Location Value Signature and Spatial Externalities in an Urban Environment

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Location Value Signature and Spatial Externalities in an Urban Environment
Huang, Zhuojie
Place of Publication:
[Gainesville, Fla.]
University of Florida
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1 online resource (92 p.)

Thesis/Dissertation Information

Master's ( M.S.)
Degree Grantor:
University of Florida
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Committee Chair:
Fik, Timothy J.
Committee Members:
Thrall, Grant I.
Qiu, Youliang
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Subjects / Keywords:
Cities ( jstor )
Economic models ( jstor )
Geodetic position ( jstor )
Housing ( jstor )
Housing units ( jstor )
Market prices ( jstor )
Modeling ( jstor )
Prices ( jstor )
Real estate markets ( jstor )
Spatial models ( jstor )
Geography -- Dissertations, Academic -- UF
externalities, location, signature, spatial, value
City of Gainesville ( local )
Electronic Thesis or Dissertation
born-digital ( sobekcm )
Geography thesis, M.S.


This research reviews the sub-station concept in the real estate literature and attempts to decompose real estate submarkets in two dimensions: the structure submarket and the spatial submarket. Various multivariate statistic techniques are used to test the validity of this subdivision. We find out that although there are many statistical methods to define a submarket, there is still a substantial gap for linking the spatial aspects of the problem with patterns of valuation as they relate to the process of urban change and development, structural attributes, and the local context in which individual properties are affected or unaffected by that change. It is proposed that each location within the urban system has a unique location value signature (or LVS), and that LVS could reflect the total or composite externality effect on the selling price or market value of a house at that location. By analyzing the means within or between different structural and spatial submarkets, the LVS could be presented as a variable surface within the urban housing market. The object of this study is not only to present a model for the estimation of housing values (a hedonic price valuation model), but to integrate a strategy to model trends in real estate submarkets to local and city-wide trends (including infrastructure development). ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
Includes bibliographical references.
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Thesis (M.S.)--University of Florida, 2009.
Adviser: Fik, Timothy J.
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by Zhuojie Huang.

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University of Florida
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Copyright Huang, Zhuojie. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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589169282 ( OCLC )
LD1780 2009 ( lcc )


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2 2009 Zhuojie Huang


3 To my Mom and Dad, Meifang Liang and Zhicheng Huang


4 ACKNOWLEDGMENTS I would like to formally than k Dr. Timothy Fik, my advisor, for his enthusiasm, hard work and guidance throughout this entire thesis process and for believing in my abilities especially gi ve me courage for English writing. I have learned so much, from analysis skills to academic writings and without you, this would not have been possible. Thank you so much for a great experience. I would like to thank Dr. Grant Thrall, for serving on my thesis committee. I appreciate your valuable comment s on my thesis and I have learned a lot from you class. Thank you for your insightful guidance throughout the past two years. I would like to express my gratitude to Dr.Youliang Qiu for serving on my thesis committee. Without your invaluable support and assistance, this study would not have been successful. I would like to thank Dr. Pete Waylen and Dr. Jane Southworth, for providing this great chance to study in the G eography department and helping me get used to the life at University of F lorida I real ly love the department Finally, I would like to thank m y parents, for their never ending love and support in all my endeavors and efforts, and for giving me the foundation to be who I am. Thank you, Mom and Dad.


5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 6 LIST OF FIGURES .............................................................................................................................. 7 ABSTRACT .......................................................................................................................................... 8 CHAPTER 1 INTRODUCTION AND CONCEPTURAL FRAMEWORK ................................................... 9 2 SURVEY OF RESEARCH AREA ............................................................................................ 16 Data Sources ................................................................................................................................ 16 Objectives .................................................................................................................................... 16 The Study Area ............................................................................................................................ 17 3 RESEARCH DESIGN AND METHODOLOGY REVIEW ................................................... 27 Hedonic Models and Spatial Econometric Literatures ............................................................. 32 Submarket Definition by Structural Clustering ......................................................................... 35 Spatial Clustering and Geographically Weighted Regression .................................................. 36 Analysis of Variance for Structural Submarket and Spatial Submarket .................................. 39 Spatial Expansion Model and Stepwise selection ..................................................................... 41 4 RESULTS AND INTERPRETATION ..................................................................................... 46 Global Hedonic Price Results ..................................................................................................... 46 Structural Clustering Results ...................................................................................................... 47 Sp atial Submarket Results .......................................................................................................... 48 ANOVA for Structural and Spatial Effects ............................................................................... 49 Interpretation of Spatial Expansion Model ................................................................................ 52 5 DISCUSSION AND CONCLUSION ........................................................................................ 81 LIST OF REFERENCES ................................................................................................................... 88 BIOGRAPHICAL SKETCH ............................................................................................................. 92


6 LIST OF TABLES Table page 3 1 Variable definition ................................................................................................................. 44 4 1 Results of global model ......................................................................................................... 57 4 2 Structural cluster results ......................................................................................................... 58 4 3 Discriminant summary using uniform kernel density .......................................................... 59 4 4 Overall ANOVA for structural and spatial categories ......................................................... 60 4 5 Slice effects by structural category and spatial category ..................................................... 61 4 6 Means of submarkets ............................................................................................................. 62 4 7 Standard errors for spatial expansion model ........................................................................ 63 4 8 Coefficients estimation .......................................................................................................... 64 4 9 Modified spatial expansion model ........................................................................................ 65


7 LIST OF FIGURES Figure page 2 1 Directional eclipse of housing unit sample in Gainesville area .......................................... 25 2 2 The histogram of building age in Gainesville ...................................................................... 25 3 1 Flowchart of analysis procedure............................................................................................ 45 4 1 Residuals distribution of global model ................................................................................ 66 4 2 Price Surface for Clusok1 ...................................................................................................... 67 4 3 Price Surface for Clusok2 ...................................................................................................... 67 4 4 Price Surface for Clusok3 ...................................................................................................... 68 4 5 Price Surface for Clusok4 ...................................................................................................... 68 4 6 Spatial distribution of structural submarket .......................................................................... 69 4 7 Spatial cluster result and GWR coefficients maps. ............................................................ 70 4 8 Comparison matrix for LNSALE .......................................................................................... 71 4 9 Box plot for mean differentiation .......................................................................................... 72 4 10 Structural clusters by location effects for area E, ME, M and MN ..................................... 73 4 11 Structural clusters by location effects for are a MS, NW and SW ....................................... 74 4 12 Least -square mean of structural cluster; CLUSOK1 and CLUSOK2 ................................ 75 4 13 Least -square mean of structural cluster; CLUSOK3 and CLUSOK4 ................................ 76 4 14 Residual analysis. ................................................................................................................... 77 4 15 Residuals' distribution for the spatial expansion model ....................................................... 78 4 16 Under estimations of residuals .............................................................................................. 79 4 17 Over estimations of residuals ................................................................................................ 80


8 Abstract of Thesis Prese nted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science LOCATION VALUE SIGNATURE AND SPATIAL EXTERNALIT IES IN AN URBAN E NVIRONMENT By Zhuojie Huang December 2009 Chair: Timothy Fik Major: Geography This research reviews the sub -station concept in the real estate literature and attempts to decompose real estate submarket s in two dimensions: the str ucture submarket and the spatial submarket. Various multivariate statistic techniques are used to test the validity of this subdivisi on We find out that although there are many statistic al methods to define a submarket, there is still a substantial gap f or linking the spatial aspects of the problem with patterns of valuation as they relate to the process of urban change and development structural attributes, and the local context in which individual properties are affected or unaffected by that change. It is propose d that each location within the urban system ha s a unique location value signature (or LVS ), and that LVS could reflect the total or composite externality effect on the selling price or market value of a house at that location By analyzing the means within or between different structur al and spatial submarket s the LVS could be presented as a variable surface within the urban housing market The object of this study is not only to present a model for the estimation of housing values (a hed onic price valuation model) but to integrate a strategy to model trends in real estate submarkets to local and city -wide trends (including infrastructure development).


9 CHAPTER 1 INTRODUCTION AND CON CEPTURAL FRAMEWORK Real estate valuation studies have largely relied on the hedonic model as a method to estimate the market price of housing in a municipal con text. A seminal work in this area was one which focused on the estimation of the marginal impact of the characteristics of property and neighborhoo d externalities (Rosen 1974) Ty pically site and situational characteristics a re utilized to determine their individual effect s on the market price of a property This work fell under the methodological framework developed by Lancaster, who had argued that the value of a housing unit i s related to a bundle of characteristics which provided utility to consumers of housing as a commodity and service (Lancaster 1966) In the past fifty years, however, various improvements on hedonic models have been introduced in the literature. A subset of this literature focus es on ways to enhance the accuracy of market value estimation through the identification and inclusion of real estate submarkets. A submarket is viewed, in economic terms, as a substitute market or strata that is perceived as being part of a group that has replaceable options or one which shares similar characteristics (in terms of site -specific or contextual qualities). In real estate apprai sal industry, submarket is defined as a division of a total market that reflects the preference of a particular set of buyers and sellers (The A ppraisal of Real Estate, p271). In other words, housing units from the same sub-market are considered to be p otentially substitutable as far as providing a bundle of characteristics and a given level of overall utility. Generally speaking, submarkets are defined by structure, location, and the combined effect of structure and location. Submarkets may also be defined in terms of socio -economic or socio demographic groups (Palm 1978; Maclennan et al. 1987; Bourassa et al. 1999; Watkins 2001) If housing units are part of a certain submarket, these units are considered sharing some general


10 attributes and similarities in terms of local externalities or other spatial related characteristics that differentiate these units from other units in the city. The use of submarkets represents a departure from traditional theory in the urban economic literature which simplified a city into a core or downtown area or Central Bus iness District (CBD) and a peripheral region which surround ed it. In the traditional models, t he value of real estate is assumed to decline with increasing distance from the city center which was known to have the highest value in relation to its locati on accessibility and centrality (Alonso 1964) Refinements of this theory included the more realistic concept of the city as a heterogeneous and poly -centric system, and not simply a homogenous landscape with a single prominent node. As such, urban housing and land values in an urban area would be different and vary over various locations, thereby, creating a housing valuation surface that was variable and discontinuous (Goodman 1978; Goodman 1981; Bourassa et al. 2003; Bitter et al. 2007). Richardson pointed out that the polycentric model could better delineate the sub -centers of a city, and that the city should be considered as a multi -nodal entity with location accessibilities that varied across space (Richardson 1988) As such the market price or valuation surface which measured housing and/or land values should reflect the multi -nodal nature of the urban milieu. Research on the multi -nodal city became a research trend that still continues today, not only in terms of descripti ve models but also with regard to predictive models that seek to estimate and untangle the effects of externalities, differences in location accessibility, and the implications of sub-markets. Another noticeable improvement in real estate market valuation models came in the form of capturing local effects introduced into to the model through the use of location sensitive variables. Statistica l techniques were implemented to assess local effects, by moving away from a global (city -wide) model to a more localized model which was able to accurately capture local


11 externalities. One method was to use the spatial expansion modeling framework pionee red by Emilio Cassetti, allowing the interaction of spatial or local attributes with physical or site attributes (Casetti 1997) A major a dvancement in the modeling local effects and local parameter estimation was introduced with the implementation of Geographic Weighted Regression (GWR), a technique deve loped by Fotheringham et al. (1997). This involved the use of a weighting matrix with a distance -decay kennel that attempt s to capture local variability of parameters estimates at each location with in the urban system ; thereby allowing location-specific coefficients to capture the uniqueness of various site and situational effects at any given location. Implementation of geo -statistical terms and variables to address neighborhood effects/externalities have now become commonplace in the literature (Dubin 1992; Adair et al. 2000; Anselin 2003; Kim W.C. et al. 2003) Pace et al. (Pace and Gilley 1997; Pace and Barry et al. 1998) ha v e extended the framework to include the effect of time by incorporat ing spatial temporal autoregressive lags to describe the inter -correlation of real estate prices and their evolution over time and space. By manipulating the weighting matrix for the vari ables, t hey were able to delineate and differentiate the factors that account for temporal price variability based on the average value in a given time period and the spatial temporal variability linked to localized effects These efforts incorporated spa tial or location variables to reflect both the spatial heterogeneity and spatial dependence in housing prices, and differentiate between the contribution of neighborhood effects and urban externalities on the market price of housing These improvements ha ve helped tackle the problem of modeling the spatial distribution of real estate values and have led to a better understanding in our ability to target and captur e the effects of sp atial proximity, accessibility, and the all important impact of location, location, location. The modeling approach of Pace et al. and the use of GWR require the construction of


12 the spatial weighting matrix ; making it necessary to specify various spatial relationship s within the sample observations before attempting to estimate a price valuation model. Improvement s of h edonic model s have also come in the form of embrac ing the use of distance and accessibility measures, including the combination of relative and absolute location directly into the model Heikkila et al. (1989) have found that the physical distance from a land parcel to the CBD (or other prominent node) would be an important factor that contributed to the val u e and price of housing. Efforts to improve real estate valuation have also come in the form of mode ls that sought to differentiate housing units in terms of environmental factors and environmental quality Studies have included consumers willingness to pay for c lean air by differentiating the marginal price of housing units (Harrison and Rubinfeld 1978) and th e impact of clean air on the increase in value of housing in relation to the reduction of the total suspended particulates (TSP) in the air (Chay and Greenstone 2005) Poudyal et al. (2009) have also included the urban amenities, by introducing the local impact of urban recreation park s in the hedonic pricing framework These research efforts are not only important for policy makers, but suggest that housing p rices must also be view ed in terms of the aggregation effect s of environmental variables in a city. It has also been suggested that the demand side of the equation be expanded to include the socio -demographic profile s of consumers and the implications of consumer preferences and consumer information ( Kestens et al. 2006) For example, Nec hyba et al. (1998) used discrete choice model s to evaluate consumer choice in the hedonic framework. All these methods have greatly reduced the er ror in price/value estimation. However, limitations do exist as model expansion has led some to speculate that these ventures are nothing more than data mining exercises with only very marginal improvements over the much simpler models In addition, it has been argued that m any variabl es or factors defy measurement, leading to potential


13 bias or model misspecification in the estimation process. Consequently, it is necessary to balance the knowledge of the submarket and the data -mining aspects of model expansion as one wrestles with the notion of refining the hedonic approach to real estate valuation through the inclusion of spatially sensitized explanatory variables that are well grounded in theory Recent appraisal methods have introduced neural networks and agent -based modeling yet t hese techniques have proved cumbersome to practitioners a s they require enormous calculations, are difficult to implement, and with high requirement of proficiency with computer -based artificial intelligence (AI) programming (Limsombunchai et al. 2004; Bossomaier et al. 2007) Although there are many modeling frameworks for real estate market valu ation the interaction of hous ing price with location of the parcel and its situational or contextual position within the larger metropolitan setting have not been fully explored. Previous studies have alluded t o the fact that parameter drift may occur in as urban setting given the auto-correlated nature of the real estate market leading to spatial dependence or spatial heterogeneity and problems in model estimation. In addition, the mechanism of the boundary which hindered parameter drift was not fully identified Little is known on the causal nature of spatial dependence in the processes that affect value or the degree to which spatial dependence affects parameter drift It is likely a byproduct of spatial externalities that have not been effectively incorporated into the va luation model. As Bitter et al. (2007) have argued, the exact nature and affect of spatial heterogeneity on housing prices is still unclear. Thus, there is a gap for linking the spatial dependence aspects of the problem with patterns of valuation as they relate to spatial externalities, the process of urban change and development and the local context in which individual properties are affected or unaffected by that change.


14 The object o f this study is not only to compare different modeling approaches in the estimation of housing values, but to integrate a strategy to model trends in real estate submarkets to local and city -wide trends (including infrastructure development) Moreover, th e approach taken in this study will seek to differentiate between the pricing components associated with structural factor s versus spatial factor s By including the development history and various urban features to data analysis a spatial temporal sensit ivity is introduced to the model The modeling framework adopted in this paper will rely on Casettis expansion method to assess both market and sub -market variations (in the spatial temporal sense) as a function of location, accessibility, site and situa tional characteristics, and local versus non local externalities. Our research could be summarized as four -folds : First, the main effects of structural submarket and spatial submarket could be validate d as heterogene ities in a hedonic model In addition, the pricing platform of the housing units is testimonial to be continuous within those submarkets by the interaction terms. Second, the spatial submarket and structural submarket is not totally orthogonal. The interaction effects of spatial submarket and structural submarket could be conclude d by historic traits of the units. The historic traits is closely related to building age presenting: 1 ) a t a certain time point, it might affect the spatial presentation of certain structural group s 2 ) In a longer period, it might cause the alternation of appreciation rate of a certain structural group in effects of the absolute/relative location of the land parcel Third, a directional bias of pricing inclination has been identified towards the beneficial urban development nodes such as employment center and interstate system This trend could be marked by the situational transition of the centroid of the units spatial distribution. Fourth, some neighborhoods could provide leverage on housing value by better management or environment


15 amenity. These neighborhood shown significant differences in value compared to the neighborhoods around them.


16 CHAPTER 2 S URVEY OF RESEARCH AR EA This chapter highlights the various data sources used in the analysis, as well as a survey of the study area. Data Sources The data for this study were collected from the following sources: 1 Map of Transportation and Road in Alachua County Source: E 911 Office, Alachua County Fire Rescue Description: This GIS data layer contains the roadway system for Alachua County, and represent s all named road -way s This layer is used for the accessibility analysis and to identify major transportation arteries such as the Interstate and US Highway s and State Road s 2 Property App raisal database for the city of Gainesville. Source: Alachua Property Appraisal Office Description: This dataset contains parcel boundaries with each parcels associated tax information as contai ned in the Florida Department of Revenues tax database. It include s structural information, parcel location information and sales history information This is the most important layer for the modeling procedures as it contains the dependent variable (s elling price) and various independent or explanatory variables as they relate to location and the parcels characteristics Objectives The objectives of this research are four -fold. Specifically, this thesis seeks to 1 S eparate the effects (and implied utility) associated with the structure versus the value associated with geographic location, based on the structural characteristics of the housing unit and its location using a hedonic model to test for a ccuracy of identified submarkets with in the city of Gainesville, Florida. 2 Test a hedonic model enhancement that accounts for spatial coefficient drift and the subsequent spatial drift of residuals by incorporating st ructural submarket tagging 3 Assess whether an analysis of the Gainesville housing market c ould be more effectively modeled using a discrete housing value platform versus a co ntinuous housing value platform, or some combination thereof ; by evaluating the boundaries of the discrete housing submarkets and the continuous neighborhoods contained within those submarkets. (Note that t his research i s conducted with the assumption that the price of housing value w as discrete in the city context, while the underlying spatial dependence was considered to be continuous on the neighborhood scal e and within submarkets/subgroups. )


17 4 Evaluate the external weighting and mapping of price differences between submarkets and the effect of various nodes (in relation to various public services ), lines (location accessibilit y measures based on the underlyin g transportation network), and polygons ( as representative of various homogenous mixtures of social and environment factors ), and implications of urban change and development within existing real estate sub -markets. The overarching goal of this research is to help understand how externalities affect housing prices and price appreciation in urban submarkets that occupy different geographic locations. It is posited that externalities affect local submarkets in ways that are varied depending on submarkets re lative location. In short, it is argued that the spatial impact of urban development will be highly variable over space and, more importantly context and/ or setting -specific. The impacts are likely to affect certain submarkets more than others. This to pic is critical toward advancing location theory in urban economic geography as it pertains to valuation modeling and will shed some light on how urban development urban spatial structure and morphology affect urban price levels in and across submarkets. Such insights may prove useful for urban public policy makers as they attempt to grapple with the issue of promoting stability in housing submarkets as part of the urban development process. The Study Area The study area for this thesis is Gainesville, F lorida. The city of Gainesville lies in the center of Alachua County and is the home of University of Florida the largest University in the Florida State University S ystem and the national champion Florida Gators football team. The U niversity of Flor ida and Shands Hospital have brought students, faculties practitioners to the area, top notch research and medical facilities, and a cultural milieu under the rubric, and support personnel to an area now known as the G ator Nation For its scenery envi ronment and friendly communities, Gainesville is considered as one of the most comfortable place s for living in the United States With all its amenities, t he population of Gainesville has been growing slowly but steadily over the last decade from 95,447 in 2000 to 114,375 in 2007; with a growth


18 rate of about 3% annually over the period. This growth and transitory nature of the urban population has resulted in active and vibrant real estate market one in which there is a fairly high turnover with the citys highly mobile, skilled and professional workforce. From a city transportation and development perspective, Gainesville is surrounded by a series of important corridors including Interstate 75 and Florida State Routes 20, 24, and 26, US 441, and th e nearby US 301. These routes have formed an extensive regional transportation network, which served as veins linking Gainesville to Ocala, Jacksonville, Tampa Orlando, and the state of Georgia The vibrant service -oriented economy of Gainesville and the major axis of Interstate 75 have driven the direction of city development from the east to west, with the majority of growth on the westerly side of the city. Exploratory analysis of the countys property appraisal database has shown that large -scale pl anned communities were established alongside business sectors that served local residential growth along a corridor that runs fairly perpendicular to I 75 and consistently west of the U niversity of Florida since the 1990s. Th is urban expansion w as relativ ely far away from the traditional CBD located on the east -central side of the city D evelopment to the east of CBD has been stagnant and virtually non -existent Hence, the imbalance of city development (and its bias to the west) and the associated redist ribution of public and private services have created a unique spatial temporal pattern that is worth scrutinizing as it is likely to play a significant role in the valuation of housing throughout Gainesville. This research has adopted a novel method to extract the effects of directionally biased development by using a procedure known as Directional Distribution in ArcG I S. A geographic mean center is found according to the mean s of X and Y from all the housing units within the urban area T hen, directional bias is considered based on the distribution of the


19 housing units and an ellipse polygon is generated to encompass growth along the resultant axes. Rather than relying on the x or y ax i s separately, th e ellipse/ polygon allows one to delineate the direction -specific distribution of t he observation s based on both axes simultaneously, including a visual device that encompasses the standard deviation of x and y coordinates ( as they pertain to longitude and latitude). Hence, the trend of the distri bution of the points can be delineated on a map and the standard distance along each axis calculated The calculation s are as follows (Mitchell 2005) : SDEX= ( Xi X )n i = 1n SDEy= ( Yi Y )n i = 1n (2 1) Where Xi, Yi re presents the coordinates of a feature i { X Y } represented the mean center of all selected feature s (n) The deviation angle of the eclipse is adjust ed using the following formula : tan =A + B C (2 2) In Equation 2.2, A B and C are specified as: A = ( X 2 n i = 1 Y 2 n i = 1) B = ( X 2 n i = 1 Y 2 n i = 1)2+ 4 ( XiYi n i = 1)2 C = 2 Xi Yi n i = 1 (2 3) Finally X and Y are viewed as the deviation from the mean geographic center. As a result, the standard deviation of x and y is as follows: x= ( Xi cos Yi cos )2 n i = 1n y= ( Xi cos Yi cos )2 n i = 1n (2 4)


20 Shown in F igure 2 1, the size of the directional eclipse is set with 1.5 standard deviation s Once established, the procedure of Spatial Selection is used to extract all the points within the directional polygon. In this study there are n= 4 815 sampled observations of housing units sold in 2005. Note that the database also included observations from outside of Gainesville (other places within Alachua County): the city of Alachua, and the towns of Archer and Newberry. The eclipse has a definite directional bias from Northwest to Southeast, a feature that reflect s the current real estate market conditions in Gainesville and the preference for locating along this high growth corridor where land is available and subdivisions are sprouting up to meet new (and pent up) demand. The record s from the appraisal office also confirm that in the past 20 years there w as more development o n the westward side of the county in compar ison to the east. Th is historic trend is illustr ated in Figure 2 2 Note that the theoretical background for this pattern could be traced back to Walter Chr i stallers C entral P lace T heory, and the geographic concept of urban a gglomeration. In central place theory, a city is considered as a distribution center located within an isotropic surface which provides goods and service to surrounding place s and communities (Christaller 1933) In the case of Alachua county and the city of Gainesville the center of the directional eclipse is found closed to t he polygon comprised of the U niversity of Florida campus and not the CBD From Figure 2 1, it can be noted that the University of Florida a nd Shands Hospital (as the largest employment centers in Alachua), form the center of the directional eclipse rathe r than the CBD which is located at the intersection of University and Main Street The notion of central place theory is to set up different threshold for various levels of concentration of demand and economic agglomeration. It is also a theory that expl ains the preferred locations for carrying out


21 retail activity or setting up new shop s or centers based on the consumers behavior and location (Clark and Rushton 1970) However, the rigid assumptions of central place theory are that population is distributed evenly along the isotrop ic surface and that population density and purchasing power are uniformly distributed as well in spite of the unevenness of the distribution of place and centers located meet the underlying demand Adjusting for differences in density and growth, the location of housing and retail establishments will be biased depending on the processes driving urban developm ent. T he mean geographic center is a mere spatial representation of the center of gravity of the urban system, and by no means assumes that the system is necessarily driven by that location given the polycentric nature of the modern city. Nevertheless, t he mean center and elliptical polygon that delineates the direction and extent of development are essential features that can be used to confirm how the geographic distribution of housing units and urban development are reflect ed within the value of housin g in the center of city or in other area s that are affected by growth and development Hence, t he geographical distribution of housing units represent and the directional bias of urban growth reveal the t ransition al nature of what can be construed as cen trality of the city of Gainesville. In the early 1900s, eastern Gainesville was more prosperous because the old rail way went through this area. It was a rail line that connected southern Florida to Jacksonville The Old Gainesville Depot in the Southea st was added as the U.S. National Register of Historic Places and was a node that witnessed the past exorbitance as a transportation hub1. The railway deteriorated during the late 1920s and early 1930s, as the preference for private transportation modes i ncreased and consumers began to rely on the automobile to meet their travel needs Instead, the formation of US 441 marked an important event on the historical landscape. This 1 See for details


22 North South oriented transportation artery ran straight through Gainesville (a long a stretch that was substantially wets of Main Street, through NW 13th street and along the eastern boundary of the U niversity of Florida campus. The de -emphasis of the Main Street corridor was the beginning of a development pattern that led to the directional preference to locate between US 441 and the I 75 corridor. Thus, the west -side of Gainesville would hold a distinct advantage in a ttracting of investment from various industries and land uses In the 1950s and 1960s this trend was further reinforced by an Industrial park that boom ed along the northern side of the NW 13th street axis that led to the city of Alachua. The emerging dev elopment in areas far west and far south of Gainesville could be viewed as a newer but lower -order development, historically and hierarchically speaking. The formation of places and clusters of establishments largely relied on traffic associated with the University of Florida Interstate 75, and westward corridors that stretched along what is now the Butler Plaza toward the town of Archer The ongoing construction of Butler Plaza stretching from 34th street (western boundary of the main campus) to I 75 (a lso in the center of Figure 2 3 ), and provide d convenience shopping and proximit y to business opportunities for the city as a whole; a retail cluster with several supermarkets, numerous clothing and shoe stores, cinemas, and restaurants The spatial patte rn is consistent with the evolution of a Lschian landscape (as an extension of the work of Christaller). The historical development patterns are also related to Webbers spatial location theory (Webber and Joseph 1978) where retail industry in the B utler P laza is known to target customers group as 1825 year old population (the largest socio -demographic group located within just a few miles of the agglomeration of establishments) The location of Butler Plaza was (and is still) appealing to investors because it has adequate retail space and is close to the target demand gr oup: the students living in the surrounding area Once the first store had set


23 up a successful business the re was less uncertainty within the market for the other similar or competitive industry. The Butler Plaza agglomeration continues to expand and introduc e more and more firms that appeal to the demands of a college age population in an area just the west of the university2. T he centrality and accessibility of the Butler P laza further enhance d residential development to proceed along the Archer road corridor and west of I 75. Given the nature and importance of agglomerated industry, one must seriously consider a gglomeration effect s in the modeling of real estate values. Mulligan ha s reviewed the processes of urban centra lization and decentralization and concluded that some points in the urban m ilieu provide distinct comparative or location advantages to the other points on the landscape (Mulligan 1984) Hence, it would be advisable to consider the patterns of long-term development when accounting for externalities in an urban system. T he history of urban expansion in the study region is associated with three waves of constructions as shown in Figure s 2 2 and 2 3: o ne is in the 1 950s, one is in the 1970s and a third in the early 2000s These trends share a common feature in that new development is c lustered together at the periphery of the existing development incrementally moving westward Th is westward expansion of the urban fringe along was fueled by i n -migrant and corresponding cash flow s to the capital market. Under existing planning codes and city development restraints, its reasonable that the developer would prefer the place s where sales revues and profits could be maximize d, in areas where growth was occurring with minimal competition from rivals Again, t he temporal dis tribution of housing development in Gainesville had a pronounced westward movement, a nd concentration s around the I 75 corridor remained favorable to satisfy both local demand and demand associated with travelers along the Interstate system The 2 Several expansion plans had been discussed in the city committee. See a concern for Butler expansion


24 agglomera tion of new developments on the west -side of Gainesville is testimony to the relative transportation advantage and convenience offered by I 75 and the UF contingent Retail and service industries along the I 75 offand onramps provide d facilities for in ter urban and intra urban travel (especially for students and families with a south Florida connection) and helped bias development away from Gainesville east -side UF and Shands, as chief economic contributor s to the Gainesville economy offered the marke t to supplement that which served Interstate commuters. By inspecting the nature of the distribution of single family housing units, the eclipse would capture the urban hierarchical structural around Gainesville and exclude hinterland areas such as farm s or conservation areas in the south and industrial areas in northern Gainesville along U S 441. Extracting the study region using the directional el lipse allows for the most active real estate transaction areas to be included in the analysis (especially areas just outside the western portions of the citys political boundary The ellipse defines the heart of the real estate market in Alachua County and would include county residents/commuters with travel time s of less than 30 minutes to work.


25 Figure 2 1 Directional e clipse of housing unit sample in G ainesville area Figure 2 2 The h istogram of b uilding a ge in Gainesville


26 Figure 2 3 Spatial d istribution of Building Age in Gainesville


27 CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY REVIEW The proposed price valuation model developed in this thesis is influenced by four observations : First, a city -wide hedonic price model w ould not be adequate to model local price variation. As the real estate market in Gainesville must be decompos ed into two dimensions: structural s ubmarket s and spatial submarket s, and in light of spatial heterogeneity in the real estate market C onventional city -wide hedonic model are inadequate for modeling disparate characteristics of the housing stock. Conseque ntly, the housing submarket s should be properly defined in order to reflect the discontinuous pricing platforms (Goodman 1981; Goodman and Thibodeau 1998; Bourassa et al. 1999; Tu et al. 2007). The localized estimation of coefficients indicates that the price of a house is a combination of housing structural and physical characteristics, as well as the externalities linked to the geographic location of the house (Can 1992). Thus, on identification of housing submarket s are required to capture the divisi onal substitution of housi ng characteristics or location situations Both Bourassa (1999) and Watkin (2001) agreed that the existence of a submarket could be ascertained by three approaches: 1) by their common structural characteristics, 2) by the spati al proximities of aggregating neighborhood or other smaller subdivision, and 3) by the inter -correlation of the housing stocks and the socioeconomic characteristics of geographical areas Since the criteria of submarket typically reflect the dominance of the structural/location factor, it is reasonable to separate the effects and implied utility associated with the structure (i.e. site characteristics) and value associated with geographic location that which is brought about by a housing unit's absolu te and relative location (i.e. situational characteristics). Hence this


28 research assumes that submarkets are formed by two standards: structural classification and spatial segmentation Second test ing the validity of structural submarkets and spatial su bmarket s as well as their interaction effects require s that various locational considerations be made If the structural submarkets hold constant across the space, it could be expected that their distinctive spatial distribution could account for the pric e variation within these structural submarket s which is known as externality effect Specifically, regardless of location factors, it is assumed that the demand s for various types of structures within a given submarket are predominant within a certain p eriod These demands would have a momentous impact of housing prices within that market above and beyond that which would be observed elsewhere. In other word s houses with similar and substitutable structural characteristics would be sold at different p ri c es solely because of the differences in their locations. As a corollary, one would not expect that all the houses in a city have the same appreciation rate based solely on site charac teristics of the dwelling alone as differences in appreciation may also be explained by the total efforts by the house owners to maintain the value of their properties In this case it is possible that 30 years ago one neighborhood may have been perceived as having prime real estate, but it depreciated more rapidly that other neighborhoods of similar vintage simply due to the fact that it was in a location far removed from the direction of city growth and development; and thus fell victim to associated and perceived set of negative spatial externalities. As a result the validity of submarkets would be confirmed. In this research, the detection of spatial effects on structural effects could be reviewed by two approaches: one is by empirical comparison of the least -square means of structural/spatial submarkets using ANOV A (Analysis of Variance), provid ing intuitional understanding of current market condition; another is by establishing a spatial


29 expansion model with incorporation of spatial/structural submarkets' dummies and other spatial/structural variables, providing quantification evaluation of the localized marginal price by the specified characteristics. Third, to adequately analyze absolute/relative location information in the hedonic regression model, it is assumed that parameter could drift on the city surface. Fik et al. (2003) argued that the absolute location information {x,y} of the land parcel had included the impact of implied spatial externalities Their research allow ed the polynomial expansion of { x,y } to interact with a variety of housing features concluding that the LVS represent ed the total spatial externality across the city Inclusion of {x,y} coordinates could also be found in Clapp (2002) and Pavlovs nonparamet ric studies to real estate market as they had mitigated the problem for omitted variables in hedonic modeling (Pavlov 2000; Clapp et al. 2002) T his approach is adopted here and the Cartes ian coordinates {x,y} would enter our model as indicators of absolute locations. Furthermore, Polar coordinates will also be used to describe a housing units absolute location T he contention of the polarization transformation rooted in Center Place Th eory, suggest s that housing unit on different sides of the central standard eclipse (Figure 2 1) might be sold for similar prices, ceteris paribus A study from Sidman and F i k (2005) has presented similar wedging techniques on the central ly oriented study of relative location of traffic sheds for local boat ramps In this transformation, t he mean center is calculated according to the spatial distribution of the units as in Figure 2 1 with calibration as zero point where each housing uni t obtains a relative { x ,y } by calculating the difference of its original geographic coordinates and the zero point To accomplish this a vector is constructed to perform the polar transform ation using the following formula :


30 r = x2+ y2 = 0 (3 1) In Equation 3 1, the relative distance NearCen and the relative angle Theta from the housing unit to the center point are obtained as the result of the relative location with respect to the citys geographic center The transformation is known to reflect the situational changes of price characteristics: the change of Theta reflects the change of relative angles to the center point, and the change of NearCen denotes the distance from the land parcel to the distributi on center. Information on the relative location is used to delineate the spatial relationships as well. In a social -economic context, the location of employment center and the layout of the transportation network are believed to have a profound influence on the housing price (Levine 1998). With the assumption that living in the vicinity of the U niversity or adjacent to major transportation network would be more preferable by the university employees or students, two variables NearUF and NearI75 are calculated to denote the distance from the land parcel to UF campus and to I nterstate 75 respectively As a university town, it is believed that the vicinity of business spots( i.e. shops, retail center, convenient stores, church etc.) would provide faci lities withi n walking or biking distance, therefore, the variable Nearbusi extracts the distance from the parcel point to the nearest business service points as shops, (searched in a .5 miles radius). These distance extraction s are conducted by an ArcG IS procedure Near which is capable to generate the distance between the designated geographical features to a particular data layer. Theoretically the absolute and relative location information enables the characteristics prices float in a smaller scale in three way s: (1) on the x axis or the y axis separately; (2) on the


31 directional vector from the mean center to the parcel point; or (3) on the d istance from the parcel point to the distinct urban node such as UF or major transportation network. Lastly structural/spatial dummies are included and interact ed with the other independent variables To accomplish this, the discontinuit ies in the Gaines ville real estate market are handled by assigning distinctive value platforms The magnitude of the platform is confined by submarket s dummies in the second set of models. The price surface is considered constant and the marginal price of characteristic s is allowed to vary according to locations. Also, the interactions reflect the covariance between variables as changes in one variable might lead to the changes of the other variable. By the interaction term, the knowledge of the urban landscape could be documented and quantified by the directional bias in Gainesville s urban development The research design follows five steps: 1) c onstruct a glob al model for hedonic estimation; 2) cluster housing units into groups according to their a -spatial commonalities; 3) cluster housing units into groups according to their spatial proximities (finding the aggregation of neighborhoods by Geographically Weighted Regression); 4) apply factoria l submarket tests by ANOVA in an OLS model to test the significance of submarket segmentation; 5) build a spatial expansion model allowing the interactions of structural grouping, spatial grouping and other characteristics. Three sets of models are const ructed and evaluated Model 1 presents a global specification by estimating a single set of parameters for the entire study zone. This model includes the six structural attributes detailed in Table 3 1, as well as three variables representing absolute l ocation and relative location. Model 2 contains two general linear models for ANOVA: one with and one without variable interaction s The means and variances from structural grouping and spatial grouping would be compared and presented in ArcGIS. Model 3 is the expansion model with interaction between the six housing attribute variables A third -order polynomial


32 form is assumed with interactive location variables (such as x2, y2, x *y) including structural and spatial submarket dummies. Note that the resi duals from the global model and the expansion model are marked and compared in ArcGIS for further analysis. Figure 3 1 presents a flowchart which summarized the analysis. Hedonic Models and Spatial Econometric Literatures Hedonic m odel s are most widely a ccepted as a standard valuation model s in the real e state literature. The classic work of Rosen (1974) affirmed that the utilities from the consumption of some characteristics in a housing bundle could be compensated by the increment of quantities of other characteristics Consider a regression model: P = X + (3 2) Where P is the property value, X is a vector of (possibly transformed) land, structural, and The intrinsic notion of a hedonic model is that a house as a composite good, in which the marketing price of a house was determined by the combin ation of its own tangible characteristics ( i.e. the area, the number of bedroom s and the number of bathroom s etc.) and intangible characteristics associated with its location. Note that the classic hedonic model weight s the importance of each of the vari able as equivalent, with the assum ption that the utilities from structural characteristics and spatial characteristics a re totally interchangeable. This simplification however does not fully account for the spatial essence of the property. Once the rea l estate is rooted in the city, it would be marked with its own Location Value Signature which in cludes externality effects such as environmental economic and geographic spill -over (Fik 2003). Often, one would observe clusters of residuals (negative or positive) in some distinct neighborhood, along transportation corridors or around the proficient business area, which leads to the violation of the independent observ ation assumption underlying OLS as the residuals are likely to be spatial auto -correlated.


33 The collaboration of econometric techniques and spatial analysis would shed light on modeling spatial relationship. Anselin (1988) had discussed two basic approaches to incorporate spatial effects directly into the hedonic model One is to transform by the inclusion of spatial weighting matrix that accounts for spatial lags and hence dependence. The model may be specified as : = + + (3 3) Where autocorrelation parameter and W is a n n*n spatial weighting matrix ( assuming the selling price of a unit would be impacted by the surrounding units -the spill -over effect). Analogue to the autoregressive terms in a uld be considered identically distributed and independent once the model is transformed (Can 1992; Anselin 2003; Anselin and Gallo 2006). T he spatial autoregressive term may lead to the inappropriate of OLS estimator, and therefore, it is recommended t hat the maxi mum likelihood estimator should be estimated Another method to delineate the spatial dependence is the decomposition of the error term, which most likely relie s on the unobserved variable. Inspecting the error term in the OLS model, a variance -covariance matrix would be constructed with a spatial weighting matrix as: E ( ) = 1= 2( I aD )( I aD ) (3 4) In which, is the covariance matrix for the error and D represents the spatial weighting matrix with a row sum of 1 and diagonal elements equal 0. Often, geo -statistical methods such as the estimation of the semi -variogram are implemented to calculate the matrix of D. Then the maximum likelihood method is


34 ( ) ml = [ X 1X ] 1X 1P (3 5) The mechanism of spatial statistics methods provides facilities to study the continuity and spatial spill -over effects, in effects following Toblers (1970) first law of geography that "Everything is related to everything els e, but near things are more related than distant things However, this method could not fully identify the heterogeneity or the discontinuous surface that differs dramatically from the surrounding area. It i s well believed that some urban interests points would have an aura like effect on surrounding units (known as spatial autocorrelation) Spe cifically, this effect originates in the inelastic ity of supply and demand in a local context (Goodman and Thibodeau 1998) It should be noted that the influence and spatial extent of these aura like effects remain uncertain though i t is likely that the physical boundar ies ( e. g. the division by a river), political boundar ies ( e.g. the division by census tracts school district ) or man -made boundar ies (e.g the division by the interstate highway) would confine the spatial influential relationship and lea d to a n idiosyncratic jum p or a decline i n the housing price. S patial heterogeneity is expressed by the anticipation that some area with an influential core would leverage the values within the boundary. Thus, submarket s emerge as a necessity to delineate the spatial discontinuity effect. A global hedonic price model is constituted, allow ing the marginal price to hold constant across the city surface This model will be used as a reference. T he residuals of the global model are mapped by C luster and Outlier Analysis procedure in ArcGIS. This procedure also includes the Local Moran s I statistics to inspect the spatial relationship. Each land parcel would obtain an attribute and a z -score (Gi -Statistics) evaluated with the assumption that the spatial distribution is randomized. A large positive Z score indicates the large value tends to cluster together while a small negative Z score indicated the small values tend to cluster in space


35 Submarket Definition by Structural C lustering The st ructural submarket definition suggests that the geographical constraints are less important than the value associated with housing units structural characteristics. Allen et al. (1995) suggested that property types be aggregated by common structural attributes and renters made decisions based on a designated property type, regardless of location. Another branch of literatures used discrete -choice model s for identifying preference of house buyers. A study from Nechyba set up census -specified percenti les for the consumption of housing structure and assumed there would be a linear relationship between these percentiles and the value of the housing unit Their study showed that a small group of household s would be indifferent to live anywhere in the stud y area as long as the cost fell within their budget constraints (Nechyba and Strauss 1998) Another study from Earnhart (2001) suggested a n income threshold for the housing preference Th is research implied that, the preference on housing structure would be largely related to the income of the buyers Thrall (2002) had also mentioned the identity of lifestyle segmentation profile based on buyers socio -demographic attributes would be important to the customers choice for housing decision. In spatial equilibrium, the increasing consumption of land was viewed as compensation for less advantageous locations within the urban market. Hence, companion with the stru ctural submarket definitio n, it i s reasonable to strip off the spatial characteristics from the housing stocks and retain the common structural characteristics so as to form distinctive structural submarket s As a diagnostic method, c luster analysis is a n ideal tool to identify the grouping s depending on the similarities of structural variables U sing cluster analysis, the internal homogeneity within the cluster and the external heterogeneity are maximized by calculating the distance between the values of the variables In previous research, Bourassa et al. (1999) used principal components analysis and clustering analysis to extract a s et of factors from the original housing-structural related variable s from the individual dwelling data


36 within Sydney and Melbournes administrati on boundary. The ir results confirmed that submarket s originat ing from statistical methods performed better than predefined submarket s based on market knowledge or neighborhoods Later, research from Chen et al. (2009) suggested that, the combination o f prior market knowledge and statistics method provide superior power over mere statistical submarket delineation In short, this research suggests that proper statistic cluster techniques would improve the performance of valuation model s In this research a t wo -step cluster method in SPSS is used for identifying cluster s based on structural characteristics. The algorithm would pre -cluster the cases (or records) into small sub clusters and later join sub clusters into the desired number of clusters For t he purposes of this analysis, k=5 clusters are used to delineate structural submarkets The number of bedroom, the number of bath room, roof type, AC type, h eat type and fuel type are taken as categorical variables. By inspecting the database, it is anticipated that the number of structural related variables is limited. Hence, this research relies on the variables directly extracted from the property appraisal database. These include lot size, the building area, perimeters of the lot and the building age of which are regarded as continuous variables. Again, sales price was not used in the two -step clustering method ; it would be the indicator of the combined effects of all the structural variables and not useful to distinguish structural submarkets. Spa tial Clustering and Geographically Weighted Regression The spatial submarket definition highlights the importance of spatial characteristics over and above structural characteristics In a spatial submarket, local spatial constraints are assumed to reflect the total externalities that are supported by distinct urban spatial structures, morphology and facilities in a certain geographic subdivision Given these constraints, restrictions on demand are known to influence the decision making process. H ence it i s believed that local in elasticity of supply and demand emerges as g eographic submarkets are


37 segmented by man -made boundary as proxy by school district s zip code s or census tract s and subdivisions (Palm 1978; Adair et al. 1996; Goodman and Thibodeau 1998) Research suggests nevertheless that political boundar ies reflect ed the actual similarities and dissimilarities in subdivisions and neighborhoods In order to avoid the bias from researchers and preconceived notions regarding spatial submarket s everal methods are proposed to group the observations by spatial likeliness including spatial scan statistics (Odoi et al. 2004) spatial lags (Pace et al. 1998) and semiv a ri o g ram classifications (Tu et al. 20 07) Here we explore an analytical way to investigate spatial clustering by using Geographically Weighted Regression (GWR). GWR is a refined local regression model proposed by Fotheringham et al. (Fotheringham et al. 1998) Th e coefficients are estimated as: Pi = 0( xi, yi) + k( xi, yi) xik+ki (3 6) Where ( xi, yi) is the coordinates of ith point in space and k( xi, yi) describes a function which is continuous and allows the parameter values and measurements of the surface taken at various points to indicate the spatial heterogeneity of the surface A n n by n matrix W ( xi, yi) i s constructed to denote distant weighting of observed data with res pect to a given point i. A kernel (fixed or adapted) functions to seek a number of observation to construct the weighting matrix for that specific observation point (Fotheringham et al. 1998) By using GWR, it is able to construct a series of coefficient maps with different ( ui, vi) Several implementation s of GWR (Fotheringham and Brunsdon et al. 2000; K estens and Theriault et al. 2006; Yu et al. 2007) ha ve been accomplished on the housing market with the purpose of compari ng GWR and OLS results Comparisons showed that the GWR out perform ed OLS and the spatial autoregressive model by providing localized regression parameters with a higher adjusted R Square and lower Akaike information criterion (AIC) value These inquiries,


38 however, did not include interaction terms of modeling parameters. Whats more, GWR require d intensive computation as the algorithm could only cope with a limited number of independent variables. Another setback rel ied on the kernel analysis for the modeling procedure : the persistence of GWR would largely relate to the sample size and the sample geometric distribution. If the proximity of the observations is higher, the GWR result would be more significant or vice versa Therefore, the object of implementing GWR here would not be modeling but using it as an analytical tool for the detection of spatial -stationary effects This is consistent with the statement f rom Fortheringham for the possibility using GWR in search of spatial relationship s (Fotheringham and Brunsdon et al. 2000) : In spatial data analysis, the data about which relationships are to be examined are related to spatial units and are used to estimate a single, or global, regression equation so that the relationships being examined are assumed to be stationary over spaceClearly, any relationship which is not stati onary over space, and which is said to exhibit spatial non -stationarity, will not be modeled particularly well by a single parameter estimate and indeed this global estimate may be locally very misleading. The discrete effect of each variable would be ref lected i n the coefficient maps produced by GWR, which is able to identify spatial heterogeneities divergently throughout the city. The spatial heterogeneities are expressed by the similarities of patterns of value between variable s: For example, large pos itive coefficient s for the number of bedroom could be related to the large positive coeffi cients of building area. Or th ese homogeneities among assorted variables with in a certain area could be categorized as belonging to the same location category due t o their similar characteristics. This research tries to overla y all the coefficients maps and inspects these analogous variable value patterns Here, f our variables (building a ge, the number of bedroom, the number of bathroom and b uilding area) entered th e Geographically Weighted Regression. Five maps (including a map of the intercept term) have been generated. Those maps would be


39 under reviewed and spatial subgroups would be identified a ccording to the inspect i ons and the actual urban landscape Dummy variables are assigned to each of the spatia l -subgroups Linear Discriminant Analysis (LDA) is a multivariate -statistical technique that constructs a predictive model from the identification of categorical integrity. The aim of LDA is to identify the group labels based on selected covariates, in which individual characteristics would be acknowledged as a pdimension vector and resulting subdivisions would be regarded as dependent variable s In this thesis building area, lot size, the number of bedroom s and the number of bathroom s, and the building age would be employed as independent variables (BA LS BE BT AGE respectfully ). The geographical label s would be regarded as responding spatial class es Note that the price of housing units did not enter the discriminant analysis, as the objective was to assign spatial identification on the basis of various structural characteristics rather than the discrimination by price Since the number of bedroom and the number of bathroom is not normally distributed, the discriminate analysis was implemented with unequal prior s, utilizing non-parametric linear function This specification allows the posterior distribution to depend on the prior distribution. Analysis of V ariance for S tructura l S ubmarket and S patial S ubmarket The previous discussion implies that a study of the main effect of the structure submarket and the spatial submarket could be carried out in terms of a two -way analysis of variance (ANOVA). ANOVA is an important statistic method for exploratory and confirmatory data analysis It is often used to analyze if the means from different groups are indicative or their belonging to the same population ( where the observations have a normal distribution and of homogenous variance. D iscrete levels are assigned to the different factors in order to detect the effects of these factors to the dep endent variable. The overall object of ANOVA is to break down their grand means into different terms that quantify the means attributed to the factors, to


40 the interaction of the factors and to th e residuals (Shaw and Mitchell -Olds 1993) The use of ANOVA in real estate literatur es is still limit ed Si -ming Li proposed an ANOVA comparison of housing consumption in Guangzhou and Beijing and later he use d ANOVA as a tool to delineate the transition of tenure occupancy in Guangzhou (Li 2000; Li et al. 2006) By using ANOVA, these researches linked identical social -economic factor s and the behavior of various demand groups on categories across th e city landscape. In market ing economies, it i s believed that expenditure on housing is the usual benchmark to represent housing consumption (De Leeuw, 1971). Thus, the inter -correlation of structural and spatial submarket s is expected to affect the local patterns of supply and demand and yield local ambiance that has its own location value signatures For example, homogenous patterns of housing structure could be related to the chronological development trend identified in Figure 2 3 as it reflects the a ggregated demands from certain group s of consumers in a particular period making ANOVA an ideal tool in the analysis of housing submarkets Usua lly, ANOVA is carried out under a g eneral l inear m odel f ramework (though the random effect could be simulated by Bayesian approaches). In this thesis the logarithm of the sale price is taken as dependent variable and the structural/ spatial subgroups are treated as different levels affecting the price Hence this research consider s the structural groups and the location groups as both ha ving a fix ed effect on the model In order to address the orthogonality of structural submarket and spatial submarket, two regression models for ANOVA would be constructed accordingly one had interaction term and the other did not. A cross table of structural categories and spatial categories would be built for reference of means Expecting that the variance between groups would be contrasting and the number of observations within cell s of a cross table are not the same an unbalance Factorial ANOVA is utilized to present the unique


41 contribution of each factor Type III sum of squares which present the marginal effect of the variable are recognized for unbalanced data structures in the structural/spatial clusters The F test is utilized to detect the price within the subgroups and between subgroups. At last, the result of ANOVA would be presented by categorical thematic maps in ArcGIS, which is expected to provide an overall understanding of the spatial patterns and rel ationships of market phenomenon and present the effects of externalities Spatial Expansion Model and Stepwise selection Casetti (1972, 1997) propos ed the spatial expansion model as an inspection tool for spatial heterogeneity. Unlike its counterpart of s patial -weighting -matrix related model, spatial expansion model regards the research area as a discontinuous space by allowing interaction of parameters and location dummies under an OLS framework. Consider a model : = + 11+ + + (3 7) is (of which there are m) are coefficients for some of the characteristics of the housing unit Then the interaction would be constructed with the variables and spatial terms as = 0+ 1( ) + 2( ) (3 8) In here (ui,vi) are the spatial coordinates associated with a given location i and ( ) implies an interaction function between spatial coordinates and structural variables. Different from GWR, spatial expansion model does not have a kernel -sampling procedure for constructing a variable weighting matrix. It relie s on the interaction term dir ectly reflecting the impact of locations on variables. Moreover it is u nder an OLS (Ordinary Least Square) framework and the coefficients drift could be speculated by the interaction of variables. Consequentially, the model


42 calibration and the testimony of the interaction could be validated by t test and F test and maximum -likelihood estimation cou ld be used to calibrate the parameters of the model. Structural dummies and the spatial submarket dummies are added to the spatial expansion model, allowing the parameter drifts in the spatial heterogeneity context Our preferred spatial expansion model could be represented as follows: LnPi = 0+ jSj i+m j = 1 rDr, i+d r = 1 rLw i+k w = 1 r, j q m j = 1( Lp, iSj i)o p= 1+ r, j q d r = 1( Lp, iDr, i)o p= 1+ j k m k = 1( Sj i vSk i w)m j = 1+ p, j k m k = 1 Lp, i Sj i vSk i w + r p, j k m k = 1 Dr, iLp i Sj i vSk i w +m j = 1 r p= 1 d r= 1 m j = 1 r p= 1i (3 9 ) In here i is an index for sample observations j is an index for structural attributes S is a vector of structural attributes. L represents location attributes P (v + w is an indicator of the implied order of the model and Sj i vSk i w (k > j ) stand for interactive terms of structure. A set of parameters of { , } represent regression coefficients in Equation 3 9 and i is an assumed random normal error term. Note that we allow a third -order polynomial expansion among variables as xxy and xyy entering the model A procedure known as GLMSELECT in SAS is applied to loop Equation 3 9 and perform a stepwise s election of the independent variables Schwarz Criterion (Schwarz 1978) is adopted as a selection criterion to detect the importance of the parameters in the model. The selection formula is as follows: SBC 2 lnL + kln ( n ) (3 10)


43 Where L is the maximum likelihood value for the estimation model, n is the number of observations, and k is the number of parameters. Under the assumption that the model errors or disturbances are normally distributed, the SBC is related to Residuals Sum of Squares (RSS) and the number of parameters Hence, a c omplex model with a larger number of coefficients would be penalized. A low BIC either indicates fewer numbers of explanatory variables or higher fit in the model or the combination effect of both. Hence, the parameters with low BIC would be retained i n the model and the parameters with high BIC would be dropped off. Its assumed that a fter the implementation of the stepwise procedure, a small and easily interpretable model with a limited number of covariates will remain for predictive scheme


44 Table 3 1 Variable d efinition Variable Definition Dependent variable: LNSALE The natural logarithm of s ale price in 2005 Independent variable : Structural variables: BA Build Area LS Lot Size BE Number of bedroom BT Number of Bathroom Age Building Age Location Information: X,Y The coordinates of the land parcel NearUF The distance from the land parcel to UF NearI75 The distance from the land parcel to Interstate 75 NearBusi The distance from the land parcel to the nearest business service. Theta: The angle after polarization of the parcels coordinates NearCen: The distance from the land parcel to the city center. Dummies NW,MS,MN,ME,M,E Equals to 1 when the parcel is in one of this area, when all=0 it means the parcel is in the SW area CLUSOK1 CLUSOK2 CLUSOK3: Generated by the structural information by cluster analysis, include the number of bedroom, the number of bathroom, ac type, roof type and other categorical structural variables. (CLUSOK1=CLUSOK2= CLUSOK3 = 0 means the fourth structural category )


45 Figure 3 1 Flowchart of analysis procedure


46 CHAPTER 4 RESULTS AND INTERPRE TATION Global Hedonic Price Results The global OLS model results in Table 4 1 are consistent with results from other studies employing hedonic models Principally, the estimated model explains roughly 81 percent of the variation in the logarithm of housing prices, LNSALE. The V ariation I nflation F actor (VIF) in Table 4 2 illustrat es that the variables does not have co linearity problem s Most of the individual variables perform as expected. For example, b uilding a rea (BA) is considered as the most important characteristics contribut ing to the selling price of a house with the largest leveraging coefficients. The effect of bui lding age (AGE) is significant with a coefficient that is negative indicating that house price s decrease with the passage of time ceteris paribus However, there might be some effects combined with the designated location which one might inspect later The in -sample coefficients on three relative location variables: NearU F, NearI75 and NearBusi exhibit significance (p <0.001), suggesting that location play s a pivotal role in determination of selling price. Surprisingly, the lot size and the number of be droom are not significan t in the global model. T he former might be related to the similarity of the shape of the housing lots across the city, and the latter reflected the indifferent preference of bathroom from the buyers' perspective The global Moran 's I index=0.12, calculated to detect spatial autocorrelation in the residuals indicates the existence of significant clusters of high and low residuals. Hence, the adoption of a single global model is not appropriate as the error structure exhibits spati al autocorrelations Figure 4 1 show s the geographical distribution of Gi -statisti cs. Each point represents an observation and is calculated from the residuals of t he global model. As the legend indicates, the color represents the range of standardization of the Z score: Blue indicates negative Z value,


47 yellow indicates Z value around zero and red indicates positive Z value. From Figure 4 1, spatial autocorrelation could be confirmed by clusters of positive and negative residuals. Urban het erogeneous effects are detected as several is otropic residual islands scattering across the urban landscape Structural C lustering Results A cluster analysis is carried out on a total 60 000 housing units in Gainesville. Four categorical dummies are creat ed from the specified cluster number (and this assumed the level of structural complexity) Each of the sample units obtains a spatial submarket label generated from cluster results Selected descriptive statistics for the four clusters are summarized in Table 4 2 Note that o ne cluster had been identified as the outlier cluster and excluded from our analysis ( which contains 144 records out of the global database and 2 in our sample). The units in the structural clusters are well separated by structural attributes (i.e. b uilding area, the number of bedrooms, the number of bathroom and the building age ). Note that t he structural submarkets are not evenly distributed across the space i n Figure 4 2 As the level of the complexity rises the centroid of the structural submarket moves westward T his positional transition might be related to the spatial agglomeration of the structural properties as the y chronicle the presence of a series of west development waves in Gainesville (as implied by Figure 2 1 and Figure 2 2) Two structural submarket s are worth further scrutinizes The first one is CLUSO K 1, with 1378 square feet building area, 11355 square feet of lot size 2 3 bedrooms and 1 2 bathrooms and an average building age of 57 year, respectfully. It has the smallest number of observation s and is viewed as Simple Structural Cluster. By examining its distribution, we could find out that most of the associated housing unit s are located on the eastern part of Gainesville. The other important cluster is CLUSOK3 which has an average 2 185 square feet building area, 12, 453 square feet lot size, units with 3 bedrooms and 2 bathrooms with an average building age of


48 17.76 years. This cluster retains the largest number of observation as it is corresponded to Gainesvilles most typical demograph ic profile A younger demographic pattern could be found in Gainesville compared to Florida statewide and nationwide.1 With a substantially higher percentage of youth adults U niversity students or graduate s start t heir own family in Gainesville Given their small family size and financial constraints they do not require large capacity and complex housing structure. Thus, it c ould be anticipated that CLUSOK3 with 3 bedroom, 2 bathroom and around 2000 square feet as a standard configuration is highly representative of the major submarkets as it satisfies the demand s of a small family in terms of housing attributes. Figure 4 2, 4 3, 44, and 4 5 have presented four pricing platforms of four different structural groups. These findings lend general support to the hypothesis that the structural characteristics of house have a high degree of covariance mat rix between locality, stru ctural attributes, and building age. In addition, one should notice the underlying spatial auto correlation effects exerted by the city infrastructures in Figure 4 6, -I 75, University of Florida and Shands Hospital -have distinct influence s on urban development and the location of various housing submarkets S patial Submarket Results By visually inspecting the interaction of five coefficient maps, we found seven areas exhibiting spatial homogeneities Therefore, the subdivisions contained in these s patial clusters are shown in Figure 4 7 Th is synthetic generalization is the outcome of overlaying the coefficient map s and the transportation network The structural clustering result could be acknowledged as manual sub -division s of a geographical region. Table 4 3 shows the cross -valida tion summary of the discriminant analysis 1 See .The median age in Gainesville is 29 years old.


49 The most discernible area is the southwest cluster ( SW ) in which 1727 units 1447 are properly classified (yielding a correct classification rate as 83. 79% ) The identification of units in the SW cluster could be explained by the largest number of observations, leading a higher density in the prior distribution in the d iscriminant a nalysis. Units in the M cluster are clearly identified with a correct rate of 62.18%. Units in E, MN, MS clusters are poorly identified with correct classification rate less than 10%. The worst one s are units in the NW cluster in which 69.68% of the observations are classified into SW group. In Table 4 3 the overall errors counts of r e -substitution analysis are 0.40 and the error counts of cross validation are 0.43, which indicates that the location labels would be in adequate to identify the spatial variation in housing attributes Hence, addi tional information from s tructural attributes would be of necessity to complement the effects in determining the housing price and for the purposes of properly identifying submarkets. ANOVA for Structural and S patial E ffects The primary hypothesis that the structural submarket and the spatial submarket have significant influence s on housing price s is supported by the results of the ANOVA model s in Table 4 4 The i nteraction terms suggest the collaborating effects of structural submarket and the spatial submarket as they combine to enhance the model explanation power from 441 to 456. Hence, structural and spatial attributes are vital complement s for bridging the structural submarket and spatial submarket. The interaction term s are presented by levels of structural dummies and spatial dummies in Table 4 5 to separate the main effects of the structural submarket and the spatial submarket. The first four rows of Table 4 5 correspond to a comparison of spatial submarket at a particular structural submarket level, whil st the last seven rows compare the structure submarket through a particular spatial submarket Each level identifies a not ice able price difference (p<0.005),


50 indicating that the housing units have been well identified by t he structural dimension and the spatial dimension Further exploration on the table implies that the location site SW M and MN contribute a large r portion of the sum of squares, reflecting that these areas have noticeable homogenous patterns in selling p rice. The E ME and MS districts contribute a lower score of the sum of squares, indicating that the explanation power of locality is lower in these areas The pricing variation found in different district s might be explained by the location of historic districts in Gainesville. T hree historic districts are in parallel with the subdivisions exposed in the GWR model in the city. The ME area primarily covers the N ortheast Gainesville historic district (embraced by 1st, and 9th Streets, 10th and East Univers ity Avenues) and the E district covers the Southeast Gainesville Residential District (bounded by East University Avenue, Southeast Ninth Street, Southeast Fifth Avenue, and Sweetwater Branch). The pricing variation is large in these two districts, as mos t units depreciated with passage of time, though some well -preserved building s had actually appreciated in value. MN covers the Pleasant Street Historic District,2 with a price variation that is smaller than other district as the units maintain a higher pricing level due to better condition and maintenance. The local prevalence of older buildings presents two no t able effects on t he market value described as the historical traits First, it implies the chronological presence of agglomerations of certai n structural groups As indicated in the last chapter the development bias towards a certain structural group maximized the developers profits and catered for the largest demand group at a certain time point. Second, it reflects the local average main tenance efforts on house s in various submarkets It is widely accepted that k eeping a house in satisfactory condition 2 See details information on historic district in Gainesville from


51 requires sustained monetary outlays from the buyer. As a result different levels of housing maintenances would create distinctive quality and characteristics on old er houses. In Figure 4 8 the tabulated m eans of structural and spatial market demonstrate that except for the M, MS and NW area s the average price within the structural submarket or the spatial submarket wo uld be fairly discernable (p -value < .001). Note that as the counter part of the d iscrimina n t a nalysis in the last section M, MS and NW districts are clearly separate d by structural variables rather than the means of the sale price. It appears reasonable th at complex structures could not provide leverage on price in these areas since the price differences between structural groups are small Buyers tend to pay more for less -complex units when living in the M, MS and NW districts Table 4 6 tabulated the power transformed means of the sale price comparison s in a cross table. Figure 4 9 presents them in boxplot form. Figure 4 10 and 411 further decompose the structural submarkets on fixed location effects. Correspondingly i n order to demonstrate the ge ographically related result, we produced a series of thematic maps are constructed in the GIS. In Figure 4 12 and 4 13, four maps of separated structural clusters are created. With the purpose of drawing comparison s between maps, seven levels of gray col or are assigned according to the equal interval of the price range. The minimum least -square s -mean sale price after power transformation is 48, 785 dollar s; whilst the maximum least-square -mean sale price is 344 017 dollar s A gray level represent s a price that would be 1.32 times higher than the price of a lighter gray level. The size of yellow circle presented the standard deviation within the spatial submarket s Several gen era liza tion s could be drawn from Figure s 4 10, 4 11. 4 12 and 4 -13. Overal l, a larger house with more bedrooms or bathrooms and a younger vintage could be sold at a higher


52 price Moreover, price rises as the housing structur e become s more complex. If we restrict attention s to the structural submarket, the simple structural clu ster CLUSOK1 tends to have less pric e variation in districts NW, ME, MN, and M. This implies th at low -income families might be paying less attention on the locations of their small houses due to budget constraints. C omplex structural groups (CLUSOK3 and C LUSOK4) have a clear east to -west pricing inclination throughout the city, indicating that the west part of the city has a higher location add -on value. Furthermore the variations within the complex structural groups are large Large variation s possibly reflect the combin ed effects of the historical traits of the housing units based on a particular district and when the units were built One exception is the CLUSOK1 units on MS district (the southern part of Gainesville ) in which the price is magnificently below the grand mean. This might be re ferred to the lack of city infrastructure in that area By contrast in the SW area exhibits higher price s. T his area is a concentrat ion of more recent developments designed to satisfy the preference of a targeted demographic group The NW district which is considered as a historical ly persevered area has raised the price for the housing units as well. T he pricing differences of distinctive structural groups are small in those areas, indicating that buyers would be able to get higher utility in those district s by paying similar large amounts of money. On the other hand, the old downtown of E and ME districts has negative impacts on price level in comparison to all other structural clusters Also, the negat ive pricing impacts associated with those areas appear to be a manifestation of the sensitivity of the market to higher crime rates in this part of Gainesville as well as related to the impression that housing quality was lower in those area s Interpretation of Spatial Expansion Model Table 4 7 and Table 4 8 indicate that c oefficients on building characteristics have plausible signs and magnitudes T welve of thirteen variables enter the model as a form of interaction


53 terms. The only variable a s individual effect is the location dummy E, which indicates marked lower housing price s in this area Structural spatial interactions could be found as the combination of structural characteristics (i.e. Building Area ), absolute location ( i e x ), and relative location (i.e. NearCen, NearUF and Near I75). Two -out of -four structural dummies (CLUSOK1 and CLUSOK2) and f ive -out of -seven location dummies (E BQ NW N MS) reveal heterogeneities and are interacti ve The significance of interaction term s support s the hypothesis that housing price is heterogeneous at the urban level but continuous at the local level The two -dimensional grouping effectively reflect s the nature of isotropic pricing island s by three degrees of freedom with structural dummies and location dummies For example, NearUF*NW*CLUSOK1, presents negative coefficients indicat ing that all housing units show a price decay as one move away from the UF campus but the elastic ity varie s across the different subma rket s NearI75*NW*CLUSOK1 provides contradicti ng effects implying that the price of housing units in the CLUSOK1 clusters decreased in NW but increase in the o ther submarket s From a structural characteristics stand point the buil t urban area identifies a small but strongly significant elasticity with structural dummies (i.e. CLUSOK1 or CLUSOK2) and spatial dummies (i.e. E and M) It implies that buyers could be compensated by higher land consumption with lower structural qualities or poor location ameni t ies Note that from a geographical per spect ive E and M areas are considered as part and parcel of Gainesville s CBD However, they provide negative location value for the market price. This is consistent with Charles Tiebout s theory : the benefits associated with land consumption could be capitalized by additional premium s on local goods and services under a specific-geographical context (Tiebout 1956) Building a ge ( AGE) exerts significant effects in two districts : M E and M S In ME where


54 older houses are poorly preserved, l ower market value s are observed and prevalent while in MS the opposite is found to be true These effects confirm the validity of historical traits that and price would change according to the cluster s age and the combined effects of the corresponding maintenance efforts as implied by income levels in these areas It should be note d that other structural variables such as the numb er of bathroom and the number of bedroom are generalized by cluster dummies and d id not appear as significant Location characteristics illustrate significant elasticity with interaction s of structural submarket s and spatial submarket s The location information helps to unveil the changes of price at the neighborhood level. Specifically, the absolute location information (i.e. X1) allows for directional shifts highlighting the micro transition of market price on x ax is with the combin ed effects of structural and spatial dummies (i.e. E and CLUSOK1) The relative location variable s (i.e. NearCen, NearUF and NearI75 theta ) present the geographical relations of a parcel s location and related urban infrastructur es This f i nding agrees with the ANOVA analysis which suggests that the means and the variation from structural submarkets var y according to location The last step is to analyze the residuals. A p rocedure known as Univariate is used in SAS to test the distribution of the residuals From the QQ plot and the histogram of the residuals (Figure 4 14), the concentration of extreme residuals indicates the overestimation of price with the existence of local autocorrelations. Th e spatial distribution of the extreme residual is identified by usi ng ArcGIS Figure 4 15 demonstrates the geographical distribution of the residuals from the spatial expansion model. As the counterpart of Figure 4 1, Figure 4 15 illustrates demonstrated that most of the negative and the positive residuals have been ne utralized by the introduction of spatial dummies and the structural dummies. Figure s 4 1 6 and


55 4 1 7 present the extreme negative and positive r esidual s recovered from the spatial expansion model The under -estimated clusters of residuals in Figure 4 1 6 is constructed with the shapes of certain communities in Gainesville. These communities are similar in terms of the services and amenity prouded. The consumer would consider these communities as brand s in the Veblen Good context which provides leverage in housing value as well as an indicator of social status of house owners (Thrall 2002) Figure 4 1 7 shows that most of the over -estimat ed outliers are located in E, M and ME subdivisions Th ese district s contain older housing units with larger selling pric e variation. The over -estimat ed residuals indicate that housing units in these area s might depreciate much faster than units located elsewhere in the city and may also be related to lower monetary outlays for optimize and maintenance and these depreciation results from the lack of management or deterioration of city facilities. Moreover, according to the annual crime report, E, M and ME district have a hig her crime rate compared to other districts.3 In all, the extreme residual s reflect heterogeneity effects at the city level; while the clusters distinct neighborhoods. In order to present spatial heterogeneity, a modified spatial expansion model is constru cted on the foundation of the spatial expansion model in Table 4 7. Eight dummies have been added to the model: Three dummies (i.e. SWUnderE, MSUnderE and MNUnderE) are generated from Figure 4 16 as indicators of whether housing units are in the spatial region of under -estimated clusters ; five dummies (i.e. MnOverE, EoverE, SWOverE1,SWOverE2 and MSOverE) are generated from Figure 4 17 for identifying whether units are located in the spatial region of the over -estimated clusters Coefficients of the new model are shown in Table 4 10 with significance of .1 levels The adjust R -squares for the new model have increased from .8680 to 3 See http://www. information/annual reports for more details. Also, monitor the crimes in the eastern part Gainesville


56 .8750. The significance s of t wo area dummies ( i.e. SWUnderE and MSUnderE) imply that those neighborhoods exert positive effe ct by leveraging the value of the housing units within those areas. On the other hand, the area dummy EOverE indicate s that those neighborhoods would reduce the values of housing units located in that area by providing negative externalities (e.g. higher crime rate and poor amenity) In sum the general status of Gainesville real estate market could be summarized as follows: from a s tructural perspective, the eastern part of the city (E, ME) exerts a negative influence on housing price. The variations wit hin E and ME are large and are indicative of variability in the conditions of housing units. Toward the city center and the northwestern part of the city ( M, MS a nd NW), housing structures play a less important role as determinants of housing price. The location effects raise values for all the structural groups. Units in the Southwestern part of the city could be considered as a landmark with a large number of CLUSOK 3 units, which are catering to the recent demands of buyers who are looking for a new r esidential property. On the other h and, old er units in the north-western part of the city are typically in well -preserved and favorable condition, thereby securing higher market values swifts compared to housing units in the eastern part of the city. Consequently s patial hedonic model s provide detailed differentiation of the marginal price of struct ural and spatial characteristics with evidence of interaction effect between submarkets. The implications here are that submarket definitions are complex and multi -dimensional, and involve considerations of structural and spatial variables that are non -separable from the vintage of housing units when determining market price.


57 Table 4 1. Results of g lobal m odel Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Variance Inflation Intercept 1 11.42399 0.02030 562.65 <.0001 0 BA 1 0.00038723 0.00000546 70.94 <.0001 3.21354 LS 1 7.90294E 8 2.482683E 7 0.32 0.7503 1.56902 Bt 1 0.04528 0.00740 6.12 <.0001 2.55460 Be 1 0.00595 0.00574 1.04 0.3003 1.78315 AGE 1 0.00236 0.00018845 12.54 <.0001 1.84521 NearUF 1 0.00000195 2.979682E 7 6.53 <.0001 1.54069 NearI75 1 0.00000531 3.394512E 7 15.63 <.0001 1.18939 nearbusi 1 0.00000486 0.00000179 2.72 0.0066 1.41638 Sample size =4814 Adjust R squares = 0.8182 Root Mean Square Error=0.18259, degrees of freedom =4806, F =2704 (significance 0.0000). G lobal Moran I = 0.12 is calculated for detection of spatial autocorrelation for model error.


58 Table 4 2 Structural c luster result s CLUSOK Number of Observations Variable Mean Std Dev Minimum Maximum 1 144 Building Area ( BA ) 1418.43 502.9845 511 3691 Lot Size ( LS ) 11355.91 7151.71 3371 58372.11 Number of Be droom(Be) 2.631944 0.676752 1 5 Number of Bathroom( Bt ) 1.28125 0.490179 1 3 AGE 54.70139 14.6106 17 108 2 1015 BA 1891.18 818.8202 540 5731 LS 13303.6 13597.45 653.5156 139988.1 Be 2.588177 0.512043 1 4 Bt 1.763547 0.682445 1 3.5 AGE 36.32217 20.13734 2 108 3 2522 BA 2185.12 485.6778 1008 4513 LS 12453.91 10616.76 2062.94 241348.6 Be 3 0 3 3 Bt 2 0 2 2 AGE 20.51427 15.60978 2 108 4 1134 BA 3255.84 914.2075 1272 7516 LS 20251.65 16774.22 2130.73 173786.9 Be 4.074074 0.281494 2 5 Bt 2.617284 0.67348 1 5 AGE 17.76367 16.59275 2 108


59 Table 4 3 Discrimina n t s ummary u sing u niform k ernel d ensity Number of Observations and Percent Classified into GWRC From gwrc E M ME MN MS NW SW Other Total E 1 0.79 51 40.1 6 62 48.8 2 0 0.00 0 0.00 1 0.79 10 7.87 2 1.57 127 100. 00 M 0 0.00 883 62.1 8 91 6.41 17 1.20 0 0.00 0 0.00 398 28.0 3 31 2.18 1420 100. 00 ME 2 0.32 181 28.5 5 378 59.6 2 0 0.00 1 0.16 1 0.16 48 7.57 23 3.63 634 100. 00 MN 0 0.00 150 27.7 8 1 0.19 23 4.26 0 0.00 0 0.00 349 64.6 3 17 3.15 540 100. 00 MS 0 0.00 38 44.7 1 10 11.7 6 0 0.00 3 3.53 0 0.00 28 32.9 4 6 7.06 85 100. 00 NW 1 0.36 48 17.3 3 14 5.05 6 2.17 0 0.00 6 2.17 193 69.6 8 9 3.25 277 100. 00 SW 0 0.00 199 11.5 2 4 0.23 25 1.45 1 0.06 1 0.06 1447 83.7 9 50 2.90 1727 100. 00 Total 4 0.08 1551 32.2 1 560 11.6 3 71 1.47 5 0.10 9 0.19 2476 51.4 2 139 2.89 4815 100. 00 Error Count Estimates For Re substitution 0.4606 E rror Count Estimates For Cross v alidation 0.4301


60 Table 4 4 Overall ANOVA for s tructural and s patial categories Source DF Sum of Squares Mean Square F Value Without Interaction With Interaction Without Interaction With Interaction Without Interaction With Interaction Without Interaction With Interaction Model 9 27 441.3377477 456.0926314 49.0375 16.8923 535.65 190.21 Error 4800 4782 439.427402 424.6725182 0.09155 0.08881 Corrected Total 4809 4809 880.7651496 880.7651496 Variable DF Type III SS Mean Square F Value CLUSOK 3 6 145.9206827 33.66263342 48.6402 5.61044 531.31 63.18 gwrc gwrc*CLUSOK 6 3 148.4979426 39.2355051 24.7497 13.0785 270.35 147.27 18 148.4979426 14.75488372 24.7497 0.81972 270.35 9.23 All p values are <0.001


61 Table 4 5 Slice effects by s tructural c ategory and s patial c ategory Slice effects by two categories gwrc*CLUSOK Effect Sliced by CLUSOK for LNSALE CLUSOK DF Sum of Squares Mean Square F Value Pr > F 1 6 2.552437 0.425406 4.79 <.0001 2 6 67.353292 11.225549 126.40 <.0001 3 6 48.910258 8.151710 91.79 <.0001 5 6 44.436840 7.406140 83.40 <.0001 gwrc *CLUSOK Effect Sliced by gwrc for LNSALE Gwrc DF Sum of Squares Mean Square F Value Pr > F E 3 3.617475 1.205825 13.58 <.0001 M 3 34.849281 11.616427 130.81 <.0001 ME 3 6.101052 2.033684 22.90 <.0001 MN 3 29.155012 9.718337 109.43 <.0001 MS 3 5.005853 1.668618 18.79 <.0001 NW 3 12.140010 4.046670 45.57 <.0001 SW 3 69.806883 23.268961 262.02 <.0001


62 Table 4 6 Means of s ubmarkets Level of Structural Submarket Market Level of Spatial Submarket E M ME MN MS NW SW CLUSOK1 94406 121368 110986 178536 48785 109619 142918 (1.195) (1.634) (1.475) (1.072) (1.445) (1.475) (1.072) CLUSOK2 93130 174127 129423 180583 157673 153561 240407 (1.303) (1.434) (1.395) (1.620) (1.445) (1.454) (1.520) CLUSOK3 121368 186706 138473 197257 199960 200837 224126 (1.207) (1.256) (1.307) (1.224) (1.284) (1.304) (1.262) CLUSOK 4 157759.405 266881.495 163987.995 327963.926 229430.883 299571.171 344017.876 (1.471) (1.323) (1.457) (1.438) (1.396) (1.293) (1.429)


63 Table 4 7 Standard e rrors for s patial e xpansion m odel Sample size =4814 Adjust R squares = 0.8680 Root Mean Square Error=0.02432, degrees of freedom = 34 F = 977.45 (significance 0.0000). Source DF Type III SS Mean Square F Value Pr > F E 1 1.57426462 1.57426462 67.89 <.0001 BA*E*CLUSOK1 4 46.05649160 11.51412290 496.52 <.0001 X1*E*CLUSOK1 4 9.15942641 2.28985660 98.74 <.0001 NearUF*NW*CLUSOK1 3 1.08563768 0.36187923 15.61 <.0001 NearUF*ME*CLUSOK2 3 0.33962811 0.11320937 4.88 0.0022 NearI75*NW*CLUSOK1 4 7.12088758 1.78022190 76.77 <.0001 BA*BA*M*CLUSOK2 3 3.44364787 1.14788262 49.50 <.0001 AGE*ME 2 7.25994861 3.62997431 156.53 <.0001 AGE*AGE*MS 2 3.00089528 1.50044764 64.70 <.0001 theta*NearCen 1 1.75598746 1.75598746 75.72 <.0001 NearI75*theta 1 0.57458822 0.57458822 24.78 <.0001 Bt*ME 2 2.21792533 1.10896266 47.82 <.0001


64 Table 4 8 Coefficients e stimation Parameter Estimate Standard Error t Value Pr > |t| Intercept 22.59710764 B* 7.76068618 2.91 0.0036 E 0 66.47925188 B 8.06855424 8.24 <.0001 E 1 0.00000000 B BA*E*CLUSOK1 0 0 0.00053766 0.00001290 41.69 <.0001 BA*E*CLUSOK1 0 1 0.00121219 0.00009662 12.55 <.0001 BA*E*CLUSOK1 1 0 0.00064680 0.00003353 19.29 < .0001 BA*E*CLUSOK1 1 1 0.00130683 0.00019243 6.79 <.0001 X1*E*CLUSOK1 0 0 0.00001235 0.00000068 18.14 <.0001 X1*E*CLUSOK1 0 1 0.00001265 0.00000068 18.51 <.0001 X1*E*CLUSOK1 1 0 0.00001243 0.00000290 4.28 <.0001 X1*E*CLUSOK1 1 1 0.00001220 0.00000290 4.20 <.0001 NearUF*NW*CLUSOK1 0 0 0.00002424 B 0.00000152 16.00 <.0001 NearUF*NW*CLUSOK1 0 1 0.00003410 B 0.00000375 9.10 <.0001 NearUF*NW*CLUSOK1 1 0 0.00002131 B 0.00000149 14.33 <.0001 NearUF*NW*CLUSOK1 1 1 0.00001427 B 0.00000284 5.03 <.0001 NearUF*ME*CLUSOK2 0 0 0.00000569 B 0.00000155 3.67 0.0002 NearUF*ME*CLUSOK2 0 1 0.00000521 B 0.00000154 3.38 0.0007 NearUF*ME*CLUSOK2 1 0 0.00000067 B 0.00000143 0.47 0.6362 NearUF*ME*CLUSOK2 1 1 0.00000000 B NearI75*NW*CLUSOK1 0 0 0.00001228 0.00000074 16.63 <.0001 NearI75*NW*CLUSOK1 0 1 0.00001897 0.00000309 6.13 <.0001 NearI75*NW*CLUSOK1 1 0 0.00001343 0.00000129 10.44 <.0001 NearI75*NW*CLUSOK1 1 1 0.00002043 0.00002095 0.97 0.3297 BA*BA*M*CLUSOK2 0 0 0.00000020 B 0.00000003 7.45 <.0001 BA*BA*M*CLUSOK2 0 1 0.00000020 B 0.00000003 7.50 <.0001 BA*BA*M*CLUSOK2 1 0 0.00000021 B 0.00000003 7.94 <.0001 BA*BA*M*CLUSOK2 1 1 0.00000021 B 0.00000003 7.73 <.0001 AGE*ME 0 0.00661006 0.00041341 15.99 <.0001 AGE*ME 1 0.00469814 0.00057573 8.16 <.0001 AGE*AGE*MS 0 0.00006379 0.00000606 10.52 <.0001 AGE*AGE*MS 1 0.00001179 0.00001159 1.02 0.3090 theta*NearCen 0.00000345 0.00000040 8.70 <.0001 NearI75*theta 0.00000255 0.00000051 4.98 <.0001 BA*BA*CLUSOK1 0 0.00000016 B 0.00000003 6.19 <.0001 BA*BA*CLUSOK1 1 0.00000000 B Bt*ME 0 0.05720378 0.00657402 8.70 <.0001 Bt*ME 1 0.02133263 0.01200055 1.78 0.0755 *B means the XX matrix could not be found


65 Table 4 9 Modified s patial e xpansion m odel Sample size =4814 Adjust R squares = 0. 8 750 Root Mean Square Error=0.02 308 degrees of freedom = 38, F = 879.22 (significance 0.0000). Source DF Type III SS Mean Square F Value Pr > F E 1 1.38507220 1.38507220 60.00 <.0001 BA*E*cl1 4 44.10906878 11.02726720 477.69 <.0001 X1*E*cl1 4 8.35976754 2.08994188 90.53 <.0001 NearUF*NW*cl1 3 1.02462877 0.34154292 14.80 <.0001 NearUF*ME*cl2 3 0.28397672 0.09465891 4.10 0.0065 NearI75*NW*cl1 4 6.36810777 1.59202694 68.97 <.0001 BA*BA*M*cl2 3 3.05048921 1.01682974 44.05 <.0001 AGE*ME 2 7.32451262 3.66225631 158.65 <.0001 AGE*AGE*MS 2 2.84248849 1.42124424 61.57 <.0001 theta*NearCen 1 1.59462079 1.59462079 69.08 <.0001 NearI75*theta 1 0.43117025 0.43117025 18.68 <.0001 BA*BA*cl1 1 0.87647799 0.87647799 37.97 <.0001 LS*Y1*Y1*Y1 1 2.05801971 2.05801971 89.15 <.0001 Bt*ME 2 2.00247438 1.00123719 43.37 <.0001 SWUnderE 1 0.08239639 0.08239639 3.57 0.0589 MSUnderE 1 0.08340844 0.08340844 3.61 0.0574 EOverE 1 0.29274282 0.29274282 12.68 0.0004


66 Figure 4 1 Residuals d istribution of g lobal m odel


67 Figure 4 2 Price Surface for Clusok1 Figure 4 3 Price Surface for Clusok2 LNSALE X1 Y1 9.0 14.0 LNSALE X1 Y1 10.0 13.5


68 Figure 4 4 Price Surface for Clusok3 Figure 4 5 Price Surface for Clusok4 LNSALE X1 Y1 9.0 14.0 LNSALE X1 Y1 9.0 15.0


69 Figure 4 6 Spatial d istribution of s tructural s ubmarket


70 A B Figure 4 7 Spatial c luster r esult and GWR c oefficients m ap s A) Location division. B) Coefficient Map.


71 Figure 4 8 Comparison m atrix for LNSALE


7 2 Figure 4 9 Box p lot for m ean d ifferentiation


73 Figure 4 10. Structural c lusters by l ocation e ffects for a rea E, ME, M and MN A) Area E. B) Area ME. C) Area M. D) Area MN. 1 2 3 5 10.500000 11.000000 11.500000 12.000000 12.500000 13.000000LNSALECLUSOK 1 2 3 4 10.000000 10.500000 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000LNSALECLUSOK 1 2 3 4 10.500000 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000LNSALECLUSOK 1 2 3 4 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000 14.000000LNSALECLUSOK A B C D


74 Figure 4 11. Structural c lusters by l ocation e ffects for a rea MS, NW and SW A) Area MS. B) Area NW. C) Area SW. 1 2 3 4 10.500000 11.000000 11.500000 12.000000 12.500000 13.000000LNSALECLUSOK 1 2 3 4 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000LNSALECLUSOK 1 2 3 4 11.000000 11.500000 12.000000 12.500000 13.000000 13.500000 14.000000LNSALECLUSOK A B C


75 Figure 4 12. Least -square m ean of s tructural c luster A) CLUSOK1 B) CLUSOK2 A B


76 Figure 4 13. Least -square m ean of s tructural c luster A) CLUSOK3 B) CLUSOK4 A B


77 Figure 4 1 4 Residual a nalysis A) QQ -plot. B) Residual Distribution. -0.76 -0.68 -0.60 -0.52 -0.44 -0.36 -0.28 -0.20 -0.12 -0.04 0.04 0.12 0.20 0.28 0.36 0.44 0.52 0.60 0.68 0.76 0.84 0.92 1.00 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 Percentresid A B


78 Figure 4 1 5 Residuals' d istribution for the s patial e x pansion m odel


79 Figure 4 1 6 Under e stimations of r esiduals


80 Figure 4 1 7 Over e stimations of r esiduals


81 CHAPTER 5 DISCUSSION AND CONCLUSION Th is thesis explore s the notion and challenge of defining submarkets in a residential housing market Previous research has shown that alternative approaches to modeling housing price variation should be caution when attempting to define housing submarkets given the complex nature of what might constitute various sub -market based on site and situational attributes and context (Watkin s 2001) Various definition s have been proposed based on structural criteria, spatial criteria and the collaboration of both (Bourassa et al. 1999; 2003). However, this research ha s not touched upon the implicit relationships among the three definitions and to what extents they may be combined to further advance hedonic modeling This research targets an important question: how submarket s under different standards are generated and how they interact ed with each other Consequently, its argued that, the price of a housing unit is c omparable to the units which have aggregated structural similarities and units located in the same spatial subdivision or vicinity, as well as those that share both attributes Empirically, it is shown that the structural effects and the spatial effects are inter -correlated with each other and are also related to the chronology of urban development patterns In short, it is shown that there is a spatio temporal pattern of structural groups (housing uni t groupings) that is directly related to the direction of urban growth and geo -historical trends in urban development. This research establishes a bridge between identifying the Location Value Signature (s) of properties and the continuity of housing sub ma rket s through the assignments of d ifferent statistically derived subdivisions or groupings It strikes a balance between knowledge of spatial data mining techniques and the use of information related to the built environment as represented by the spatial patterns and evolution of urban development in the study region I t provides a link between adopting positive modeling methods and normality modeling methods A positive


82 modeling point of view, which is often implemented by the economists, delineate s the distribution of observation s and variations that relate to economic trends, non -spatial attributes, and/or market forces and factors V arious models have also been derived to integrate the aggregate effects of certain characteristics of the observations in t he city environs. However it can be argued that the inclu sions of the spatial heterogeneity effects which are viewed as discontinuous on the underlying theoretical pric e/valuation surface have gained inadequate attention in e conomic model s A n ormality point of view which is often held by city planner, uses political division to shape or adjust the urban landscape From this aspect, the city is considered as a combination of several segments with different order of hierarchies and could be controlled by the government in which the continuous effects at the neighborhood scale are often neglected This research provide s a multi -factor approach to modeling housing prices within the urban environment by the separation of structur al and spatial variables. Combining those points of view structural submarkets and spatial submarkets are analyzed interactively: the former are generated by the consideration of non-spatial attributes and the latter are defined by location and proximity. Specifically, variation and discontinuities of pricing effects are controlled by structural/spatial submarket dummies and the use of continuous pricing surfaces which are assumed within structural/spatial submarkets by the int eractions of absolute and re lative location (s) Hence, consistent with previous research the heterogeneity effect in the urban area should be advocated as follows : some district would have significantly higher or lower effects on housing value, ceteris paribus ; while at the same location, housing price s or market value would vary according to their differentiation of structural attributes Also, it could be anticipated that some neighborhoods have distinctive amenities or housing structures which


83 deviate from the gene ral market condition thereby contrasting market value to the neighborhood effect and the type of housing units that are located within those neighborhoods The structural agglomerations of housing units are shown to be spatially related to the chronologic al development of the urban area itself and the nature of urban infrastructure and the built environment Since t he city s spatial structure or morphology can influence or determined the extent and type of spatial heterogeneity the uniqueness of urban ch aracteristics consistently provide different externality leverages to the units around them ; factors which should be internalized in the selling price of residential housing units depending on their age or vintage and their location or neighborhood affilia tion The s e discrete effect s could be anticipated nevertheless by the interaction between absolute/relative location, spatial and structural submarkets, and other characteristics of housing units. Conclusively, urban features (i.e. transportation network and the physical layout of the urban environ ) and economic nodes (i.e. employment and service center s ) persistently shape the development of the real estate market with longterm externality effects Trends of housing development are believed to be influ ential in determining the beneficial aspects of location and the location of important nodes and linkages on the urban landscape. This research suggests that t he effects of interaction of spatial and structural submarket s must be viewed in relation to the historic traits associated with urban development, as represented by the attributes of the housing units that were built during various periods The historic traits are closely related to building age or vintage reflecting: 1) the outcome of the force s or supply and demand for various housing attributes at a certain time point, and how price levels are affected by the spatial features of certain structural groups; 2) over a longer period, urban developments impact on the appreciation rate of a certain structural group as determined


84 by the absolute and/or relati ve location of the land parcel s and corresponding housing units The temporal presentation of structural groups implies the chronological appearance of agglomerations of certain structural groups is a realization of the sub-markets ability to mee t the collective demands o f consumers at a certain point in time. As suggested earlier th is development bias towards certain structural group s potentiall y maximized the developers profits and catered for the larges t or most influential demand group. Local ly aggregated maintenance efforts could also be reflected by the historical traits as the market evolves and as residential units depreciate or appreciate depending upon their location and vintage. The total maintenance effort on housing units within a given sub -market can be thought of as an indicator of the intrinsic value of a given housing stock (proxied by monetary outlays and the physical efforts r elated to upkeep), and represents the hidden value of location or association with a given sub -market As a result, spatial variability in hous ing quality and condition in relation to upkeep can influence or determin e the value of housing both in the present and in the future as the urban development process continues to unfold to meet the changing demands or preferences of consumers. Of course, historical trends are all important in determining the extent to which a given housing stock at a given location is valued All i n all the localized structural factor and hidden historical and spatial factor s are keys in the determination of market price This research outlines various procedure s for real estate practitioner s to apply in the hope of better understand ing the nature of market forces that affect of the market value of housing in a urban setting (Figure 3 1) Nowadays, interactive web -based GIS system s are advocated for querying or presenting the sales of housing in a certain area1 by the estimation of pricing index es for house units based on observed sales in the vicinity or within a given sub -market However, 1 See: and


85 web based services d o not typically provide information on the evolution of price or market value from a structural and local context By using the method s suggested here p ractitioners w ould be facilitated in their attempts to perform spatial -statistical analysis and model patterns and trends in valuation, as well as trends in appreciation. The methodology adopted within this thesis conveniently moves us closer to deriving a potential map ping strategy for exposing the underlying Location Value Signatures associated with residential properties The construction of location valued map s or price trend surface s by market or sub-market could provide user s with a useful reference or benchmark by which to compare price trends throughout a real estate market as they relate to the condition vintage, and attributes of the properties in question, sub -market affiliation (spatial and/or structural) and the geo -historic aspect of u rban development as implied by properties relative and absolute location Price trends should reflect the influence of certain structural group s that emerged during various and crit ical time periods in the evolution of the built environment or the appearance of prominent sub -markets in response to the demand for specific types of residential housing Through the identification of temporal based trends practitioner could become more effective in assessing market signals as they attempt to gain a deeper understanding of the local real estate market through the identification of spatial and structural submarkets and examin ation of the inter related spatial and temporal structure of urb an development Finally, this research provides a practical guide as to the effects of transportation corridors in an urban environment T his research provide d an example of the dragging effects of the interstate highway and its impact of drawing urban development in a given direction ( in this case a w est erly direction ).


86 Future inquiries of the interaction effects of spatial and structural submarkets could advance in three directions. F irst, stud ies could seek to analyze the u rban externality effects over a long period using panel data from cross -sectional studies ; analyzing the long -term dynamics of housing price variation and interaction effects in a spati al -temporal context. Second, studies could focus on directional trends of urban development to evaluate the extent to which directional shifts affect housing values in and along high -growth corridors It is acknowledged that urban development is not equa lly balanced in all directions, and spatial heterogeneity is related to the chronology of urban development. Analysis of the imbalance in directional growth and the assessment of the impacts of new urban infrastructure ( s ) could facilitate researchers in their attempt to unveil predict ions on how the se trends might affect the real estate prices in designated sub -markets in future time periods Lastly, a deeper understanding of intra urban variability in the appreciation rate s of residential housing may be gained through a closer inspection of the monetary outlays and maintena nce efforts with in various spatial and/or structural submarkets In all, this research presents a n effort to explore the concepts of submarkets and quantify the interaction effects of site/situational characteristics with various spatial and/or structural submarkets S ubmarkets under different standards are generated and interacted with each other within a hedonic model Location information was used to present the neighborh ood scale drift and its impact on estimated parameter s. S tructural and spatial a gglomerations of housing units that comprise the various sub -markets are shown to be related to the history of urban development. It is suggested that s tructural and spatial patterns are temporal manifestations of consumer demands f or housing with particu lar site and situational characteristics Urban features and economic nodes have presented longterm externality effects on the evolution of the


87 urban landscape and the relative location of housing with respect to these features and nodes play a signific ant role in determining real estate market values. This research not only construct s a b ridge between positive and normative modeling ( merging the mindsets of Economists and Planners) but it also provides a procedure for real estate practitioner s to differentiat e value on the basis of submarkets, in accordance with structural and spatial attributes


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92 BIOGRAPHICAL SKETCH Mr. Zhuojie Huang got his b achelor s degree with a focus on land resour ce management at South China Agricultural University in 2007 and now he continued his graduate study in the Department of Geography, University of Florida