tourism also comes out of applications of discrete
choice modeling. Haider and Ewing (1991) apply discrete choice modeling techniques to
simulate the choices made by tourists among several Caribbean islands. Stopher and
Ergun (1982) used two-way segmentation to analyze the behavior of persons
participating in urban recreation. Stynes and Peterson (1984) provide a review of logistic
modeling techniques and possible applications to modeling choices of recreation. There
are many more examples beyond these, but this paragraph simply provides a broad look

at some representative publications.

Geographic Information Science

Geographic Information Systems have various deﬁnitions (Coppock and Rhind
1991, Johnson et al. 1987, Laurini and Thompson 1992, Maguire 1991), yet there are
several common themes among them. Geographic Information Systems are deﬁned as
the hardware, software, and related materials that deal with issues of spatial or
geographic analysis and spatial data handling. Marble and Sandhu (1994) state that GIS
deals explicitly with spatial information. Issues such as spatial data capture,
manipulation, overlay, visualization, and analysis are all part of GIS.

While the system itself, such as the Arc/Info software package, can be seen as a
tool, and Goodchild (1990) calls the system a “toolbox” from which to solve spatial
problems, the distinction must be made between the Geographic Information System and
the Geographic Information Science that underlies it. A tool relies upon some sort of

knowledge, science, or theoretical underpinnings to function. By way of analogy,

25

mathematics would be the science, while a calculator would be the tool used to aid in the

implementation of that science.

Goodchild (1992) discusses the main issues or components of a perceived

Geographic Information Science as follows:

1.

2.

7.

8.

Data collection and measurement
Data capture
Spatial statistics

Data modeling and theories of spatial data

. Data structures, algorithms, processes

Display
Spatial analysis

Management and ethics

In all cases, these subjects are studied from a spatial perspective. Issues such as spatial

autocorrelation (e. g.. Grifﬁth 1987), spatial visualization and rendering (e. g. Monmonier

1993, Orland 1994), and algorithm design (e.g. Openshaw and Clarke 1996) would all be

components of Geographic Information Science. Spatial models make frequent use of

Geographic Information Systems (GIS) to compile, analyze, and display the modeling

results (Fischer 1996). Likewise, the theories and design behind the development of the

system (Marble and Sandhu 1994) would be part of this as well.

GIS and Recreational Tourism

GIS is not commonly applied to tourism based research. When it is, it is used as a

planning tool (Wilks et al. 1993), a database management system (Sheldon 1993, Vlitras-

26

Rowe 1992), or simple mapping utility (Filippakopoulou and Nakos 1995, May and
Schmidley 1999, Phillips and Tubridy 1994). Other GIS-like technological approaches to
tourism include expert systems and decision support (Crouch 1991 , Gamble 1988) or

management and planning applications (Poon 1988).

GIS, Seasonal Homes, and Real Estate

The literature is silent on the subject of the use of GIS to study the processes of
seasonal home development. One link between GIS and this ﬁeld comes in the form of
GIS’ impact on real estate markets. The use of GIS in site selection strategies (Daniel
1994) has long been the primary linkage between GIS and real estate. Also the Multiple
Service Listing (MLS) tool used by all realtors to identify and analyze available
properties (Longley and Clarke 1995) has begun to include mapping capabilities. GIS is
also used with the real estate market in matters of property tax assessment and

management of publicly owned real estate assets (Castle 1994).

Conclusion

This chapter provides an overview of the pertinent literature surrounding the three
major divisions of this project. The foundations of geographic theory that this project
draws ﬁom were examined, in terms of location analysis and the relevancy to land use.
A brief description of the intersections of the literature of tourism development,
landscape ecology, and GIS was also examined. It can be seen that while these three
areas have their commonalties, they rarely (if ever) signiﬁcantly overlap with one

another. While GIS is an ideal tool for examining the spatial patterns of both landscape

27

ecology and tourism development, it is not often used for this purpose. The following
chapter will take a closer look at the three states making up the study area of this project

and their relation to seasonal homes.

28

Chapter 3: Study Area

The Upper Great Lakes States and Seasonal Homes

The Upper Great Lakes States region consists of: Michigan, Wisconsin, and
Minnesota. The Great Lakes form a control for climate in the area, causing increased
intensity of storms in and around the lakes in the winter, but decreased intensity of
weather in the spring and summer (Albert 1995). The Upper Great Lakes States feature a
diverse physical landscape with thousands of lakes and depressions across the landscape
(Albert 1995).

The northern reaches of the Great Lakes region of the United States have seen
tourism become their principal source of income (Chubb 1989). Declining agriculture
and sawrrrilling, combined with manufacturing plant closures have led areas to shift their
economies to tourism-based ones. Hart (1984) notes that the 3-state region gained over
935,000 people between the 1970 and 1980 censuses; the fast growth areas targeted the
northern portion of Michigan’s Lower Peninsula, northern Minnesota, and north-central
Wisconsin.

In the Upper Great Lakes states of Wisconsin, Minnesota, and Michigan,
approximately $9 billion was spent on tourism-based activities in 1995, generating $3.2
billion in income and supporting 214,000 jobs (Stynes 1996). The United States Travel
Data Center (1998) estimates that in 1997, a total of $10.1 billion was spent in total travel
expenditures in the state of Michigan, generating over 157,000 jobs and nearly $3 billion

in wages and salaries, consistent with Stynes’ (1996) research.

29

The Upper Great Lakes Region features an overwhelming number of inland lakes
with opportunities for waterfront property development. Michigan contains more than
11,000 lakes, Wisconsin more than 15,000, and Minnesota over 10,000 inland lakes. The
region contains an abundance of natural and public land as well. Much of Michigan’s
scenic areas are preserved from development as state or federal lands. There are over
224,000 acres of national parks and lakeshores in the state, over 111,000 acres of national
wildlife refuges, and over 2.7 million acres of national forests (Spotts 1991). Another
260,731 acres are set aside for state parks, 28,925 acres for state boating and ﬁshing,
nearly 300,000 acres for state game and wildlife areas, and over 3.8 million acres for state
forests. Wisconsin boasts over 59 state parks or forests (WDNR 2000) totaling 60,570
acres of state parks and 471,329 acres of state forests (Wisconsincom 2000). There are
70 state parks in Minnesota, encompassing more than 240,000 acres of land (MDNR
2000)

With these types of natural features and the amount of outdoor recreation they
represent, it is not surprising that seasonal home development has been steadily
increasing in the Upper Great Lakes States over the last several decades. In 1940,
seasonal homes were originally concentrated near major cities such as Detroit and
Milwaukee (Hart 1984). However, over time, rural areas in the Lake States began to
steadily gain more seasonal homes, while those areas around major cities were
overshadowed by the grth of more permanent residences (Hart 1984).

Figure 3.1 shows the number of seasonal homes per county in the three states for
the years 1970, 1980, and 1990. The northern parts of Minnesota and Wisconsin

(particularly areas in Adams, Vilas, and Oneida counties) have seen steady grth along

30

 

 

Number of seasonal homes
- 00

[:10 13
[:11301
[:1 2592
ET! 3884
|:] 5175
[J 5467
7753
-
-1

 

 

31

 

Figure 3.1: Number of seasonal homes in the Upper Great Lakes, 1970 - 1990

with the Upper Peninsula and northern Lower Peninsula of Michigan. This northward
spread of seasonal homes can be partially attributed to lower land prices and the distance
away from the larger cities in the southern portions of the states.

Also of note are the counties in southeast Wisconsin (particularly Walworth
county) and southwestern Michigan, which are steadily growing over time. The
proximity to the huge urban market of Chicago in the immediate vicinity is certainly
playing a part in the level of vacation homes in those counties (Preissing et al. 1996). In
Minnesota, the northern-most counties are seeing individuals from the Twin Cities of
Minneapolis-St Paul purchasing seasonal homes there (Preissing et al. 1996). This
seasonal migration has also led to a population redistribution in the Lake States
(McDonough and Parker 1995), as more people are making the move to second homes

and recreational vacation residences.

Spatial Distribution of Seasonal Homes

According to 1990 Census records, Michigan had 3,847,926 housing units with
224,030 being classiﬁed as seasonal. Minnesota had 1,848,445 housing units with
104,838 being classiﬁed as seasonal. Finally, Wisconsin had 2,055,774 housing units
with 150,280 being classiﬁed as seasonal. Thus, over the three state area, there were an
estimated 479,148 seasonal homes in 1990. These account for more than 6% of the total
housing stock in the three states.

Figure 3.2 shows the proportions of the total housing stock that is seasonal of the

Upper Great Lakes Region by Minor Civil Division (MCD) in 1990. The highest

32

 

 

m
229:2? cor

 

.2633 .529".

 

 

Figure 3.2: Percentage of the total housing stock that is seasonal, 1990

concentrations are at a distance away from the metropolitan urban centers of the states
such as Detroit, Lansing, Milwaukee, and Minneapolis-St. Paul. A closer examination of
the data shows that while these areas may be low in percentages of seasonal homes, the
metro areas contain relatively high numbers of seasonal homes. Table 3.1 shows the

number of seasonal homes in each of the MCDs located at the heart of the metro area.

 

 

 

 

 

 

 

MCD Name Number of Seasonal Homes
Detroit City 174
Lansing City 137
Minneapolis City 287
Milwaukee City 260
St. Paul City 216

 

 

 

Table 3.1: Metro MCDs and their number of seasonal homes, 1990

However, the seasonal homes rank as an insigniﬁcant percentage of the total
housing stock for each of these MCDs (the data lists them as being 0%). Thus, while
seasonal homes may exist within highly metro areas, they are overshadowed by the
number of permanent residences.

Examination of Figure 3.2 shows clusters of seasonal homes in areas away from
major cities and closer to the lakeshore of the Great Lakes. High proportions of seasonal
homes can also be found in areas within public land boundaries or near waterfront
property. Analysis of this distribution shows certain patterns associated with higher- and
lower- proportion clusters on the landscape. Table 3.2 shows the average proportion of
seasonal homes for certain groupings of MCDs. For areas containing waterfrontage of
major water bodies, a minimum of 1 ha of waterfront property was assumed. For public
lands, if the centroid of the MCD was contained within the public land boundaries, it was
considered part of the analysis. “Large cities” are deﬁned as those places with a

population of more than 100,000 persons.

34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Type of MCD Average %
Seasonal
Contains waterfront 18%
Contains Great Lakes lakeshore 24%
Distance of 25 miles from GL lakeshore 15.9%
Distance of 25 miles from large cities 2%
Distance of 100 miles from large cities 8.1%
Distance of 200 miles from large cities 12.1%
Population > 5000 persons 1%
Population > 10000 persons 0%
Population < 1000 persons 16%
Within public land boundaries 37%

 

Table 3.2: Types of MCDs and the average % seasonal they contain

Higher proportions of seasonal homes can be found in MCDs containing more
natural features, such as water and Great Lakes lakeshore, or within relatively close
proximity to the Great Lakes shoreline. The higher percentages of seasonal homes found
within public lands’ boundaries can possibly be attributed to the nature of public lands in
the Lake States as outlined in Chapter 2. Select areas of public lands are being sold off as
private lands, and thus only limited amounts of space are available for building. This
could account for the higher proportions of seasonal homes in these areas. Lower
average proportions of seasonal homes are found in areas with higher populations, while

higher average proportions are found in less populated MCDs.

Conclusion

This chapter provides an overview of the study area and a description of the
distribution of seasonal homes in the region (to fulﬁll objective 1). The Lake States
contain a large array of landscape features which lend themselves to outdoor recreation.
Seasonal home distribution in the Upper Great Lakes states is largely situated in areas

away from large cities and has been historically growing in more remote, northern

35

locales. The presence of natural features, water bodies, and the Great Lakes adds to a

higher proportion of seasonal homes found in those MCDs.

36

Chapter 4: Methods

Introduction

This chapter will outline the methodology used in the project and provide a look
at the overall modeling approach. The modeling framework will be described, along with
the description of the variables and how they were constructed in the GIS. Lastly, the

types of models used in the study will be speciﬁed.

Modeling Framework
The modeling framework and technique used in this research project will be based

upon some of the tenets of the Land Transformation Model (LTM) (Pij anowski et al.
1995). The LTM is a GIS-based modeling approach, which is used to predict land use
change. While land use change is not being performed in this study, some of the basic
functions of the LTM are utilized. The basic six steps of the modeling framework that the
LTM utilizes are as follows (Pijanowski et al. 2001a):
1. processing and coding of data
2. applying spatial transition rules
3. applying integration method (such as the neural network)
4. using a Principal Index Driver to forecast over the temporal period being modeled
5. examination of spatial error
6. dynamic forecasting of future time steps through the use of population, per capita use

demands, and economic trends.

The framework used in this project utilizes some of these tenets, including the

37

processing of data, application of spatial transition rules, application of the neural
network for prediction (of one time period rather than a transition between two time
steps), and examination of the spatial error signal.

The LTM operates on spatial data. Predictor variables are generated in the GIS
from a series of base layers, representing land uses (such as agriculture parcels or urban
areas) or features on the landscape (such as roads, rivers, or lakeshores). The predictor
variables are built out of four distinct spatial interactions: neighborhood functions, patch
size, site speciﬁc characteristics, or distance from a feature.

In land use change modeling, the LTM learns about land use transitions through
different integration methods, including the use of an artiﬁcial neural network
(Pijanowski 2001a), the Stuttgart Neural Network Simulator (SNNS). An interface
written in C code links the output from the GIS to the neural network. The LTM’s neural
network capabilities have been used to examine land use changes within Grand Traverse
County and then predicting subsequent land use changes within the six counties (Benzie,
Leelanau, Grand Traverse, Antrim, Kalkaska, and Charlevoix) making up the Grand
Traverse Bay’s watershed (Pij anowski et al. 2001a). The LTM has also been applied to
forecasting urban developments in the Minneapolis-St Paul and Detroit metropolitan
areas (Pijanowski et al. 2001b). In addition, the LTM has been utilized in a variety of
circumstances for prediction of land use change: exploring the linkages between land
use/cover and subsequent impacts to surface and groundwater quality in an area of the
Great Lakes Basin (Boutt et al. 2001); dynamically modeling predictors of land use
change in the Saginaw Bay Watershed (Pijanowski et al. 2000a); and examination of land

use change and urban development in Kuala Larnpur (Pijanowski et al. 2000b).

38

Given computing limitations, these predictor variables can only be constructed on
a three-state-wide level at no less than 100m cell size. All computations were performed
on a Pentium III Duel Processor PC, with access to roughly 45 Gb of storage space.
Arc/Info, ArcView, SNNS, and C programming tools were used as tools for design of the

variables, models, and model interfaces.

Unit of analysis

The unit of analysis in this project is the Minor Civil Division (MCD) level of the
US census. MCDs are primary divisions of counties established under state law.
According to the US Census, MCDs are deﬁned as “A type of governmental unit that is
the primary legal subdivision of a county in 28 states, created to govern or administer an
area rather than a speciﬁc population. The several types of MCDs are identiﬁed by a
variety of terms, such as town, township, and district, and include both functioning and
nonfunctioning governmental units. Many MCDs represent local, general-purpose
governmental units, which makes them required areas for presentation of decennial
census data” (Census 2000). MCDs are identiﬁed by a ﬁve digit F IPS (Federal
Information Processing Standards) code. In this project, MCDs for the three states of
Michigan, Wisconsin, and Minnesota will be utilized.

The initial MCD database was put together by the Great Lakes Ecological
Assessment project and the US Forest Service. The dataset required some ﬁxing of
inaccuracies within it (such as digitizing errors or numerous sliver polygons).

Consequently, a few small polygons were lost in the “clean up” process. The MCD

39

database used in this project consists of 6,1 12 unique polygons spread across the three

states.

Dependent Variable

The dependent variable used in this study is the percentage of housing units per
MCD that were seasonal in 1990 (shown in Figure 3.2). As MCDs vary in size, using the
straight number of seasonal housing units as the dependent variable may provide skewed
results. Predictions for a particular MCD may be higher simply due to its size. Likewise,
using the number of seasonal homes divided by the MCD size (i.e. seasonal housing
density) may also be inaccurate, due to the varying sizes of MCDs.

Using the percentage of housing units that are seasonal per MCD as the dependent
variable reﬂects a better measure of the number of seasonal homes in a particular MCD.
However, there are some caveats that need to be accepted with this variable. Firstly, this
proportional value of seasonal homes will vary according to the number of permanent
homes in the area. A low (or zero) value will usually indicate an area with few seasonal
homes, little seasonal migration, and a large number of permanent residences (such as
predominantly urban areas). A high value will usually indicate those areas which have
few permanent residences, or those areas where seasonal migrants outweigh the year-

round populace.
Spatial Autocorrelation

Spatial autocorrelation is a measure of the correlation of values of the same

variable at different spatial locations (Bailey and Gatrell 1995). This measure will aid in

40

determining where seasonal home distribution is clumped together, and how far one
observation of seasonal homes has on other observations. Spatial autocorrelation will
also aid in testing to accept or reject the null hypothesis that there is no detectable spatial
variance in the distributions of seasonal homes.

Spatial autocorrelation analysis can be measured through the usage of the
Moran’s I indice. The results of Moran's I range from +1 meaning strong positive spatial
autocorrelation, to 0 meaning a random pattern to -1 indicating strong negative spatial
autocorrelation. Thus, the results of this analysis would aid in rejecting the null
hypothesis and explaining the patterns of seasonal home distribution.

Variogram analysis is another method used in measuring spatial dependence. A
semivariogram is used to compare the similarity between pairs of points a given distance
apart and then mathematically expresses the average rate of change over a distance
(Bailey and Gatrell 1995). Variograms are used to compute the average spatial
dependence of the data and are ﬁt through computing three parameters: the range, the sill,
and the nugget. The sill is the point of variance where the variogram ﬂattens out. The
range is the distance at which the sill is reached (i.e. the limit of spatial dependence). The
nugget is the intercept value. A ﬂat variogram (one that is “pure nugget”) would have no

spatial dependence.

Independent Variables
From the literature review in Chapter 2, several variables that aid in the prediction
of the percentage of seasonal homes within the total housing stock can be identiﬁed.

However, the choice of predictor variables is limited by several factors. Availability of

41

data plays a strong role in the choice of variables that are used. As noted before, origin-
based data would reveal much about the socio-economic characteristics (i.e. age, race,
income level) of who is purchasing or utilizing a second or seasonal home. As this is a
landscape-based study, such origin data was unavailable. Likewise, land values play a
strong role in the choice of seasonal home location. However, without origin-based data
of when seasonal homes were purchaSed, this type of variable cannot be taken into
account.

Land prices for many locations have changed dramatically over the last several
decades. What could have been bought cheaply in the 1960’s is now very expensive in
the 1990’s. Thus, using 1990 land valuation prices for an independent variable would not
provide much of explanatory power of what the variable represents. While factors such
as age, education, and income are key demographic estimates of evaluating the tourist
usage of a site (Loomis and Walsh 1997), they are unfortunately inapplicable in this
instance. Characteristics such as these reﬂect the qualities of the tourists or users of the
second homes, yet this study is a land use-based one. Origin information is unavailable.
Factors such as age, education, and income level can be compiled only for the destination
MCD. These factors will more than likely have no direct correlation to the age,
education, or income level of those arriving to utilize the second homes. Also, the scale
of this project limited the types of factors that could be used. Factors such as locations of
boat launches or marinas may help to explain the locations of high proportions of
seasonal home distribution, however such data were unavailable.

Many of the independent variables used in this study are based on land uses or

natural features on the landscape. As noted in chapter 2, in many instances it is the land

42

use and land cover features that provide the impetus for seasonal home development,
along with the numerous outdoor recreation activities that can be derived from them. For
instance, public lands not only contain much in the way of unspoiled nature, but are also

the home to popular activities such as cross county skiing, hiking, boating, and hunting.

Development of Independent Variables

The independent variables were estimated for all MCDs within the three state
region. Some variables (based on census data) will assign a single value to an MCD.
However, variables that cover a wide spatial area (such as the distance and density
functions) will have numerous values associated with them. In cases such as these, an
average of the values within the MCD will be taken and a single value assigned to the
MCD as a whole. For most variables, the mean value will be used so that all townships,
regardless of size, may be evaluated equally.

Variables are created in the GIS (using ArcView) as follows:

(1) put the MCD theme in a View containing the predictor variable theme;

(2) Use the “Summarize By Zones” function — this computes statistics for each
polygon in the MCD theme using the predictor variable grid. The F IPS code
variable in the MCD theme is used to insure that zones are summarized by
individual MCDs. A variety of statistics are created, including “mean” and
“sum.” The “mean” option represents the average value of the predictor
variables per MCD. In most cases, except where noted below, the mean value
for each MCD will be used to give an average estimate of the variable for

each MCD.

43

(3) Join the table produced by the Summarize Zones function to the table of
original MCD theme. This will result in the statistical value table being joined
to the spatial data of the MCD theme.

(4) Convert the theme to a grid, using a statistical attribute and the extent of the
predictor variable grid (and 100 m cell size). This will create a grid of the
requested value (usually mean) of the predictor variable per MCD. Thus, each
MCD has one value for each predictor variable.

Each of the tables created per variable can be exported in dbase format, which is

useable in several statistical based products for further analysis in this project.

Each of the independent variables can be constructed in the GIS for the models as

follows:

1. All landscape density functions: The particular classiﬁcation of the data may
be extracted into a separate layer, and a neighborhood operation (with a
window size of 1.1 km and a “focal sum” option chosen) can compute a
measure of density for that land use (this follows similar variable construction
in Pijanowski et al. 2001a and Pijanowski et al. 2001b).

2. All distance functions: The distance option of the LTM can be used on the
necessary layer. Euclidian distance is computed from the base layer to all
other cells.

3. All amount functions: Land use data is available for each of the three states.
By overlaying the MCD layer on the land use layer, a count of the cells in the

area (which can be computed to acreage — one grid cell of 100 meters square

44

is equivalent to 1 ha) for each MCD may be obtained. In these cases, the

“sum” option for the summarize zones will be used.

In Chapter 2, several factors contributing to the locations of seasonal homes were
described. The best available sources of data were used to create the independent
variables in this project. With data from commercial or government sources, or data
processed by others and used in previous projects, some inaccuracies may be found in the
datasets, especially when working at such a broad three-state scale. Maps of each
independent variable can be found in Appendix A. Speciﬁc independent variables were

created as follows:

1. Water related

Three water-related variables were created. The source of the water data for the
three states was derived from USGS l:100,000 DLGs of hydrographic sources developed
in conjunction with other projects, which included a polygon coverage of major water
bodies in the three states, including lakes and rivers. The polygon ﬁle was also built as a
line ﬁle to represent the water frontage rather than the water area. This new “water front”
coverage was converted to a grid and the “sum” option as described above was used to
ﬁnd a summation of the amount of waterfront per MCD. The variables created are as
follows:

0 distance from major water bodies: this shows the distance from water bodies to all

other areas.

45

density of major water bodies: this reﬂects the abundance and clustering of water
bodies and thus implies more area for recreational opportunities in the area.
amount of waterfront per MCD: this variable provides a measure of the amount of

water frontage, and thus the amount of area potentially available to build on.

Great Lakes related

The most accurate Great Lakes shoreline boundary ﬁle was derived by taking the

polygon ﬁle for the MCDs and editing out all arcs not on the lakeshore. Two variables

were created from this data:

Distance from Great Lakes Lakeshore: this reﬂects the distance from the lakeshore to
all other areas

Amount of Great Lakes Lakeshore: reﬂects the amount of lakeshore available per
MCD to potentially build on. Like the “amount of water front” variable described
above, this is a summation of the amount of Great Lakes lakeshore each MCD

contains.

3. Urban areas and population

The US Census Bureau maintains a “place names” list for places throughout the

United States. This contains the latitude and longitude coordinates, names, and 1990

populations for towns and cities throughout the country. This provided the best available

measure of the locations of towns and cities, as well as their populations. Places within

Michigan, Minnesota, and Wisconsin were extracted, along with the databases for the

neighboring states of Iowa, Illinois, Indiana, and Ohio. These extra states were chosen as

46

there may be signiﬁcant markets from these neighboring cities (especially in Chicago)

that may be contributing to recreational use, or seasonal home use or purchase in

Michigan, Wisconsin, or Minnesota.

Population density ﬁgures were available from US Census records on a per MCD
basis, measured as population per square mile. The best available source for hospitals in
the region came from ESRI’s Street Map product, which stored hospital locations as point
ﬁles (hospitals in Michigan, Wisconsin, and Minnesota were used along with hospitals in
Indiana, Iowa, Illinois, and Ohio). The following variables were created from this data:

0 Stratiﬁed distance from cities: This variable is an attempt to simulate the effect of
proximity to amenities in more rural settings, as well as the distance from larger
metropolitan areas. The place names database was used as the source of the locations
and population counts. Cities were broken up into the following ﬁve categories:

(a) Distance from places of less than 500 persons

(b) Distance from places between 500 and 1000 persons

(0) Distance from places between 1001 and 10000 persons
((1) Distance from places between 10001 and 100000 persons
(e) Distance from places with more than 100000 persons

0 Distance from hospitals: This variable reﬂects access and proximity to major health
care facilities.

0 Distance ﬁom designated “tourist attractions.” This is intended to be a simple list
(not a detailed all-inclusiVe one) that is representative of some major attractions
within the three state area. These places were selected from a variety of sites

including Spotts (1991), Wisconsincom (2000), Ofﬁce of Minnesota Tourism (2000),

47

and Delorrne (2000a, 2000b, and 2000c). The locations of tourist sites were selected
from the “places” database and distance functions were computed from them. The
tourist sites selected for use in this project are as follows:
- MI: Birch Run Village, Bridgman City, Dearbom City (Henry Ford Museum
/ Greenﬁeld Village), Detroit, Flint, Frankenmuth, Holland, Mackinaw City,
Mackinac Island, Munising, Petoskey, St. Ignace, Saugatuck, Sault St. Marie,
Traverse City
- WI: Baraboo, Green Bay, Milwaukee, Sturgeon Bay, Wisconsin Dells
- MN: Bloomington (the Mall of America), Duluth, Shakopee, Minneapolis, St.
Paul, Taylors Falls

0 Population Density: reﬂecting the number of persons per square mile.

4. Public lands

Minnesota public lands data came from the Minnesota branch of RESAC
(Regional Earth Science Applications Center) in the form of GIS layers digitized from
7.5 minute DRGs. Wisconsin public lands information came from the Wisconsin DNR
(Department of Natural Resources) fashioned from a variety of sources (including
1:24000 DRGs, l:100,000 DRGs, and 1:15940 data sources). Michigan public lands
information came from the Michigan DNR, fashioned from the Michigan Public Lands
survey system. All of these public lands ﬁles represent the most accurate public lands
information available for this project. Included in these data are state forests, national
forests, state parks, national parks, and protected wildlife areas. Two variables were

created from this data:

48

0 Distance from public lands: reﬂecting access and proximity to public lands
0 Density of public lands: this variable reﬂects the abundance and clustering of public

lands.

5. Land Use / Land Cover Related
1990 NLCD (National Land Cover Database) data were available in a rectiﬁed
format for the three state area. Derived from early-to-mid—l990’s Landsat TM satellite
imagery, the NLCD is a 21-class land cover classiﬁcation scheme applied consistently
over the United States. The spatial resolution of the data is 30m. Land covers were
extracted and used as the source for the land use and land cover related variables used in
this project. Land cover types were resampled to 100m resolution to keep them in line
with other variables used in this project. This allowed the best available access to data
about the locations of land use / land cover features such as agriculture, forest, water, and
wetlands. This was the source of the agriculture-related variable used in this project, as
well as two of the aesthetic quality related ones. The following variables were derived
from this data:
0 Density of agriculture: This variable reﬂects areas high in agricultural land use (using
the land cover categories of pasture / hay, row crops, and small grains).
0 Density of natural areas: Natural areas in this case are deﬁned as open water, all
forested land cover types, and woody and non-woody wetlands from the NLCD

database. This variable simulates the natural (aesthetic) quality of the area.

49

0 Amount of forests: The amount of forests (all forested types and woody wetlands) in
an area is an important variable for aesthetic quality. A summation of all forested

cells within an MCD is used in this variable.

6. Terrain related

A 90m DEM (Digital Elevation Model) of the three-state area was obtained from
USGS sources in conjunction with other projects. This was resampled to 100m to be
consistent with the other variables used in this project, and used to construct a measure of
landscape variability. A neighborhood operation similar to the density functions was
performed using a 1.1km window, but using the standard deviation option, rather than a
summation on (a similar method was used by Pij anowski et al. 2001a). The following
variable was created from this:
0 Landscape variability: this simulates an aesthetic measure of the “hilliness” of the

area’s topography.

7. Accessibility

The best available measures of accessibility came from data derived from ESRI’s
Street Map product (which is in turn derived from US Census TIGER ﬁles). This
provided a road network for the three state area of Michigan, Wisconsin, and Minnesota,
along with the northern portions of Illinois, Indiana, Iowa, and Ohio. The road network
ﬁle classiﬁes each road segment according to its CFCC (Census Feature Class Code).
Thus, the road layers used in this project are those selected according to their CFCC

classiﬁcation. The following variables were created from this data:

50

0 Distance from local roads: This reﬂects access to places via local roads, rather than
more mass-movement road systems.

0 Distance ﬁom US highways: This reﬂects access to places from major US highways.

0 Distance from interstates: This reﬂects access to places from major US interstates.

0 Distance from vehicular trails: As no concise database of the locations of snowmobile
trails for the three states is available, this measure is used as a surrogate for

snowmobile or off-road vehicular trails.

Correlation of the Dependent and Independent Variables
Bivariate correlations between the dependent and the independent variables were
run to examine the strength of their linear relationships. The bivariate correlation results

are shown in Table 4.1.

Principal Components Analysis

With 23 variables and 6,112 observations per variable, there is likely to be a high
degree of correlation between some of the variables. Some of them will be reﬂective of
similar properties and have high correlation.

Principal Components Analysis (PCA) was used (with the SPSS software
package) to reduce the number of variables to a set of new independent variables (Taylor
1977). This will “reduce a large number of variables to a smaller number of factors for
modeling purposes, where the large number of variables precludes modeling all the
measures individually” (Garson 1999). PCA will combine two or more correlated

variables into a single component. The concept of PCA involves a variance maximizing

51

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VARIABLE Correlation
DIST MORE 100K .266
DIST TOURISM .005
DIST 10K TO 100K .289
DIST HOSPITALS .226
DIST GREAT LAKES -.262
DIST INTERSTATES .257
DIST 1K TO 10K .450
DENS NATURAL .702
DENS AG -.518
DIST PUB LANDS -.321
DENS PUB LANDS .493
DIST VEHICULAR -.361
DIST LESS 500 .289
DIST 500 TO 1K .294
AMOUNT FORESTS .426
AMOUNT GL SHORE .190
DIST LOCAL RDS .034
POP DENSITY -.251
DIST HIGHWAYS .364
DENS WATER BODIES .273
DIST WATER BODIES -.222
AMT WATERFRONT .314
VARIABILITY .015

 

 

Table 4.1: Bivariate correlations

52

 

(“varimax”) rotation of the original variable space (Taylor 1977). The rotation
maximizes the variance captured by the new output variable (a component) while
minimizing the variance around this new variable (Statsoﬁ 2000). These new
components will be orthogonal in n-dimensional space and uncorrelated with each other
(Taylor 1977). Each component produces a set of factor scores, which can be used as the

new set of independent variables in the modeling procedures.

Logistic Regression and the Logit Model

Logistic regression is based on the known values of the dependent variables being
represented by the presence or absence of an occurrence, and applies maximum
likelihood estimation to estimating the probability of an occurrence. Logistic regression
does not assume a linear relationship between the dependent and independent variables
(Garson 1999). However, logistic regression usually requires the dependent variable to be
a binary response function (i.e. the dependent variable is either a value of zero or one).
This is generally used to indicate the presence of absence of a phenomenon. However, as
the dependent variable in this project is a proportional value ranging between 0 and 1,
binary logistic regression cannot be performed.

The solution to this is to calibrate a logit regression model. The output of the logit
regression model will be bounded between 0 and 1 regardless of the values of the
independent variables (Statsoﬁ 2000). The logit model takes the following form:

y = exp(bo + b1*x1 + + bn*xn)/{l + exp(bo + b1*x1 + + bn*xn)}

The coefﬁcient values are obtained through maximum likelihood estimation using

the quasi-Newton algorithm (Statsoft 2000). Maximum likelihood is a technique to

53

maximize the likelihood that the dependent variable values occur within the sample
(Statsoft 2000). The greater the value for the likelihood, the better the ﬁt of the model.

The maximum likelihood estimation for logit models takes the form of:

log(Lr) = 2.11 [yi*log(pr ) + (l'Yi )*log(1-pr )1

where L is the loss function to be minimized. Seeds for the initial beta coefﬁcient
values are necessary. They were obtained by running a linear regression on the variables
(Gupta 1999).

With these initial coefﬁcient values in hand, the Solver program in Microsoft
Excel was used to provide the best ﬁt to the model via maximum likelihood estimation.
Once the best ﬁt was found to minimize the loss function, Solver stored the new values of
the coefﬁcients. These new coefﬁcients were then used in the logit model to ﬁnd an

estimate for the dependent variable.

The Artiﬁcial Neural Network model

Artiﬁcial Neural Networks are tools designed to simulate the learning processes
of the interconnected neurons of the human brain. Neural networks are able to sort
patterns and learn from trial and error about data. One of the ﬁrst neural networks was
the perceptron (Rosenblatt 1958), a simple linear machine consisting of a single node
capable of receiving weighted inputs and thresholding them according to a deﬁned rule.
This type of neural network can classify linear data.

Current neural network technology processes data in a non-linear fashion. The
MLP (multi-layer perceptron) neural network algorithm is non-linear. The MLP neural

net consists of three layers: inputs, hidden, and output and thus can separate data

54

that are non-linear in nature (Skapura 1996). Figure 4.1 shows a diagram of the design of

 

 

1 1 t

Input Hidden Output
Layer Layer Layer

 

 

 

Figure 4.1: Basic Architecture of a MLP Neural Network

a simple neural network. Neural networks feed information forward from the inputs
through the hidden layer and ﬁnally to the output layer. Weights are associated with the
connections between nodes, which modify the signal propagating through the network.
Weighted summations are computed at each node. Each hidden node computes a sum
based on the input from the previous layer. This sum is then altered, usually using a
logistic sigmoid function (Bishop 1995) to reduce it from the range (+inﬁnity, -inﬁnity)
to values between (0,1). The output from this node is computed to be the “activation
function” for that node to “ﬁre” and send its data forward through the network. This
process continues until the output node is reached. In this fashion, the data are learned.

The weights in a neural network are determined by a training algorithm, the most
prevalent of which is the backpropagation algorithm (Skapura 1996). Initial weights
along the connections are randomly determined. The given value for a particular

observation is compared to the estimated value. The difference between observed and

55

expected for all observations is calculated as a mean squared error. The total error value
is then distributed backwards through the system, resetting the weights to new values.
The signal is then fed forward through the network again. This process of feeding input
forward and then propagating the error backwards through the system continues for
several iterations until some speciﬁed threshold value for the error is reached. At this
point, the neural network is considered sufﬁciently “trained” on the data.

The use of neural networks as models comes when the training data is applied to
another data set to test upon. Once the network has learned about the patterns in one set
of data, it will apply what it has learned to another set of data. These two phases, the
“training” and “testing” stages are what make up the functionality of using neural
networks in modeling.

In this project, the input layer of the neural network represents the independent
variable inputs, while the output represents the values of the dependent variable (see
Figure 4.1 for a graphic of the network). The Stuttgart Neural Network Simulator
(SNNS) software package is used to create and implement the network. The
backpropagation algorithm is used for the training procedure and the neural network
takes the form of a set of input layers (one for each independent variable), a set of hidden
layers (where the training occurs), and 1 output layer (representing the estimate of the
dependent variable). A stratiﬁed random subset of the data were used for the training,
and the remaining data used for the testing.

The structure of the neural network used in this project is modeled after the
architecture used in Pijanowski et al. (2001a) and Pijanowski et al. (2001b). These other

projects utilize the same neural network software package (SNNS), and software

56

interface, large data sets with a neural network trained at 500 cycles, a structure of one
hidden node for each input node, and the use of the logistic sigmoid function. Simple
investigation into reducing the number of hidden nodes showed that the mean squared
error result did not signiﬁcantly change. The MSE began oscillating at a point just after
500 cycles. For this project, the structure outlined by Pij anowski et al. (2001a) and
Pijanowski et al. (2001b) was used, while the number of training cycles was selected as

1000.

Conclusion

This chapter has “presented the general format for the procedures used in modeling
the relationship between the predictor variables and the dependent variable. Spatial
autocorrelation techniques will be used to examine the dependent variable to draw
conclusions about the relative clustering and pattern of seasonal homes on the landscape.
Principal Components Analysis will be used to reduce the number of independent
variables to a smaller set of new independent variables to be used in the modeling
processes. Two nonlinear models, a logit regression model and an artiﬁcial neural
network model, will be used to evaluate the relationship between the dependent and
independent variables. Chapter 5 will present the results of these models, as well as

methods for model evaluation.

57

Chapter 5: Model Results and Analysis

Introduction

This chapter examines the results from the modeling approaches described in
Chapter 4. The results of the models are discussed, along with metrics for analyzing
those results. A comparison of the modeling approaches is given, as well as a means for
identifying those variables that best explain the relationship between the independent and

dependent variables. Images in this dissertation are presented in color.

Spatial Autocorrelation

Spatial autocorrelation analysis was performed using the S-PLUS program, which
computes a Moran’s I value on the data. The centroids of the MCD polygons were
computed and used as point data in S-PLUS. Thus, each point contained the value of the
dependent variable. Spatial autocorrelation was calculated using the four nearest
neighbors for each point. The Moran’s I was 0.625, indicating highly positive spatial
autocorrelation. This can be interpreted as MCDs with similar proportions of seasonal
homes (whether high or low) are found clustered together in a smooth and continuous
fashion. In this case, the null hypothesis of no detectable spatial variation can be
rejected.

The semivariogram of the dependent variable was ﬁt using functions in S-PLUS
(shown in Figure 5.1). The best ﬁt was found with a range = 105500, a sill = 365, and a
nugget = 70. This indicates that 105.5 km is the average limit of spatial dependence and

the “drop-off” point for the autocorrelation effect of a particular MCD.

58

Isotropic Variogram of Data

 

400
l

gamma
300
l

200
l

100
r

 

 

 

l l T l

0 200000 400000 600000

distance

Figure 5.1: Variogram of the dependent variable (distance in meters)

Isotropic Variogram of Residuals

 

gamma
1 50
l

 

 

 

T I l N

200000 400000 600000

distance

Figure 5.2: Variogram of the residuals of the dependent variable (in meters)

59

After removing the ﬁrst order trend surface, a new semivariogram of the residuals
(what cannot be explained by the trend surface itself) may be created (see Figure 5.2).
The best ﬁt of the residual variogram was found with range = 41.5, sill = 318, and nugget
= 1. In this case, those factors that are unexplained (the residuals) have their “drop-off”
point of spatial dependence at 41.5 km. The percentage of seasonal homes has a spatial
dependence of over 105 km, but to ﬁnd those factors accounting for the unexplained

variation, more local trends (such as those within 41.5 km) must be examined.

PCA Results

The Principal Components Analysis produced 6 components with eigenvalues
greater than 1 (see Table 5.1), explaining 63.1% of the variance in the independent
variables. According to the Kaiser rule, components with eigenvalues of 1 should be kept
and others discarded (Guttman 1954). The six components are orthogonal and
uncorrelated with each other. Each component has a set of standardized factor scores
(having a mean of 0 and a standard deviation of 1) for each observation that can be used

as new independent variables in further analysis.

 

 

 

 

 

 

 

 

 

 

 

 

 

Component Total % of Variance Cumulative %
1 5.218 22.686 22.686

2 3.812 16.572 39.258

3 1.658 7.210 46.468

4 1.495 6.499 52.967

5 1.288 5.601 58.568

6 1.053 4.579 63.147

Table 5.1: Initial Eigenvalues

The rotated factor loadings for each variable in the components are shown in

Table 5.2. By examining the rotated factor loadings, each component can be assigned

60

 

VARIABLE

C1

C2

C3

C4

C5

C6

 

DIST MORE 100K

.899

 

DIST TOURISM

.850

 

DIST 10K TO 100K

.787

 

DIST HOSPITALS

.685

 

DIST GREAT LAKES

.541

.512

—.430

 

DIST INTERSTATES

.526

 

DIST 1K TO 10K

.510

-.410

 

DENS NATURAL

-.824

 

DENS AG

.708

 

DIST PUB LANDS

.693

 

DENS PUB LANDS

-.567

 

DIST VEHICULAR

-.438

.511

 

DIST LESS 500

.703

 

DIST 500 TO 1K

.655

 

AMOUNT F ORESTS

.599

 

AMOUNT GL SHORE

.545

 

DIST LOCAL RDS

.796

 

POP DENSITY

-.686

 

DIST HIGHWAYS

.571

 

DENS WATER BODIES

.761

 

DIST WATER BODIES

-.625

 

AMT WATERFRONT

.412

.619

 

 

VARIABILITY

 

 

 

 

 

 

.914

 

Table 5.2: PCA Rotated Component Matrix

61

 

an interpretation. As Burley and Brown (1995) point out, the names of the new
components are somewhat subjective, but are very useful in interpreting the results. The

new variables are described as follows:

1. Distance from large cities: the highest positive factor loadings come from the
variables of the distance from areas of more than 100,000 persons, distance
from areas of between 10,000 and 100,000 persons, distance from hospitals,
distance from tourism sites, and distance from interstates.

2. Absence of natural areas / presence of agriculture: the variable with the
highest factor loading in this component is the density of natural lands.
However, this component is loading highly negative. The next highest
loading comes from density of agriculture, a high positive loading. This
component also includes high positive loadings for distance from public lands,
and distance from commercial tourism sites, as well as a high negative loading
for density of public lands. This can be interpreted as “absence of natural
lands” or areas low in natural lands and public lands, with a high density of
agriculture.

3. Distance from small towns: Distances from towns of less than 500 persons
and from places of between 500 and 1000 have the highest factor loadings,
along with the amount of forest and the amount of Great Lakes lakeshore.

4. Distance from local roads / accessibility: This component is categorized by a

high positive loading for distance from local roads, and a high negative

62

loading for population density, with a high positive loading for distance from

highways.

5. Presence of water: The highest factor loading is for the density of water

variable. Also loading high is the negative loading for distance from water.

6. Landscape Variability: This variable is categorized by a high loading in

landscape variability.

Logit Model Results

As noted in Chapter 4, the seed values for the coefﬁcients of the logit model were

obtained using a linear regression of the variables. After applying maximum likelihood

estimation to calibrate the logit model, the coefﬁcients changed considerably. Table 5.3

shows these changes in coefﬁcients.

A correlation between the observed and estimated results of the logit model was

found to be 0.727. This value can be squared to calculate a “pseudo-R2” value for the

overall ﬁt of the model. The pseudo-R2 value for the logit model was 0.53.

 

 

 

 

 

 

 

 

 

 

Beta Seed value Solved value
b0 .126 -2.47

b1 0.068 0.29

b2 -.092 -1.05

b3 0.047 0.28

b4 0.043 0.26

b5 0.058 0.41

b6 -0.008 0.07

 

 

 

Table 5.3: Initial beta values and solved values

Model veriﬁcation and validation was performed to test the robustness of the

model. A random sample of 20% of the MCDs was chosen to calibrate the model, while

63

the remaining 80% was used to test the model. The model was ﬁt by running a linear
regression using the 20% sample to obtain the initial seed values for the beta coefﬁcients.
The model was then tested on the remaining 80% of the data, resulting in a correlation
coefﬁcient of 0.72, or a pseudo—R2 of 0.53. These values are very similar to the overall

ﬁt of all the data, indicating a robust model.

Neural Network Model Results

As noted in Chapter 4, the neural net model needs data to train on and to test on.
A stratiﬁed random sample of 80% of the MCDs was chosen and separated from the
remaining 20%. The neural network was trained on the 20% sample and then tested on
the remaining 80%. This gave a correlation value of 0.79 between the observed and
estimated values, resulting in a pseudo-R2 value of 0.63 for overall ﬁt of the model.

The 20% sample size was chosen due to concerns of “overtraining” the data, or
giving the neural network too much to work with. Another concern with a large training
sample is that if the model is learning about the majority of the data, intuitively one
would think that it should have a relatively decent ﬁt to the smaller testing sample. For
instance, a model presented with 99% of the data should be able to provide a good
estimate of the remaining 1%. Therefore, a smaller sampling size was chosen to test the

model.
Examination of Independent Variables

To fulﬁll the second objective of this dissertation, the independent variables

contributing the most to the overall model must be found. The PCA culled the list of the

64

initial 23 variables down to a set of 6 new variables. However, to fulﬁll objective 2 as
laid down in Chapter 1, the principal predictors of the proportion of seasonal home

distribution must be identiﬁed.

Logit Model

In the logit model, the principal predictors of the dependent variable can be
identiﬁed by examining the beta coefﬁcients of the independent variables. These give a
measure of not only the importance, but also the direction (negative or positive) that the
variable takes. Table 5.3 shows the beta coefﬁcients for the model. As can be seen, the
highest values associated with a factor is that of the second variable, the one representing
the absence of natural areas and presence of agriculture with a value of -. 1 .05. This
indicates that the absence of natural areas has a very strong negative effect on the model,
meaning that the presence of natural areas has a very strong positive effect on the model.
Also, this indicates that the presence of agriculture land has a strong negative inﬂuence
on the distribution of seasonal homes.

The variable with the next highest beta coefﬁcient is the ﬁrst one, representing the
presence / density of water, with a value of 0.41. Ranked next with a value of 0.29 is the
variable representing the distance away from urban areas. These results indicate that

these two variables have a strong positive effect on the overall ﬁt of the model.

Neural Network Model

Unfortunately, neural networks do not produce coefﬁcients to ﬁt to structured

equations, and thus one cannot directly infer from neural networks the explanatory power

65

of the model. All of the processing occurs within the “invisible” portion of the model,
namely the hidden layers and their associated weights moving to and from the inputs,
hiddens, and outputs. Unlike the logit model, the importance of each variable to the
overall model cannot be extracted.

However, there is a way of examining the relative importance of each
independent variable in the overall model. Sensitivity analysis allows for the model to be
run multiple times with a single variable removed from the model. Thus, with 6
independent variables, there will be 6 new models created, each containing 5 variables.
Each of these “reduced variable” models represents the model without the contribution of
one of the variables. The changes in pseudo-R2 values between the reduced variable
models and the overall model simulate the relative contribution of each independent

variable to the model. Table 5.4 shows the pseudo-R2 values of each reduced variable

 

 

 

 

 

 

 

 

 

 

model.
Variable removed NN Model’s
Pseudo-R2

1: Distance from cities 0.59

2: Absence of natural areas 0.47

3: Distance from small towns 0.557

4: Accessibility/ Local roads 0.56

5: Presence of water 0.525

6: Landscape variability 0. 63

 

Table 5. 4: Reduced variable runs of neural network

As can be seen, the overall ﬁt of the model drops to a pseudo-R2 value of 0.47
when the second factor (absence of natural areas) is removed from the model. This
indicates that the absence of natural areas variable contributes the most to the overall ﬁt

of the model. The second largest drop in model ﬁt comes when the ﬁfth factor (water) is

66

removed from the model, reducing the overall ﬁt to 0.525. These variables correspond

with the top two predictors found by the logit model.

The Principal Predictors

Both the logit model and the neural network model identify ﬁrst the absence of
natural areas (or presence of agriculture) as the principal predictor of seasonal home
distribution and secondly the presence of water. The third through ﬁfth ranked variables
of distance from large cities, distance from rural towns, and distance from local roads /
accessibility are close together and their ranking varies only slightly from each model.
Finally, both approaches agree that the landscape variability factor contributes the least to
the overall model.

Table 5.5 shows how each variable is ranked in its importance to the model. Note
that while the “reduced variable” model gives some approximation of the contribution of
that variable to the overall ﬁt of the model, they cannot tell if the variable has a positive

or negative effect, as the logit model coefﬁcients can.

 

 

 

 

 

 

 

 

 

 

Logit model Neural network model

1. Absence of natural areas 1. Absence of natural areas

2. Presence of water 2. Presence of water

3. Distance from large cities 3. Accessibilityto local roads
4. Distance from small towns 4. Distance from small towns
5. Accessibility to local roads 5. Distance from large cities
6. Landscape variability 6. Landscape variability

 

Table 5. 5: Comparison of model rankings of principal predictors

Spatial Distribution of Seasonal Homes
This project has provided a measure of the principal predictors of seasonal home

distribution across the Upper Great Lakes states of Michigan, Wisconsin, and Minnesota.

67

From the results of the logit and neural network modeling approaches, the “absence of
natural lands density / presence of agricultural density” variable had the strongest effect
on the model. In the logit model, this was shown to have a high negative coefﬁcient,
indicating that absence of natural lands (forest, water, and wetlands) and the presence of
agriculture has a strong negative effect on seasonal home distribution. This indicates that
the presence of natural lands and the absence of agricultural lands has the strongest
positive inﬂuence on the model. This ﬁts in with the general theory and literature
outlined in chapter 2, outlining that an impetus for utilizing a seasonal home is to remove
oneself from an urban environment out to a more rural one. Natural areas of forest and
water provide a wide range of recreation opportunities, either in maintained public lands
areas or in other natural areas. Also, the natural areas present a more pleasing aesthetic
quality than urban areas. Similarly, high density of agriculture has a negative effect on
seasonal home location, similar to ﬁndings by Chubb and Chubb (1981), possibly
indicating the land being used for more farming than seasonal homes.

The next principal predictor is presence of water bodies. The literature indicates
that water plays a key role in the location of seasonal homes. Water bodies provide a
wide range of outdoor recreation opportunities, including boating, ﬁshing, and
swimming. Also, the presence of water indicates a more aesthetically pleasing, or
perhaps even a “soothing” effect from more urban settings.

The next three principal predictors of seasonal home location revolve around
urban areas, cities, towns, and access to and from them. Their order of importance is
ranked differently between the two models, although they are still ranked at a level of

third through ﬁfth, with coefﬁcients in the same general range. The literature notes that

68

seasonal homes are purchased to remove oneself from an urban environment into a more
rural setting. Thus, distance away from cities should be a key factor here. Similarly, the
the distance from smaller towns (reﬂecting distance from more rural locations) and a
distance from local roads provide similar explanations. Smaller towns reﬂect more rural
settings that may still provide basic amenities such as food, lodging, gasoline, or other
necessary items. However, while they provide amenities, they are very different from the
heavy urbanization of larger cities. The local roads / population variable reﬂects two
types of access: residential roads in urban areas and more local backroads to rural
destinations. This provides a measure of access ﬁ'om all types of housing areas. These
factors reﬂect some of the ideas in the literature that seasonal homes may be found in less
urbanized and more rural areas, but that still have easy road access to them.

The ﬁnal factor ranked last in importance by both models is categorized by
landscape variability. The changing character of the landscape has little role in
explaining the distribution of seasonal homes in the area. A possible explanation for this
may lay in the concept that it is not the abruptly changing landscape that contributes to
the area’s aesthetic quality, but rather what can be seen from certain vantage points. For
instance, a high elevation may allow a wide view, but the quality of what can be seen
may not be pleasing to the observer. The approximation of this variable may be a crude

way of showing the nature of the landscape.
Model Comparison

Several methods were used to compare these two modeling approaches. The ﬁrst

of these are the pseudo-R2 values (or the square of the correlation coefﬁcient). These

69

provide a measure of the overall ﬁt of the model. The logit model’s pseudo-R2 of 0.53 is
less than the neural network’s pseudo-R2 of 0.63. Judging solely from this measure,
neural networks give a better predictive power.

However, a pseudo-R2 is not the ﬁnal word in appraising model performance. For
instance, neural networks are not explanatory models where the logit model is. If the
only model used was the neural network model, the power to explain the strength and
direction of variables would be very limited, and thus objective 2 could not be accurately
met. This can be seen in examining the strongest variable in the model, absence of
natural lands. From the logit model, the coefﬁcients indicate the overall strength of the
model. More importantly, they indicate that this variable has a strong negative effect on
the model, which can thus be interpreted that the presence of natural lands have the
overall strongest effect. The neural network has no such similar ability. The “reduced
variable” models give some approximation of how the model reacts without that variable
in place, but nothing about its effect, positive or negative. As removing the “absence of
natural lands” variable from the neural network corresponds to the greatest drop in its
predictive power, one may be led to believe that it is the absence of natural lands that has
the greatest effect on explaining seasonal home distribution. However, with the sign of
the coefﬁcient supplied from the logit model, one can more accurately infer that it is the
presence of natural lands that has the strongest inﬂuence on the model.

Another technique that can give additional insight into the models is mean
absolute deviation (MAD). The value for MAD gives a way to measure the variability or

spread of a set of numbers by computing their average distance to the mean (Sclove

70

1998). The MAD will compute the mean of the absolute value of the differences between
the supplied values and the arithmetic mean of all values. The formula for MAD is:

MAD=(Sum(X-u))/n
Where: IF the number of observations, X = the supplied values, and u: the arithmetic
mean of all the values.

Table 5.6 shows the results of the MAD for the observed and expected values
used in the logit and neural network models. As can be seen, the spread of values is
relatively close, with both models having small differences between the observed and
expected values. The logit model computes a slightly lower deviation between the MAD

for observed and expected values.

 

Logit model Neural network
.1088 .1327
Table 5.6: Mean Absolute Deviation of the modeling approaches

 

 

 

 

 

The Spatial Error Signal and Residual Analysis

To better examine the differences between the estimated and the observed values,
the model residuals were spatially mapped. The value of the observed minus estimated
score was taken and mapped in the GIS. Figure 5.3 shows the spatial error of the logit
and neural network models (note that the missing areas on the neural network map are
from the 20% random sample of the MCDs removed for the training phase). As can be
seen, the largest clusters of over or under prediction of values are occuning in sections of

northern Minnesota, Wisconsin, and the Upper Peninsula and northern lower peninsula of

71

 

   

Logit Model Residuals

Logit Res Final
-1 - -0.5

100 Kilonnlen

 

 

 

 
 
   

Neural Network Residuals

NN Resid ﬁnal
- - .5

100 O 100 Kilometers
:E

 

Figure 5.3: Logit and Neural Network Residuals

 

 

   

Logit Model Residuals

Logit Ros Final
-1 - 0,5

 

 

 

 
 
   
  

Public Lands Boundaries

[:3 Publandapoiy
Logit Res Final

.1 . 41,5

41.5 - as
3 - 0.2

100 0 100 Kilometers
5:

 

Figure 5.4: Logit Residuals with Public Lands Boundaries Overlayed

 

 

   

roe: 2.8m; mmmacmﬁ

 

 

 

E95 .99 Megan Emacs—m

74

 

Michigan, with clusters of the highest positive and lowest negative values spread across
the three states.

The model residuals appear to be spatially correlated. The ﬁrst pattern to the
residuals relates to the boundaries of public lands. Figure 5.4 shows the logit model
residuals again with the public lands ﬁle overlayed on top of them. An analysis between
the residuals and the public lands showed the following:

0 Of the 567 MCD polygons which have their center within public lands
boundaries (the most accurate measure of ﬁt between the two overlays), 565
of them contained an MCD with at least some residual (observed minus
estimated) greater than zero.

0 Of the 567 public land MCD polygons, 196 of them contained a residual value
of greater than 20.

Thus, MCDs falling within public land boundaries are being over or under
estimated by the logit model. As noted in Chapter 2, public lands are areas that need to
have special consideration taken when dealing with them. Not only does seasonal home
development take place within their boundaries, but also commercial and residential
development as well. Strict controls are placed on these developments, and they can only
occur in certain parcels of land that are privately owned. Thus, the proportions of
seasonal homes within public lands boundaries are a special case, as can be explicitly
identiﬁed through mapping of the spatial error signal of the models.

Other clusters of residuals were examined as well. Three examples were chosen
to demonstrate different effects of residuals in the analysis. Figure 5.5 indicates these

circled on the map of logit model residuals.

75

The ﬁrst of these (marked with an “A”) on the map, is a cluster of townships in
southwestern Minnesota. Upon closer examination, these four townships are part of
Murray County and centered upon a body of water and a public land polygon. From the
Murray County website (Murray County 2000), some key information about this residual
cluster can be obtained. Lake Shetek is home to a number of church camps, including the
Shetek Lutheran Bible Camp and Lakota Retreat Center. This facility can hold up to 100
persons in the winter and up to 180 in warmer times. These facilities (along with a
Baptist Bible Camp and a Boy Scout Camp) may be considered seasonal residences, and
thus are factors unaccounted for by the model.

The second cluster of residuals (marked with a “B”) is located in the upper
northern portion of Minnesota. This area is predominantly covered by land for the Red
Lake Indian reservation (with a population of 5000). Although the area seems to ﬁt many
of the criteria for seasonal home development, none seems to be happening on Native
American territorial boundaries.

The third cluster of residuals (marked with a “C”) is located in lower central
Wisconsin. This grouping, predominantly centered on townships in Waushara County,
contains many residuals. A closer look at the area in the Delonne Gazetteer of Wisconsin
(Delorme 2000b) shows that there are numerous designated public boat launches ringing
many of the lakes. In addition, there are designated hunting areas posted throughout the
region. Also notable are the number of landing strips marked on the map, perhaps
indicating many rural pilots in the area. A downhill ski resort is also located in the area.
Most notably, however, are several small public land boundaries marked as state wildlife

areas that are missing from the public lands database. This shows a number of factors

76

unaccounted for in the model (such as ski resorts and boat launches), as well as pointing

to some holes in the available statewide data supplied from the Wisconsin DNR.

Logit Estimates vs. Neural Network Estimates

One ﬁnal test was done for model comparison. The estimated results of the logit
model and the neural network model were compared with one another to see just how
similar the results of each model were. To keep the comparison accurate in terms of
numbers and which observations were being compared to what, the 80% sample of the
logit model used in the model validation procedure (the same 80% used in the testing of
the neural network model) was used for comparison. The estimated values of the two
models were found to have a correlation coefﬁcient of 0.87. Furthermore, the values
were placed into a Principal Components Analysis (another measure of linear
correlation). The results of the PCA found the two sets of results rotated into the same

component. Thus, the two models are explaining very similar things.

Conclusion

This chapter provided an analysis of the results of the various stages of the
modeling approach. PCA reduced the predictor variables to a new set of independent
variables, while the results of the logit and neural network model were compared and
contrasted. This also achieved the last of the objectives that were laid out in Chapter 1: to
identify the principal predictors of seasonal home location as well as to test the various
modeling approaches. The next chapter places these results in the context of the theory

and literature, and provides a more in-depth discussion of these results. Some of the

77

limitations of the data, variables, and modeling approaches are also discussed. Finally,

some greater implications for areas of growth beyond this project are examined.

78

Chapter 6: Discussion

Introduction

This chapter will take a closer look at the results of this dissertation in the context
of the overall theory and literature, and the contribution that this research makes to that
theory. This dissertation encompassed a wide range of ideas and concepts, drawing from
many different areas of theory and literature and combining them together. The nature of
the model results and how they relate back to the literature and theory will be discussed,
as well as some thoughts on the nature of the variables.

Also, this dissertation provided an exercise in model building in terms of deﬁning
variables and the formation of models to explain their contribution to the distribution of
seasonal homes. However, there are some limitations to the study, not the least of which
is the large data set used as the dependent variable, and the data sets used to construct the
independent variables. A greater discussion of the modeling approaches and the
limitations of linking huge data sets together with them are examined. Lastly, the use of
geographic information systems provided a means at looking at the science underlying

the system.

Dependent Variable

The dependent variable used in this project is the percentage of the total housing
stock per MCD that is seasonal homes. This provides a good approximation of the
inﬂuence of seasonal homes over permanent homes in a particular area, especially when

taking into account the varying sizes of townships. A larger township may have a greater

79

number of homes due to its size, just as a much smaller township will have less. The
proportion of seasonal homes to the total housing stock provides an attempt to adjust for
this discrepancy in MCD size.

Another way of approaching the problem that future researchers may wish to
examine is the use of the total number of seasonal homes per MCD. While this would
give the best measure of the exact number of seasonal homes in the area, using this as the
dependent variable introduces new problems and potential sources of error into the
model. First, this does not account for the varying size of MCDs. A larger MCD would
potentially contain more seasonal homes than average-or-smaller sized MCDs. A larger
MCD in a “hot” area for seasonal home development would contain an inordinate
number of seasonal homes when compared to other regions and would ahnost become an
outlier in the model, even though it is an important factor. Also, as noted in Chapter 3
some areas with high numbers of seasonal homes exist within the township boundaries of
large cities. Even though these areas would represent an insigniﬁcant portion of the total
housing stock, they would be much higher than other areas. Lastly, the methods used in
this project would require signiﬁcant changes or adaptations to be used with such a study.
The logit model and the neural network are designed to produce output scaled between 0
and 1 as a way to approximate the proportion variable. Different methods to ﬁt this new
dependent variable would need to be evaluated and selected, or several changes made to
the data and methods being used here.

Another limitation of the data is the deﬁnition of what constitutes a seasonal
home. Census deﬁnitions of seasonal homes cover a wide range of housing types

including small cabins and cottages, to fully stocked and winterized homes, to large scale

80

condominium developments and time-shares. All of these varied types of homes are
encompassed under the Census deﬁnition of “homes held for seasonal or occasional use.”
This can lead to certain clusters of outliers in the model that were unaccounted for. For
instance, the townships in Murray County, MN contain several seasonal cabins for
numerous camps that may have increased the numbers of what is considered “seasonal
homes” in that area.

The dependent variable contains over 2000 observations of “0” and another
1600+ observations between “1” and “5” indicating an overwhehrring number of
permanent homes in each township when compared to the number of seasonal homes.
This could be due to areas of very little housing development, or heavily urbanized areas
where permanent homes far outrank the seasonal ones. One hypothesis for dealing with
the nature of the variable would be to remove all urbanized areas from the dependent
variable as the models should be trying to exclude areas of heavy urban usage.

Some simple analyses were done by removing all observations from the data for
townships that had a population of greater than 5000 persons and had a seasonal home
percentage of less than 5. 535 townships ﬁt this criteria, corresponding to urban areas in
the three states including Detroit, Milwaukee, and Minneapolis-St. Paul. The models
were re-run with this new dataset. The logit model slightly improved to a pseudo-R2 of
0.535. The rankings of the coefﬁcients changed slightly, as distance from cities lost
some of its strength, reducing from an 0.29 to an 0.20 beta coefﬁcient. The neural
network model dropped from a pseudo-R2 of 0.63 to a value of 0.60.

These results would indicate that there is a deﬁnite spatial pattern of seasonal

home usage on the landscape occurring in urban areas. The neural network was

81

“learning” about the patterns of very low values in the dependent variable, and its overall
ﬁt dropped when those patterns were removed from its learning process. Similarly, it can
be seen that the “distance from cities” variable was partially responsible for explaining
the values of seasonal homes within heavily urban areas. One conclusion that can be
drawn from this is that seasonal home distribution within urban areas is not an outlier, but

part of the overall pattern of the dependent variable.

Independent Variables

This leads back to the general landscape ecology and human / environment
theories on the nature of pattern and process (e. g. Fonnan and Godron 1986, Navah and
Lieberman 1984, Skole and Gage 2001). In this theory, it is the patterns on the landscape
(such as the arrangement of lakes, forests, and elevation) that lead to some process (in
this case, the distribution of seasonal homes). The variables in this project were chosen
to reﬂect the landscape patterns and they in turn are related to this process.

The choice of a seasonal home is dependent on a variety of factors, including
several socio-economic ones, as well as personal choice. However, no matter if the
reason for a second home purchase is eventual retirement, a weekend getaway, a cabin
used for hunting, a time-share condo, or a place to park the snowmobile, there are
numerous landscape features which are prevalent in some aspect of the choice of seasonal
home location. Chapter 2 reviewed a number of land uses that relate to seasonal home
development (or the lack of it) including waterfront, urban areas, natural areas,
transportation, and public lands. It is the pattern of these land uses that in turn leads to

the process of seasonal home location.

82

This is not to say the list of variables is all-inclusive. The ﬁt of the models
indicates some variables are missing from the analysis. The addition of origin-based data
would likely also improve the overall ﬁt and explanatory power of the models. Both
Tombaugh (1970) and Gartner (1987) utilized survey data to gain origin-based
information about socio-economic characteristics of seasonal homeowners and their
purpose for purchasing a seasonal home. However, as noted in Chapter 2, this type of
data was unavailable for this research. Land price is certainly a factor of where seasonal
homes would be located. However, using 1990 land valuation variables would not get at
the true nature of the dependent variable in the models. Without origin based data, there
is no way to tell when seasonal homes were bought: several decades ago when the land
they now reside on was relatively inexpensive, or in more recent years when the land is
much more expensive. Also, the addition of a measure of township zoning would be
beneﬁcial to the model. The amount of land per township that can be developed would
be another useful indicator of the distribution of seasonal homes. Areas with ample
available land or lacking zoning regulations may be seeing greater numbers of homes,
both seasonal and permanent.

Weather is another factor unaccounted for in the model. Areas that receive heavy
snowfall may be high in proportions of seasonal homes whose owners wish to partake in
winter sports. Snowmobiling and skiing both rely on snowfall for enjoyment. Likewise,
areas experiencing milder climes in the summer may be more plentiful in seasonal home
proportions since they would be better suited for more days of outdoor recreational
activities such as boating, ﬁshing, or swimming. The nature of weather and climate in

these models is one that requires much further investigation.

83

As Stewart (1994) points out, individual choice also has much to do with the
location of where to purchase a seasonal home. Also, origin-based data such as the race,
age, income level, and reason for purchasing the second home would also be useful in
providing more explanatory power, along with a measure of how far the purchasers
would be traveling to utilize their new second home. At the three state level of analysis,
these values would have to be averaged by township to be utilized in the modeling
framework.

However, these are additional choice variables to help the predictive or
explanatory power of the models. Returning to the idea of landscape pattern leading to a
seasonal home process, perhaps “predictor variables” are not the best name for the set of
independent variables used in this project. Perhaps “process driver” variables would be
more apt to describe their function. In this way, the link to land use would be more

explicitly laid out.

Bias in the system

The nature of the dependent variable will be causing bias in the models. Not all
MCDs are the same size — they range from small villages dotted throughout the three
states to near—county level sized MCDs in reaches of northem Minnesota or Michigan’s
Upper Peninsula. The construction of the independent variables attempts to account for
this by using a mean value for most of the variables. For example, the distance-related
variables compute the euclidian distance from each feature to all other cells in the study

extent. For the boundaries of each MCD, the mean value of the variable is computed in

84

the GIS. This was an attempt to not only assign a single value to each MCD, but to also
try to account for the varying sizes of each MCD.

A source of bias in the data comes with the introduction of variables that do not
represent the mean value for each MCD, most particularly the three “summation”
variables — amount of waterfront, amount of Great Lakes lakeshore, and amount of forest
per MCD. In these cases, the MCDs with the biggest size will be receiving higher values
simply because they are larger. Likewise, smaller MCDs will be receiving much smaller
values simply because of size. This problem becomes compounded with some of the
larger MCDs in Michigan’s Upper Peninsula or areas of northern Minnesota which have
copious amounts of waterfront or forest, or places like the Drummond Island MCD off
the eastern coast of Michigan’s Upper Peninsula which has a very large amount of Great
Lakes lakeshore. In these cases, these MCDs will have much higher values for each
variable than other large MCDs and much higher values than smaller MCDs. In effect,
due to their size, they have become outliers, or sources of bias, in the model.

These sources of bias then become perpetuated through the system. For instance,
the Principal Components Analysis rotates variables together that are highly correlated,
and then constructs standardized z-scores to be used as factor scores. Components
containing high loadings for variables containing the largest values for the summation
variables are receiving some observations of inordinately high z-scores due to their
having values so much higher than the other observations for each variable. The
components in which these variables load highly will be receiving this “bias” inﬂuence of

these larger MCDs (or the extremely large ones). These high factor scores can be seen as

85

a source of bias in the logit model. Other extreme values could lead to similar sources of
bias.

This source of bias also contributes to the neural network model. Neural
networks can theoretically accept input values of any size. However, due to the nature of
the neural network transfer (or “squashing”) function (such as the logistic sigmoid
function), the input values should ideally take on the range of approximately (-1, +1).
Input values signiﬁcantly beyond this range will still be included in the analysis, but the
neural network will be less sensitive to their presence and some saturation may occur
(Statsoft 2000). With the standardized scores being slightly skewed by the extreme
values of some summation observations, this could be changing how the neural network
trains and tests on the data. The neural network could potentially then be learning less
about those observations with the highest z-scores (in effect, those observations with the
most extreme values anyway) and learning more about the majority of the observations.

This effect on the neural network could be interpreted in two ways. First, the
neural network could be learning less about the most outlying patterns in the data, and
learning more about general trends and patterns. In this way, the neural network itself is
acting as a sort of “ﬁlter” on the data, leaming less about the sources of bias and more
about the non-noisy patterns. This could account for the higher pseudo R2 of the neural
network when compared to the logit model. However, secondly, the neural network
could be potentially missing out on learning about certain necessary patterns of seasonal
home distribution, and applying only more general learning to the process. “Overﬁtting”
of the data may be occurring. This is one possible hypothesis for why the neural

network’s pseudo-R2 is higher than the logit model.

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These are sources of bias that future researchers should be cautious about in
dealing with this type of data, scale, and variables. However, there are some potential
alternatives to removing the bias from the system. First, the largest-sized MCDs could be
removed from the analysis. This, however, is not solving the problem as the size of the
various MCDs has been attempted to be accounted for by using the “mean” value for the
independent variables. The varying sizes of townships are something that must be
accounted for, not simply eliminated. Another alternative is to drop the extreme outlier
values ﬁom the procedure entirely. This is much the same as dropping the MCDs, only
dropping them after the variables have been computed and ﬁnding which ones are
contributing these overly high values.

Another choice would be to remove the summation variables from the analysis, or
replace them with other surrogates. However, the theory and literature concerning
seasonal home distribution indicates that these are important variables in the analysis.
For instance, the amount of waterfront is the best indicator of the potential building space
around a lake or river. Simply using the amount of waterfront per MCD (a ratio) may
give skewed results. For example, a 100 square mile MCD containing 10 miles of
waterfront would produce a value of 0. 1. A 10 square mile MCD containing 4 miles of
waterﬁ'ont would produce a value of 0.4. In this case, the MCD with less waterﬁ'ont
would be weighted higher than the MCD with more waterfront. Thus, using a ratio value
to produce a percentage will not give accurate results. Much cruder estimators
potentially could be constructed and used as surrogates (such as percentages of MCD

perimeters), however, these may have problems associated with them as well.

87

A ﬁnal alternative would be to not use the factor scores from the Principal
Components Analysis in future modeling efforts, but rather to use the highest loading
variable in each component. However, this introduces a new host of different potential
problems to the modeling process. The object of using the factor scores was that they
represented values for orthogonally rotated components in n-dimensional space. These
components, being orthogonal, were uncorrelated with each other, and thus the new
variables created from the factor scores represented observations of truly uncorrelated
variables. These new variables could safely be used in a reconstituted regression in the
logit regression model without violating the assumption of no multicolliniarity. By using
the highest loading variable, this introduces multicolliniarity into the model and violates
one of the assumptions. This could cause other problems with the model that are
accounted for by using the factor scores.

Similarly, using the variables with the highest loading in each component could
cause problems with the neural network as well. The variables would have to be linearly
normalized (selecting the highest value among the observations and dividing all
observations by that value), thus reducing the range of the variable to between 0 and 1.
However, any signiﬁcant outliers in the observations will throw off the range of the data.
For instance, if one of the summation variables (i.e. amount of waterfront) was the
highest loading variable, it would have a small number of observations that were
signiﬁcantly higher than the others. Normalizing this variable for use in the neural
network would mean dividing by the highest value (i.e. an extreme outlier with an
observation value much higher than all other values), and thus signiﬁcantly altering the

variable. It would be left with a handful of high values, with the majority of the other

88

values reduced so low they would probably be seen as constants when contrasted with the
other observation patterns the neural network would be learning about. Thus, the neural
network would be learning very little, if anything, about that particular variable. Similar
results could occur if an anomalous value (or a signiﬁcantly higher value) for one of the
other variables was part of the dataset.

While these are some examples of the effect of bias in the data used in this
project, they are not unique when dealing with large data sets. Examining the seasonal
home phenomenon at such a broad three-state-range, while dealing with the non-uniform
sizes of MCDs will cause problems of bias to occur throughout the analysis.

With large data sets, it is often difﬁcult to pinpoint exactly where errors or
sources of bias are coming from. Sources of bias may be uncovered, but are difﬁcult to
locate or determine due to the large size, nature, and complexity of the data set.
Anomalous or missing values may prove difﬁcult to locate or correct. Also, when using
large data sets from such a wide variety of sources, mismatches between data sets may
occur. As such, the results emanating from large data sets cannot simply be taken at face
value — investigation into potential sources of bias and inaccuracy is required as part of
the examination of the validity of the results. Future researchers should be aware of these
potential problems when working at the MCD level or dealing with large ecological

datasets.
Methods and Model Building

The second and third objectives of this dissertation revolved around model

building concepts, namely testing approaches to predict the seasonal home distribution on

89

the landscape and provide an explanation of this process. The two non—linear modeling
formats (the logit and the neural network models) provided a means of coupling the
initial GIS-based framework of the LTM to the outputs. In this sense, the movement
from pattern to process is again followed: the GIS is used to identify the shapes and
patterns of landscape phenomena, while the models are used to explain the process.
However, this use of the term “explanatory power” should truly be applied to the logit
model. While the logit model had less predictive power than the neural network, its
explanatory value (as outlined in Chapter 5) is much greater than the neural network.

Neural networks provide no explanatory power about the data. Due to their
structure, neural networks do not make assumptions about how data and the relationships
between them are structured. The nature of the neural net is such that it can examine data
without needing assumptions about this structure, while statistical models do make
certain assumptions about what relationships the data will take.

Neural networks are often labeled as a “black box” since the processes of the
learning and distribution of the weights, and thus the manner of just what contribution the
variables are making to the end result of the model are all invisible to the viewer. The
changes in weights that occur during the training cycles are also invisible. Weights may
become altered in unexpected ways, growing larger or smaller than expected, but these
functions cannot be viewed by the user of a neural network. Likewise, changes in the
number of hidden nodes, or the number of hidden layers can theoretically affect the
outcome of the model, as the number and variety of the weightings would be changed. In
essence, tinkering with the structure of the hidden layer(s) is forming a new model. A

problem with this process is that neural network theory is at such an embryonic stage that

90

there really are no set guidelines on how many hidden nodes or hidden layers are the
optimal number to provide the best ﬁt of the model. In this case, statistical models may
be preferential, as they follow speciﬁc rules and utilize speciﬁc equations for which
parameters may be speciﬁed. In addition, these coefﬁcients and parameters of the model
may be speciﬁed and examined to ﬁnd explanatory power in the statistical model.

Neural networks have similar qualities to logistic regression as both are non-linear
in nature. Neural networks and logistic regression are commonly used techniques in
medical research (Piantadosi et al. 1994). It is noted that “neural processes will always
give you results as good as statistical techniques and usually better” and that “they
(neural networks) get you a much closer ﬁt of the data in a lot less time” (Statcon 2000).
Sclove (2000) notes that while logistic regression and neural networks are similar
approaches, “standard and non-standard statistical techniques need to be compared with
neural networks to understand the relative advantages and trade-offs among these
different tools.” Also, the two methods share the use of the logistic transfer function. As
noted in Chapter 4, the neural network used in this project utilizes a sigmoid function that
converts the summations of the hidden nodes from their values to ﬁt a logistic curve of
values between 0 and 1. In this fashion, the neural nets are attempting to approximate the
data in the hidden nodes to the non-linear form of the logistic curve. Thus, both methods

are using similar methods to ﬁt the data to the functional logistic form.

The Science Under The System

From the theories of pattern to process to model building, the question must be

raised of where does this ﬁt in to the nature of GIS? Is GIS just a toolkit for processing

91

information, or is there an underlying science behind using a GIS-based framework for
this analysis? This is currently a much-debated topic in the ﬁeld of geography: is GIS a
geographic information system or a geographic information science? This debate seems
to polarize into two camps —- those who see GIS as a tool and those who View it as a
science. The GIS internet discussion group GIS-L featured many responses dealing with
the subject of GIS as a tool or a science (Wright et al. 1997b) indicating a great deal of
interest by the research community in relation to the nature of GIS. The study by Wellar
et al. (1994) indicated a large number of published journal articles concerned with the
link between GIS / Quantitative procedures and scientiﬁc inquiry.

Goodchild (1992) notes that “science is an understanding of the issues that
underlie a system.” Likewise, Fisher (1997) deﬁnes a science as “the state of fact of
knowing knowledge or cognizance of something speciﬁed or implied knowledge
acquired by study ... a particular branch of knowledge.” Similarly, Fisher (1997) sees a

9, 66

“system an organized or connected group of objects a set or assemblage of things
connected, associated, or independent so as to form a complex unity a whole
composed of parts in an orderly arrangement according to some scheme or plan.” In the
case of GIS, the “system” (or tool) would be the hardware, software, and related tools
used to implement tasks, while the “science” would be the underlying theory and design
which the system is implementing.

The validity of Geographic Information Science has been championed by many in
the ﬁeld (Goodchild 1992, Openshaw 1998, Fisher 1997, Wright et al. 1997).

Historically, there has been a strong underpining of the science of spatial data handing

beneath the system. Spatial manipulations such as overlay operations have been

92

documented back to 1912 (Steinitz 1976) with uses in environmental quality issues or
land use planning. Likewise McHarg (1969) used spatial overlay operations to try and
maximize social beneﬁt and minimize environmental cost in landscape planning
operations. The science has been there all along, while computer programs such as
ESRI’s Arc/Info and ArcView are all GI Systems for doing more modern and advanced
forms of these spatial data operations. When the original Geographic Information
System (the Canada Geographic Information System) was developed by Roger
Tomlinson in the 19605 (Marble and Sandhu 1994) it was not technology driven (given
the state of computer systems technology at that time). Rather, there was an underlying
science behind the system.

This research can be seen as an examination of some of the science underlying the
system. The spatial construction of the variables in the GIS shows some underlying
science to the system — analyses such as distance or neighborhood functions incorporate
spatial techniques. Likewise, studying this type of phenomenon at a spatial level adds
another component rather than just tabulating statistics. For instance, the ability to
spatially map out residuals provides a link between the underlying spatial science (in

terms of visualization and analysis) and the software of the system.

Implications for Land Use and Potential Land Use Change

Though this project provided a look at one point in time, the examination of areas
of high proportions of seasonal homes carries some implications beyond one time frame.
The concepts and ideas outlined in this section are beyond the scope of the results of this

project (and fodder for future research), yet there is some room for inference and

93

speculation partly based on the modeling results. Tombaugh (1970) similarly made
predictions of ﬁrture developments based on an analysis of one point in time, though he
notes that a strong degree of caution should be exercised in making such forecasts.

The development of a new seasonal home at a particular site brings with it a
number of effects, the ﬁrst among these is the onset of further development. The results
of the spatial autocorrelation analysis partly drive this idea. Areas of the higher
proportions of seasonal homes may be areas where more seasonal homes may be found in
the ﬁrture. This ﬁts in with Butler’s (1980) life cycle concept, which seems applicable to
this aspect of recreational tourism. Butler posits that destinations will grow until a
stagnation level is reached and then will plateau and either reinvent themselves or fall
into decline. Some areas with higher proportions of seasonal homes may grow in
numbers of both permanent and second homes, becoming more of an area catering to
increased numbers of tourists and seasonal migrants.

As the natural areas draw in more seasonal home development, the area becomes
despoiled as new seasonal homes are built. Further land use changes occur when the
seasonal population increases, and a need for basic amenities is created. Construction of
grocery stores, gas stations, and medical facilities can soon lead to development of
restaurants, shopping facilities, and hotels for tourists. Thus, areas which are highly
clustered in seasonal homes could see development of both seasonal and permanent
homes in the adjoining area or properties. This can also be seen as a continuance of the
“self destruction” idea of tourism (Holder 1988).

In some ways, seasonal homes can be seen as endemic of some of the problems

associated with ecotourism. The concepts of ecotourism revolve around tourists and

94

visitors arriving into an area to enjoy some natural feature, whether wildlife or
“untouched” landscape features. The ﬁequent slogan behind ecotourism is for visitors to
“take only pictures, but leave only footprints,” implying that while tourism may take
place in a locale, that location will remain untouched by the wake of the tourist. This
type of “green” or “low-impact” tourism is frequently identiﬁed as the future of tourism
and an ecologically viable alternative to mass tourism and development (Mader 1988,
Romeril 1989, Hunter and Green 1995). However, as other authors point out (Butler
1990, Wheeler 1991, J arvilouma 1992) ecotourism is bringing tourists and visitors into
sites that were otherwise inaccessible to them. As these areas grow in popularity and
word gets out about them, more visitors will arrive, perhaps more than the area can
handle. With this increased tourism to the site, new developments must be made to
accommodate the rising inﬂux of visitors, thus leading to new developments, and the
eventual rise of the area on Butler’s life cycle model (Butler 1980) from untouched to
developed. Strapp (1988) found similar results when examining a predominantly
seasonal home area in the Sauble Beach region of Ontario, Canada, and found it to be in
the stagnation or decline stages of the life cycle while developing into a more permanent
home area.

This same sort of theory can be applied to the development of seasonal homes.
Frequently, seasonal homes are developed in areas away from large cities and in
proximity to natural areas. In fact, as seen in Chapter 5, the presence of water and the
density of natural areas were identiﬁed as the principal variables involved with the
proportion of seasonal homes in an area, with factors such as distance from cities playing

a part. However, it is development at these natural or more distant areas that leads them

95

to become steadily less natural or less remote. Lundgren’s (1974) model of seasonal
home development in Canada showed the initial seasonal home (or cottage) region at
some distance outside the city. As the city grew and expanded, this seasonal home region
is gradually overtaken by the expansion process, leading to it being subsumed within the
city proper. Thus, a new seasonal home area is established farther out from this new city
boundary. The implication is that as the city continues to grow, this new seasonal home
area will be consumed into the city environs, leading to the establishment of a third
seasonal home region further out from the city. Like ecotourism, development of
seasonal homes can be seen as having short term beneﬁts but long term effects.

An example of this type of scenario can be seen in Door County, Wisconsin. The
Door Peninsula j uts into Lake Michigan from the eastern shores of Wisconsin, and with
its 250 miles of shoreline is one of the top tourist destinations in the state. The earliest
visitors came to the area from Chicago and Milwaukee to enjoy the scenic landscapes,
picturesque beaches, and quiet lifestyle of the peninsula (Hart 1984). Door County rose
to prominence after being described as “A Kingdom So Delicious” by National
Geographic magazine in 1970 (Bossellman et al. 1999). Today, Door County is a prime
destination for all manner of tourists, boasting itself as one of the ten best places in the
world for cross country skiing (Hart 1984) as well as numerous opportunities for boating,
swimming, hiking, sightseeing, as well as unique shopping and dining experiences. In
addition, Door County has become a popular choice for seasonal home construction,
particularly large condominium developments which are used as time-shares (Bossellrnan

et al. 1999).

96

According to the 1990 Census, Door County has a year-round population of
26,000 persons (Scheberle and Pagel 1999). However, during peak tourist season, there
are approximately 40,000 tourists and seasonal residents per day in the county (Scheberle
and Pagel 1999). Door County has seen its number of seasonal home units increase by
more than 50% between 1970 and 1990, with seasonal homes accounting for roughly
34% of the total housing stock in the area (Scheberle and Pagel 1999). It is estimated that
second homes in Door County are priced between $100,000 and multi-millions (Ronan
1999). Frequently, one can see beachfront homes (with fenced or roped off areas
declaring the land to be private property) crowded in and among resorts and areas
jammed with tourists.

This level of seasonal and tourist development has brought many land use
changes to Door County. For instance, residential land use in the county is on the rise,
slowly but steadily, along with growing values for developed land use. Agriculture land
use is in decline, along with the total natural land use of the area (Scheberle and Pagel
1999). With much shoreline development under protective private ownership or public
control, development has grown in the inland rural areas. Door County appears to have
been an area once used as a seasonal vacation getaway that is now slowly becoming a
more commercial tourist area along with a growing and rising trend in seasonal homes.
One small example of the growing tourist inﬂuence is the presence of the unique “ﬁsh
boil” seen at numerous restaurants in the area and billed as a Door County specialty.
However, as Hart (1984) points out, this is a deﬁnite invention to draw tourists, as this
“ancient Scandinavian tradition” (as it is billed) was actually invented at an early stage of

the 20th century.

97

Conclusion

This chapter provides a ﬁnal discussion of some points of the dissertation and
how its place in the overall theory of geography. Seasonal home development may
largely be a tourism-related phenomenon, but it can be traced to other branches of theory
and development, and is heavily inﬂuenced by the patterns of use and cover of the
landscape. Similarly, the model-building portion of this project sheds new insight on the
nature of statistical models when compared to the new theories of neural networks.
Limitations of the use of large data sets and the varying sizes of MCDs have been
examined as a source of bias that gets uniquely perpetuated through the system. Also, the
role of science of GIS is examined. Finally, some speculations as to potential
implications and extensions of this study are examined. This project folds in on itself,
drawing from several branches of theory and returning to those theories once more.

The ﬁnal chapter of this dissertation uses the results of this project and some
topics raised in this discussion to outline a series of future directions for research that can

use this project as a starting point to build from.

98

Chapter 7: Future Directions

A Baseline Approach

The project has value and signiﬁcance as original research, both in contributing to
theory and to application. This project is relevant in its contribution to the branches of
theory of landscape ecology, tourism development, and geographic information science.
This project brought together three disparate ﬁelds of theory that have been rarely
considered together. As a landscape ecology project, this study aids in identifying the
weight of various landscape factors to the distribution of seasonal homes. Likewise, the
ﬁeld of tourist development will beneﬁt from the focus placed on this project. As noted
previously, little research has been done in the area of spatially predicting areas of
seasonal homes, or in spatial modeling of tourism and seasonal home development. The
project can also contribute to geographic information science as it has tested the strength
of the modeling approaches in an overall GIS-based modeling framework. In regards to
the theory of spatial distribution, this project shows a validation of those theories in the
notion that the patterns of the landscape are factors in driving overall human processes.

This project also provides an applied test of the GIS-based framework and the
LTM’s functions in development of independent variables, and while no true land
transformation is being measured, the LTM’s modeling techniques are being tested in the
prediction of seasonal home areas. The results of this project may prove of use to state,
county, or township planners to aid in identifying areas of seasonal home distribution.

From these results, future modeling efforts of examining temporal change may be done.

99

By identifying the principal factors of second home location, as well as the weight
and contribution of each factor, the ground is readied so that future predictions of
seasonal home developments can be made. Spatial residuals from the model are targets
for learning; planners will have direction where to go for more information to learn why
these areas are over or underestimated by the model. This notion can be especially seen
in the spatial error signal analysis presented in Chapter 5. Many residual areas were seen
to be highly correlated with the distribution of public lands. As noted in Chapter 2, while
public lands play host to a wide range of natural features and outdoor recreation, there are
numerous problems involved with them, including misidentiﬁcation of borders and
growing privatization and development within their boundaries.

This research also contributed to the science of model building. Though it is not a
heavily methodological project, several results can be made concerning the notion of
explanatory vs. predictive power of models. Also, the combination of several factors
(extremely large data sets, statistical techniques, and basic neural network approaches)
pointed out some limitations and shortcomings of the various applications. This project
has identiﬁed several areas requiring ﬁrrther study or development, and hints at other
techniques that could be used.

The use of this project should be considered a baseline for things to come. The
theory behind the project and its link to geography has been addressed, as well as
development of independent variables through GIS. Various modeling approaches have
been deﬁned, and their abilities and shortcomings noted. As this project utilizes such a
large scale, it should be seen as a “broad brush” in the sense that several of the project’s

limitations are created by setting the study in such a large region. While this project is

100

complete unto itself, it provides numerous ﬁrture directions from which to proceed.

These are described as follows:

Regionalization

The broad sweep of seasonal home distribution at the three-state level is captured
in this project. At such a level, many generalizations had to be made, and the varying
geography was one source of noise in the models (as noted in Chapter 6). With this
baseline study complete, more detailed work can be done at a smaller regional scale. At a
smaller scale, better data sources could be utilized for some of the variables. For
instance, if the study was being done at a county or multi-county level, perhaps more
accurate public lands data could be obtained. In a smaller region, more accurate data
could be created by hand or obtained from local sources, things that were unfeasible at a
three-state level. In addition, a smaller, regional, data set would be much more
manageable to work with; data observations could be closely examined and sources of
noise or error would be more readily identiﬁable.

Similarly, additional data could be obtained to utilize in the model. Information
that was unavailable at a three-state level could be collected at a more regional level.
Data such as locations of public boat launches, airstrips, ski resorts, or snowmobile trails
could be obtained at a smaller scale. Working at a regional scale would also allow more
detailed information about the types of urban areas, their extents, and information about
local seasonal home patterns or developments. In addition, more localized data such as
zoning regulations, potential zoning plans, or information regarding the amount of

available land that can be developed on can all be collected at a smaller scale.

lOl

Working at a smaller scale could also allow for the collection of origin-based
data. Survey data taken at a community level could provide insight into many of the
missing variables as outlined in Chapter 6. Socio-economic data about individuals,
patterns of use, and travel time to and from a seasonal home. Furthermore, information
about the purpose of the home, the year bought, and the value of the land could all prove
beneﬁcial to the models’ overall ﬁt and explanatory power.

This regional scale is adjustable. Studies could be done within a largely seasonal
community, requiring work at the parcel level scale. An entire township could be
modeled as well. Scaling up to the county level would allow for an adaptation of the
analyses presented here, where controls could be developed to account for variations in
township size. Counties such as Door, WI, Grand Traverse, M1, or Otter Tail, MN would
be sites to perform such analysis. Finally, a more broad regional scale could encompass a
multi-county area, such as the six counties comprising the Grand Traverse Bay
Watershed. At this type of regional scale, the techniques used in this project could be

incorporated with a host of new variables that are missing from the original study.

Temporal Modeling

With the imminent arrival of the 2000 Census, data will be available to perform
temporal modeling. This would take the form of modeling changes between townships to
see if they went up or down in their percentage of seasonal homes between 1990 and
2000. From there, development trends could be modeled. Once again, a broad baseline

study could be performed, or this could be used to follow up on one or more regional

102

studies. In this sense, a regional study at 1990 could be performed, another study of the
same area with 2000 data, and the results could be compared.

There is a deﬁnite need for studying the trends of seasonal home development, as
it is on the rise. In 1999, 377,000 seasonal homes were purchased or built, up from
345,000 units in 1997 (NAR 2000). This ﬁgure is up considerably from sales of 296,000
in 1995 (NAR 2000). This rise in seasonal home development and sales comes at the
same time as a tax-law change in 1997, which “essentially did away with the capital gains
tax penalty for most buyers wishing to trade down to a smaller primary residence and
also use some of their equity to purchase a second home” (N AR 2000). With the
favorable economy that the 1990’s have enjoyed and changes in the tax law structure to
allow for an easier purchase of seasonal homes, there has been a corresponding boom in
seasonal home sales. Approximately 6% of all homes sold each year are seasonal homes
(NAR 2000).

There is a deﬁnite growing trend of seasonal development, as the number of
seasonal homes in the United States has increased over time. Table 7.1 shows the total

number of seasonal homes in the US from 1940 through 1990.

 

 

 

YEAR 1940 1950 1960 1970 I980 1990
Seasonal 739,594 1,050,466 2,024,381 2,020,087 2,794,054 3,1 16,867
All Homes 37,325,470 45,983,398 58,326,357 68,679,030 88,41 1,263 102,263,678

 

 

 

 

 

 

 

 

 

Table 7.1: US Housing and Seasonal Homes by year (source: US Census Bureau)

Figure 7.1 shows the geographic distribution of seasonal homes in the US for the

same time period. As can be seen, the numbers of seasonal homes in the US is growing

103

 

 

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22.0. - Emma i
8.54. - 59; D

880: 3538 .o .onE=z

 

 

 

Figure 7.1: Number of seasonal homes in the United States, 1940-1990

at a steady rate. By 1990, seasonal homes account for roughly 3% of the total housing
stock in the US. Areas in the south (including Florida, which leads the US in the number
of seasonal homes) and the mid-Atlantic are growing, and also regions in the north,
including parts of New England and the Lake State region of Wisconsin, Minnesota, and
Michigan. California has seen a boom in seasonal home development. In fact, in 1999,
Sugarloaf, California saw 93.3% of all housing sales in the area come from seasonal
home sales (Fogarty 2000).

Thus, there are deﬁnite growing trends in seasonal home development in the
United States. As can be seen, this type of study has applications to areas outside the
Michigan, Wisconsin, and Minnesota area. Places in California (the aforementioned
Sugarloaf) or Florida (in booming seasonal home markets such as Naples) would be

prime candidates for other regional and temporal studies.

Adapting for Land Use Change

An extension of the temporal modeling project would be to utilize the data to do
true land use change modeling. The literature lacks models that explicitly focus on
recreation or tourism as land use change drivers, so this project would be able to
contribute to the theory of land use change as well as develop a new type of modeling
approach that has not been done as yet. As Campbell (1998) notes, there is more to
human-environment interaction than simply the biophysical level of study. For example,

the Kite framework (Campbell and Olson 1991) provides a means of encapsulating the

105

dimensions of human interaction, the nature of power, and the environmental changes
occuning.

Future uses of the land (in relation to seasonal home development) may also be
forecasted through the use of these modeling techniques. As one of the goals of this
study is to identify the predictor variables of seasonal home location, this portion of
future analysis is already completed. Thus, future research for true land transformation
studies can begin at a higher plane.

The use of the LTM in these types of studies takes advantage of its full capacity
as a model of land use change. By examining land use at two time steps, the change
between the two can be modeled. This would build off of the “temporal modeling”
approach previously outlined, and would probably be best to study at a regional scale.
Gathering data about locations of seasonal homes could be best done at a parcel level,
where tax records could give indications of which homes were held for seasonal use and
which were permanent at two time steps. Process-driver variables of housing
development could be constructed and the resulting land use changes (in the form of
further seasonal home development) could be examined.

Another application would be to take the results of the temporal change study and
identify areas high in seasonal home development (i.e. areas which showed a strong
increase in seasonal homes between the 1990 and 2000 census), and do land use change
modeling on those areas. The results of this project point to some of the principal
predictors of seasonal home development that could be used as variables in the model.

Areas that changed to a residential land use would then be predicted by the model.

106

A limitation to this type of study is the reliance on historical patterns to forecast
future trends. A regression style land use model (Theobald and Hobbs 1998) will be
doing just this. If seasonal home development areas have fallen into the stagnation of
decline stages of Butler’s life cycle model (similar to a case study examined by Strapp
1988), then population trends may give spurious results. In cases such as this, on site
evaluation may be necessary to determine the type of changes occurring. Otherwise, the
model may be forecasting a saturation effect of urbanization in the area where no such
development is occurring. However, if the area is experiencing fast growth due to
seasonal home development (or other factors) then population forecasts may be too low
for the area.

Land use change modeling approaches can be used for other forms of recreational
based tourism as well, beyond seasonal homes. Tourism has been seen as an “engine of
development” (Roehl and Fesenmaier 1987), as localities throughout the US have made
the transition to a tourism-based economy. Several initial tourism developments occur to
provide economic beneﬁts to a particular area G’earce 1989, Witt and Moutinho 1994), or
to meet the demands of travelers to the region (Ryan 1991). In fact, tourism comprises
the world’s largest economic sector (WTO 1995) and carries with it signiﬁcant changes
to the landscape and physical environment (Cohen 1978, Pigram 1980, Stroud 1983, May
1991, Ryan 1991, McKercher 1992). The land is changed from its natural state to new
usages speciﬁcally designed for tourism, such as resorts, amusement parks, shops,
parking areas, airstrips, and boat docks. Tourism drives changes in population and the

local economy. These factors in turn spur changes in the way land is utilized.

107

For instance, Walker (1991) notes that the natural ﬂora at Heron Island, Great
Barrier Reef, has been disturbed by tourism development to the point where exotic
species now outnumber the natural ones. The Sikkim Himalaya region provides another
example; tourism has caused a greater degree of pastoralization, and thus a marked
increase in timber harvesting and forest destruction for fuel and fodder (Rai and
Sundriyal 1997). Coastal areas have seen sewage disposal, desalinization, inigation,
inﬁlling, and sediment from construction contribute to the degradation of coral reefs
(Hawkins and Roberts 1994). It is these types of effects that application of land use

change models to tourism-related phenomena would be of beneﬁt.

Other Applications of the Framework

The modeling framework outlined in this project, at its most extremely basic level
takes a number of spatially constructed variables and uses them as independent variables
in varying modeling approaches to predict a dependent variable bounded by 0 and 1,
rather than a binary response of 0 or 1. This basic modeling framework can be adapted
and applied to other sources of data as well. For instance, one application of the model
could be to explain the spread of farms across the landscape. Data would have to be
collected to represent the proportion of farms of the total housing stock in a particular
area. A new set of independent variables would be required to be built from new
branches of theory and literature, but the basic modeling framework to undertake such a

study is now in place.

108

Methodological Exploration

Much more can be done with neural networks than is shown in this project. Their
use in this project is to examine another potential modeling approach and to provide a
comparison with established statistical techniques. Numerous other forms of neural
network learning algorithms are available to use, including bidirectional associative
memory, adapted resonance theory, and counter-propagation networks (Freeman and
Skapura 1992). Likewise, as noted in Chapter 6, altering the number of hidden nodes or
hidden layers changes the structure of the network and its learning abilities. Too many or
too few hidden nodes can cause generalization errors in the system (Sarle 2001). There is
no set rule for the number of hidden nodes to use (Swingler 1996), and examples may be
constructed to nullify some rules of thumb (Sarle 2001). The correct number of nodes
seems to depend on much exploration of the data, the number of training cases, and the
complexity of the function involved (Sarle 2001). Addition of extra hidden layers is
another concept that requires investigation, but is beyond the capabilities of the neural
network software used in this project.

The problems with the data as outlined in Chapter 6 were causing certain
problems with the functionality of the neural network. The following analysis is beyond
the range of the results, but one hypothesis is that this noise in the data could potentially
be causing what is called “activation function saturation” in the neural network (Skapura
1996). If enough saturation occurs, the derivations for the weights may be reduced and
learning may be slowed (Reed and Marks 1999). A typical cause of saturation is large

external inputs (Reed and Marks 1999) that are the outlier data values. This could cause

109

the model to be overﬁtting or underﬁtting the data. Reed and Marks (1999) suggest that
the data should be altered to ﬁt to a reasonable range, yet the standardization procedure of
the PCA has done just this. However, simply altering values will not solve the problem,
as the weight initialization range to avoid saturation is dependent on many effects,
including the number of inputs to a node, and the correlations between inputs (Reed and
Marks 1999). Even accounting for this, Reed and Marks (1999) note that since the
weights of a neural network change during the learning process, saturation may develop

at later levels. Obviously, this is not a problem with a simple solution.

Neural network research is still at an embryonic stage of development. There are
very few hard and fast rules that are applicable to questions concerning the usage of
neural networks. Neural networks provide strong predictive abilities, but care must be
given to interpreting those results. As this study has shown, a neural network suffers
from a multitude of problems including how it handles data, the structure of its own
architecture, and its label as a “black box.” Unlike statistical models, one cannot easily
peer into the innards of the neural network and derive results.

A highly methodological paper on the architecture of neural networks and how
they relate to spatial problems is suggested as a future direction for research. Many of
the above concepts are speculations about how the neural network is handling the data
and potential problems with the data. A heavy investigation into the structure and usage
of neural networks would aid in clearing up several of these mysteries and may possibly

ﬁnd solutions to them.

110

 

Spatial Statistics Approaches

There are other modeling approaches that can be used to predict the distribution
of a phenomenon across a landscape. Spatial statistics (and in particular spatial
interpolation methods) can provide a measure of patterns on the landscape. A random
sample of points on the landscape can in turn provide a measure of the values of nearby
points. Numerous applications can be done with this type of data. Cross-validation
(Bailey and Gatrell 1995) is a method involving removing one observation from a dataset
and using all other points to interpolate the missing value. Ordinary kriging is a
technique that estimates a local mean (Bailey and Gatrell 1995) and is a common tool in
predicting values along a continuous surface.

To use these spatial techniques with seasonal home distribution, the MCD
polygons would ﬁrst have to be converted to point data. The centroids of each MCD
were found, and as they are so clustered in space, the MCDs can be evaluated as points
(in a similar method to the spatial autocorrelation method described in Chapter 5). From
there, ordinary kriging can be performed on a subset of the data to interpolate the surface.

A simple experiment was done with ordinary kriging to determine the usefulness
of this application in future studies. Ordinary kriging was chosen as makes no
assumption of a local trends. However, ordinary kriging assumes a mean of 0 (Isaaks and
Srivastava 1989). While the seasonal home distribution data does not meet this criteria,
the residuals do, so kriging will be performed on them. The semivariogram shown in
Chapter 5 was used to compute the range, sill, and nugget for the kriging. A randomly
selected sample of 20% of the polygons (the same 20% used in the neural network

testing) was used and ordinary kriging was done to interpolate out the remaining 80%.

111

The estimated output values were compared to the observed values and a
correlation coefﬁcient and pseudo-R2 were computed to compare the estimates with the
other results. Using a 20% sample produced a correlation coefﬁcient of .69, which
becomes a pseudo-R2 of .47, indicating a good ﬁt to the landscape. This is a simple
experiment, but shows the applicability of additional techniques such as spatial statistics
to this project. Future research could expand on these methods with more in-depth and
detailed examinations of the applicability of spatial statistics to seasonal home or

recreational tourism data.

Conclusion

This chapter has shown that this study, while a broad brush over three states, can
be used as a baseline for a myriad of future projects to come. The results and conclusions
can be adapted for use on a smaller, more regional setting. This type of environment may
provide the best setting for studying a phenomenon such as seasonal home distribution as
more local factors can be accounted for. In addition, greater amounts and more accurate
data can be obtained at a regional scale.

With the advent of the 2000 Census, temporal change between 1990 and 2000 can
be computed as well. This project also lends itself to land use change modeling. The
framework of the study could be utilized in other environments to predict similar
measures, such as farms. Finally, a more in-depth examination of neural networks is
suggested, especially with regard to their format, design, architecture, and applicability to
other projects within the social or natural sciences. Lastly, other techniques, such as

spatial statistics, can be utilized in future extensions of this project.

112

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125

 

 

APPENDIX A
INDEPENDENT VARIABLE MAPS

 

126

 

Distance from places
of more than 100,000 persons

   
 
 
  

M1011
1521404 - 73179.727
781 .727 - “.219
14833219 - 2151135..
218735325 - 315012.156
315012166 - “126.063

 

 

 

Distance from places
between 10K and 100K persons

u10|m1wk
591.865- 20651335

21351. - .07
3593.07 - 547213.578
547213.578 - 82140.8”
82140572 — W797.”

  
     

 

 

 

 

   
  
   

Distance from places of
between 1000 and 10000 persons

u1|m101

I: 411.3211- 7314.45
7344.45. 11516951
11516.951- 1mm
16923.393- sea
maes- mm

 

 

 

Distance from places
between 500 and 1000 persons
mm
2375254155582
1 .582- 1663267
15632.67-m1s049

2316.049 - $830.75
SWIM - 137613.$1

     

 

 

128

 

 

 

u '1: 7' '1 )0 %‘

 

 

 
  
  
     

Distance from places
of less than 500 persons

Us 500

$355 - mm
mm - 1328.6”
1283.825 - 1mm
18650443 - “19.424
M19424 - 1m.21 ‘l

 

 

 

 

    

Distance from selected
tourism sites

Tam-n
758.410 - 52446.0”
446.679 - “21 .014

1 405.
1214M363- 103111.047
183111.047 - 454470.75

 

 

 

 

    
   

Distance from hospitals
Mm Hm:

5023.932 - 21694”
3194:839- means
M.HO- 77372172
77372172- 199133.734

 

 

 

Population Density
(Persons per square mile)

 

 

 

 

 

 

   
  
  

Distance from major highways

mm W
QZZ- M704
mum-21108339
308133-4074
4074-5643177

mun-«mm

   

 

 

 

   

5460.988 - 15m.087
15M.087 - 24014.30
24014258 - 3437.133
343157.063 - 1010605

 

131

 

 

 

Distance from vehicular trails

  
  

mthTris
726-8882582

 

 

 

Distance from local roads

 

 

 

 

132

 

 

 

   
    

Inf.
1:: .-

Density of Natural Areas

0- 1 .130
19.138- 44.114
44114-

$743

531743- 111.012

111.012- 1211922

 

 

 
  
 
 
 
 

Agricultural Density

MD“

0- 55$
5.589 - 8.312
3.312 - 70.07
70.97 - 99.04

99.04- 121

  

 

133

 

 

    
 
  

Distance from public lands

WWW:

793a - 211331.910
21081.916- m1 .305

 

 

 

 

Density of public lands

worm“
D

 

 

 

I

1;

.4.

 

 

 

 

Distance from major water bodies

 

 

 

 
 
 
 

100
Density of major water bodies
Dornttoydm
0- 0.552
0.552 - 2.047
2.047 - 6.131
8.131 - 110.790
l
100
E:

 

 

135

 

 

   

Amount of forests

5122-16903
1m- 251121

 

 

 

 

 

 

 

 

 

 

Amount of Great Lakes lakeshore

 

 

 

Distance from Great Lakes
lakeshore

    

Dinawe'rome L.

“E

184947.172 - 27m .344
277251.344 - 40134.

 

137

 

 

 

 

Landscape Variability

 

 

138

 

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