Quantitative Methods and Applications in GIS - Chapter 4 pptx

There are several methods for delineating trade areas: the analog method, theproximal area method, and the gravity models.. Because of this book’s emphasis on GIS applications, two case

Analysis and Applications

in Business Geography and Regional Planning

“No matter how good its offering, merchandising, or customer service, everyretail company still has to contend with three critical elements of success: loca-tion, location, and location” (Taneja, 1999, p 136) Trade area analysis is acommon and important task in the site selection of a retail store A trade area issimply “the geographic area from which the store draws most of its customersand within which market penetration is highest” (Ghosh and McLafferty, 1987,

p 62) For a new store, the study of proposed trading areas reveals marketopportunities with existing competitors (including those in the same chain orfranchise) and helps decide on the most desirable location For an existing store,

it can be used to project market potentials and evaluate the performance Inaddition, trade area analysis provides many other benefits for a retailer: deter-mining the focus areas for promotional activities, highlighting geographic weak-ness in its customer base, projecting future growth, and others (Berman andEvans, 2001, pp 293–294)

There are several methods for delineating trade areas: the analog method, theproximal area method, and the gravity models The analog method is non-geographic, and more recently is often implemented by regression analysis Theproximal area method and the gravity models are geographic approaches and canbenefit from GIS technologies The analog and proximal area methods are fairlysimple and are discussed in Section 4.1 The gravity models are the focus of thischapter and are covered in detail in Section 4.2 Because of this book’s emphasis

on GIS applications, two case studies are presented in Sections 4.3 and 4.4 toillustrate how the two geographic methods (the proximal area method and thegravity models) are implemented in GIS Case study 4A draws from traditionalbusiness geography, but with a fresh angle: instead of the typical retail storeanalysis, it analyzes the fan bases for two professional baseball teams in Chicago.Case study 4B demonstrates how the techniques of trade area analysis are usedbeyond retail studies In this case, the methods are used in delineating hinterlands(influential areas) for major cities in northeast China Delineation of hinterlands

is an important task for regional planning The chapter is concluded with someremarks in Section 4.5

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56 Quantitative Methods and Applications in GIS

4.1 BASIC METHODS FOR TRADE AREA ANALYSIS 4.1.1 A NALOG M ETHOD AND R EGRESSION M ODEL

The analog method, developed by Applebaum (1966, 1968), is considered the firstsystematic retail forecasting model founded on empirical data The model uses anexisting store or several stores as analogs to forecast sales in a proposed similar oranalogous facility Applebaum’s original analog method did not use regressionanalysis The method uses customer surveys to collect data of sample customers inthe analogous stores: their geographic origins, demographic characteristics, andspending habits The data are then used to determine the levels of market penetration(e.g., number of customers, population, and average spending per capita) at variousdistances The result is used to predict future sales in a store located in similarenvironments Although the data may be used to plot market penetrations at variousdistances from a store, the major objective of the analog method is to forecast salesbut not to define trade areas geographically The analog method is easy to implement,but has some major weaknesses The selection of analog stores requires subjectivejudgment (Applebaum, 1966, p 134), and many situational and site characteristicsthat affect a store’s performance are not considered

A more rigorous approach to advance the classical analog method is the usage

of regression models to account for a wide array of factors that influence a store’sperformance (Rogers and Green, 1978) A regression model can be written as

where Y represents a store’s sales or profits, x’s are explanatory variables, and b’sare the regression coefficients to be estimated

The selection of explanatory variables depends on the type of retail outlets Forexample, the analysis on retail banks by Olsen and Lord (1979) included variablesmeasuring trade area characteristics (purchasing power, median household income,homeownership), variables measuring site attractiveness (employment level, retailsquare footage), and variables measuring level of competition (number of competingbanks’ branches, trade area overlap with branch of same bank) Even for the sametype of retail stores, regression models can be improved by grouping the stores intodifferent categories and running a model on each category For example, Davies(1973) classified clothing outlets into two categories (corner-site stores andintermediate-site stores) and found significant differences in the variables affectingsales For corner-site stores, the top five explanatory variables are floor area, storeaccessibility, number of branches, urban growth rate, and distance to nearest car park.For intermediate-site stores, the top five explanatory variables are total urban retailexpenditure, store accessibility, selling area, floor area, and number of branches

4.1.2 P ROXIMAL A REA M ETHOD

A simple geographic approach for defining trade areas is the proximal area method,which assumes that consumers choose the nearest store among similar outlets (Ghosh

Y =b0+b x1 1+b x2 2+ + b x n n

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GIS-Based Trade Area Analysis and Applications in Geography and Planning 57

and McLafferty, 1987, p 65) This assumption is also found in the classical centralplace theory (Christaller, 1966; Lösch, 1954) The proximal area method implies thatcustomers only consider travel distance (or travel time as an extension) in their shoppingchoice, and thus the trade area is simply made of consumers that are closer to the storethan any other Once the proximal area is defined, sales can be forecasted by analyzingthe demographic characteristics within the area and surveying their spending habits.The proximal area method can be implemented in GIS by two ways The firstapproach is consumers based It begins with a consumer location and searches forthe nearest store among all store locations The process continues until all consumerlocations are covered At the end, consumers that share the same nearest storeconstitute the proximal area for that store In ArcGIS, it is implemented by utilizingthe near tool in ArcToolbox The tool is available by invoking Analysis Tools >Proximity > Near

The second approach is stores based It constructs Thiessen polygons from thestore locations, and the polygon around each store defines the proximal area for thatstore The layer of Thiessen polygons may then be overlaid with that of consumers(e.g., a census tract layer with population information) to identify demographicstructures within each proximal area.1 In ArcGIS, Thiessen polygons can be gener-ated from a point layer of store locations in ArcInfo coverage format by choosingCoverage Tools > Analysis > Proximity > Thiessen For example, Figure 4.1a to cshow how the Thiessen polygons are constructed from five points First, five pointsare scattered in the study area as shown in Figure 4.1a Second, in Figure 4.1b, linesare drawn to connect points that are near each other, and lines are drawn perpen-dicular to the connection lines at their midpoints Finally, in Figure 4.1c, the Thiessenpolygons are formed by the perpendicular lines

The proximal area method can be easily extended to use network distance or traveltime instead of Euclidean distance The process implemented in both case studies 4Aand 4B follows closely the consumers-based approach The first step is to generate adistance (time) matrix, containing the travel distance (time) between each consumerlocation and each store (see Chapter 2) The second step is to identify the store withinthe shortest travel distance (time) from each consumer location Finally, the informa-tion is joined to the spatial layer of consumers for mapping and further analysis

4.2 GRAVITY MODELS FOR DELINEATING TRADE AREAS

4.2.1 R EILLY ’ S L AW

The proximal area method only considers distance (or time) in defining trade areas.However, consumers may bypass the closest store to patronize stores with betterprices, better goods, larger assortments, or a better image A store in proximity toother shopping and service opportunities may also attract customers farther than anisolated store because of multipurpose shopping behavior Methods based on thegravity model consider two factors: distances (or time) from and attractions of stores.Reilly’s law of retail gravitation applies the concept of the gravity model to delin-eating trade areas between two stores (Reilly, 1931) The original Reilly’s law wasused to define trading areas between two cities

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58 Quantitative Methods and Applications in GIS

Consider two stores, stores 1 and 2, that are at a distance of d12 from each other(see Figure 4.2) Assume that the attractions for stores 1 and 2 are measured as S1

and S2 (e.g., in square footage of the stores’ selling areas) respectively The question

is to identify the breaking point (BP) that separates trade areas of the two stores.The BP is d1x from store 1 and d2x from store 2, i.e.,

(4.1)

By the notion of the gravity model, the retail gravitation by a store is in directproportion to its attraction and in reverse proportion to the square of distance

FIGURE 4.1 Constructing Thiessen polygons for five points.

FIGURE 4.2 Breaking point by Reilly’s law between two stores.

(c) (b)

C A

E

D B

GIS-Based Trade Area Analysis and Applications in Geography and Planning 59

Consumers at the BP are indifferent in choosing either store, and thus the gravitation

by store 1 is equal to that by store 2, such as

(4.2)

solving for d1x yields

(4.3)Similarly,

(4.5)

where P ij is the probability of an individual i selecting a store j, U j and U k are theutilities choosing the stores j and k, respectively, and k are the alternatives available(k = 1, 2, …, n)

In practice, the utility of a store is measured as a gravity kernel Like in Equation4.2, the gravity kernel is positively related to a store’s attraction (e.g., its size insquare footage) and inversely related to the distance between the store and a con-sumer’s residence That is,

60 Quantitative Methods and Applications in GIS

where S is a store’s size, d is the distance, β> 0 is the distance friction coefficient,

and other notations are the same as in Equation 4.5 Note that the gravity kernel in

Equation 4.6 is a more general form than in Equation 4.2, where the distance friction

coefficient β is assumed to be 2 The term is also referred to as potential,

measuring the impact of a store j on a demand location at i

Using the gravity kernel to measure utility may be purely a choice of empirical

convenience However, the gravity models (also referred to as spatial interaction

models) can be derived from individual utility maximization (Niedercorn and

Bechdolt, 1969; Colwell, 1982), and thus have its economic foundation (see

Appendix 4) Wilson (1967, 1975) also provided a theoretical base for the gravity

model by an entropy maximization approach Wilson’s work also led to the

dis-covery of a family of gravity models: a production-constrained model, an

attraction-constrained model, and a production–attraction-constrained or doubly constrained

model (Wilson, 1974; Fotheringham and O’Kelly, 1989)

Based on Equation 4.6, consumers in an area visit stores with various

probabil-ities, and an area is assigned to the trade area of a store that is visited with the

highest probability In practice, given a customer location i, the denominator in

Equation 4.6 is identical for various stores j, and thus the highest value of numerator

identifies the store with the highest probability The numerator is also known

as gravity potential for store j at distance d ij In other words, one only needs to

identify the store with the highest potential for defining the trade area

Implemen-tation in ArcGIS can take full advantage of this property However, if one desires

to show a continuous surface of shopping probabilities of individual stores, Equation

4.6 needs to be fully calibrated In fact, one major contribution of the Huff model

is the suggestion that retail trade areas are continuous, complex, and overlapping,

unlike the nonoverlapping geometric areas of central place theory (Berry, 1967)

Implementing the Huff model in ArcGIS utilizes a distance matrix between each

store and each consumer location, and probabilities are computed by using

Equation 4.6 The result is not simply trade areas with clear boundaries, but a

contin-uous probability surface, based on which the simple trade areas can be certainly defined

as areas where residents choose a particular store with the highest probability

4.2.3 L INK BETWEEN R EILLY ’ S L AW AND H UFF M ODEL

Reilly’s law may be considered a special case of the Huff model In Equation 4.6,

when the choices are only two stores (k = 2), P ij = 0.5 at the breaking point That

is to say,

Assuming β= 2, the above equation is the same as Equation 4.2, based on which

Reilly’s law is derived

For any β, a general form of Reilly’s law is written as

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GIS-Based Trade Area Analysis and Applications in Geography and Planning 61

(4.8)

Based on Equation 4.7 or 4.8, if store 1 increases its size faster than store 2 (i.e.,

increases), d1x increases and d2x decreases, indicating that the breaking point

(BP) shifts toward store 2 and the trade area for store 1 expands The observation

is straightforward It is also interesting to examine the impact of the distance friction

coefficient on the trade areas When β decreases, the movement of BP depends on

the store sizes:

and d 2x decreases, indicating that a larger store is expanding its trade area

and d 2x increases, indicating that a smaller store is losing its trade area

That is to say, when the β value decreases over time due to improvements in

transportation technologies or road network, travel distance matters to a lesser

degree, giving even a stronger edge to larger stores This explains some of the success

of superstores in the new era of retail business

4.2.4 E XTENSIONS TO THE H UFF M ODEL

The original Huff model did not include an exponent associated with the store size

A simple improvement over the Huff model in Equation 4.6 is expressed as

(4.9)

where the exponent α captures elasticity of store size (e.g., a larger shopping center

tends to exert more attraction than its size suggests because of scale economies)

The improved model still only used size to measure attractiveness of a store

Nakanishi and Cooper (1974) proposed a more general form called the multiplicative

competitive interaction (MCI) model In addition to size and distance, the model

accounts for factors such as store image, geographic accessibility, and other store

characteristics The MCI model measures the probability of a consumer at residential

area i shopping at a store j, P ij, as

(4.10)

where A lj is a measure of the lth (l = 1, 2, …, L) characteristic of store j, N i is the

set of stores considered by consumers at i, and other notations are the same as in

62 Quantitative Methods and Applications in GIS

If disaggregate data of individual shopping trips, instead of the aggregate data

of trips from areas, are available, the multinomial logit (MNL) model is used to

model shopping behavior (e.g., Weisbrod et al., 1984), written as

(4.11)

Instead of using a power function for the gravity kernel in Equation 4.10, anexponential function is used in Equation 4.11 The model is estimated by multinomiallogit regression

4.2.5 D ERIVING THE ββββ V ALUE IN THE G RAVITY M ODELS

The distance friction coefficient β is a key parameter in the gravity models, andderiving its value is an important task prior to the usage of the Huff model Thevalue varies over time and also across regions, and thus ideally it needs to be derivedfrom the existing travel pattern in a study area

The original Huff model in Equation 4.6 corresponds to an earlier version ofthe gravity model for interzonal linkage, written as

(4.12)

where T ij is the number of trips between zone i (in this case, a residential area) and j (in this case, a shopping outlet), O i is the size of an origin i (in this case, population

in a residential area), D j is the size of a destination j (in this case, a store size), a is

a scalar (constant), and d ij and β are the same as in Equation 4.6 RearrangingEquation 4.12 and taking logarithms on both sides yield

(4.13)

That is to say, if the original model without an exponent for store size is used, thevalue is derived from a simple bivariate regression model shown in Equation 4.13.See Jin et al (2004) for an example

Similarly, the improved Huff model in Equation 4.9 corresponds to a gravitymodel such as

GIS-Based Trade Area Analysis and Applications in Geography and Planning 63

Equation 4.15 is the multivariate regression model for deriving the β value if theimproved Huff model in Equation 4.9 is used

4.3 CASE STUDY 4A: DEFINING FAN BASES OF

CHICAGO CUBS AND WHITE SOX

In Chicago, it is well known that between the two Major League Baseball (MLB)teams the Cubs outdraw the White Sox in fans regardless of their respective winningrecords Many factors, such as history, neighborhoods surrounding the ballparks,pubic images of team management, winning records, and others, may attribute tothe difference In this case study, we attempt to investigate the issue from a geo-graphic perspective For illustrating trade area analysis techniques, only the popu-lation surrounding the ballparks is considered The proximal area method is firstused to examine which club has an advantage if fans choose a closer club Formethodology demonstration, we then consider winning percentage as the only factorfor measuring attraction of a club,2 and use the gravity model method to calibratethe probability surface For simplicity, Euclidean distances are used for measuringproximity in this project (network distances will be used in case study 4B), and thedistance friction coefficient is assumed to be 2, i.e., β = 2

Data needed for this project include:

1 A polygon coverage chitrt for census tracts in the study area

2 A shapefile tgr17031lka for roads and streets in Cook County, wherethe two clubs are located

addresses of the clubs and their winning records

The following explains how the above data sets are obtained and processed.The study area is defined as the 10 Illinois counties in the Chicago consolidatedmetropolitan statistical area (CMSA) (county codes in parentheses): Cook (031),DeKalb (037), DuPage (043), Grundy (063), Kane (089), Kankakee (091), Kendall(093), Lake (097), McHenry (111), and Will (197) See the inset in Figure 4.3

showing the 10 counties in northeastern Illinois The spatial and correspondingattribute data are downloaded from the Environmental Systems Research Institute,Inc (ESRI) data website and processed following procedures similar to thosediscussed in Section 1.2 The census tract layer of each county is downloaded one

at a time and then joined with its corresponding 2000 Census data Finally, thecounties are merged together to form chitrt by using the tool in ArcToolbox:Data Management > General > Append For this project, only the populationinformation from the census is retained, and saved as the field popu One mayfind other demographic variables, such as income, age, and sex, also useful, anduse them for more in-depth analysis

The shapefile tgr17031lka for roads and streets in Cook County, where thetwo clubs are located, is also downloaded from the ESRI site This layer is used forgeocoding the clubs

64 Quantitative Methods and Applications in GIS

Addresses of the two clubs (Chicago Cubs at Wrigley Field, 1060 W.Addison St., Chicago, IL 60613; Chicago White Sox at U.S Cellular Field, 333 W.35th St., Chicago, IL 60616) and their winning percentages (0.549 for Cubs and0.512 for White Sox) in 2003 are found on the Internet and are used to build thefile cubsoxaddr.csv with fields club, street, zip, and winrat

FIGURE 4.3 Proximal areas for the Cubs and White Sox.

Cubs

W Sox

Cubs trade area

W Sox trade area

Club location

0 5 10 20 30 40

Kilometers Study area

County

Cook DeKalb

Kendall Kane McHenry

DuPage Lak e

Grundy

Kankakee Will

N