Quantitative Methods and Applications in GIS - Chapter 6 pdf

Analysis of changing population distribution patterns is astarting point for examining economic development patterns in a city or region.Urban and regional density patterns mirror each o

Regressions and Application in Analyzing Urban and Regional

Density Patterns

Urban and regional studies begin with analyzing the spatial structure, particularlypopulation density patterns As population serves as both supply (labor) and demand(consumers) in an economic system, the distribution of population represents that

of economic activities Analysis of changing population distribution patterns is astarting point for examining economic development patterns in a city or region.Urban and regional density patterns mirror each other: the central business district

(CBD) is the center of a city, whereas the whole city itself is the center of a region,and densities decline with distances both from the CBD in a city and from the centralcity in a region While the theoretical foundations for declining urban and regionaldensity patterns are different (see Section 6.1), the methods for empirical studiesare similar and closely related

This chapter discusses how we can find a function capturing the density patternsbest, and what we can learn about urban and regional growth patterns from thisapproach The methodological focus is on function fittings by regressions and relatedstatistical issues Section 6.1 explains how density functions are used to examineurban and regional structures Section 6.2 presents various functions for a monocentricstructure Section 6.3 discusses some statistical concerns on monocentric functionfittings and introduces nonlinear regression and weighted regression Section 6.4examines various assumptions for a polycentric structure and corresponding functionforms Section 6.5 uses a case study in the Chicago region to illustrate the techniques(monocentric vs polycentric models, linear vs nonlinear and weighted regressions).The chapter is concluded in Section 6.6 with discussion and a brief summary

6.1 THE DENSITY FUNCTION APPROACH TO URBAN AND REGIONAL STRUCTURES

6.1.1 S TUDIES ON U RBAN D ENSITY F UNCTIONS

Since the classic study by Clark (1951), there has been great interest in empiricalstudies of urban population density functions This cannot be solely explained by2795_C006.fm Page 97 Friday, February 3, 2006 12:16 PM

98 Quantitative Methods and Applications in GIS

the easy availability of data Many are attracted to the research topic because of itspower of revealing urban structure and its solid foundation in economic theory.1McDonald (1989, p 361) considers the population density pattern as “a criticaleconomic and social feature of an urban area.”

Among all functions, the exponential function or Clark’s model is the one usedmost widely:

(6.1)

where D r is the density at distance r from the city center (i.e., CBD), a is a constant(the CBD intercept), and b is also a constant for the density gradient Since thedensity gradient b is often a negative value, the function is also referred to as the

negative exponential function Empirical studies show that it is a good fit for mostcities in both developed and developing countries (Mills and Tan, 1980)

The economic model by Mills (1972) and Muth (1969), often referred to as the

Mills–Muth model, is developed to explain the empirical pattern of urban densities

as a negative exponential function The model assumes a monocentric structure: acity has only one center, where all employment is concentrated Intuitively, aseveryone commutes to the city center for work, a household farther away from theCBD spends more on commuting and is compensated by living in a larger-lot house(also cheaper in terms of price per area unit) The resulting population densityexhibits a declining pattern with distance from the city center Appendix 6A showshow the negative exponential urban density function is derived in the economicmodel From the deriving process, parameter b in Equation 6.1 is the unit cost oftransportation Therefore, declining transportation costs over time, as a result ofimprovements in transportation technologies and road networks, lead to a flatterdensity gradient This clearly explains that urban sprawl and suburbanization aremainly attributable to transportation improvements

However, economic models are “simplification and abstractions that may provetoo limiting and confining when it comes to understanding and modifying complexrealities” (Casetti, 1993, p 527) The main criticisms lie in its assumptions of themonocentric city and unit price elasticity for housing, neither of which is supported

by empirical studies Wang and Guldmann (1996) developed a gravity-based model

to explain the urban density pattern (also see Appendix 6A) The basic assumption

of the gravity-based model is that population at a particular location is proportional

to its accessibility to all other locations in a city, measured as a gravity potential.Simulated density patterns from the model conform to the negative exponential func-tion when the distance friction coefficient β falls within a certain range (0.2 ≤β≤ 1.0

in the simulated example) The gravity-based model does not make the restrictiveassumptions as in the economic model, and thus implies wide applicability It alsoexplains two important empirical findings: (1) flattening density gradient over times(corresponding to smaller β) and (2) flatter gradients in larger cities The economicmodel explains the first finding well, but not the second (McDonald, 1989, p 380).Both the economic model and the gravity-based model explain the change of densitygradient over time through transportation improvements Note that both the distance

D r =ae br

Function Fittings by Regressions and Application in Analyzing Density Patterns 99

friction coefficient β in the gravity model and the unit cost of transportation in theeconomic model decline over time

Earlier empirical studies of urban density patterns are based on the monocentricmodel, i.e., how population density varies with distance from the city center Itemphasizes the impact of the primary center (CBD) on citywide population distri-bution Since the 1970s, more and more researchers recognize the changing urbanform from monocentricity to polycentricity (Ladd and Wheaton, 1991; Berry andKim, 1993) In addition to the major center in the CBD, most large cities havesecondary centers or subcenters, and thus are better characterized as polycentriccities In a polycentric city, assumptions of whether residents need to access allcenters or some of the centers lead to various function forms Section 6.4 willexamine the polycentric models in detail

6.1.2 S TUDIES ON R EGIONAL D ENSITY F UNCTIONS

The study of regional density patterns is a natural extension to that of urban densitypatterns as the study area is expanded to include rural areas The urban populationdensity patterns, particularly the negative exponential function, are empiricallyobserved first, and then explained by theoretical models (either the economic model

or the gravity-based model) Even considering the Alonso’s (1964) urban land use model as the precedent of the Mills–Muth urban economic model, the theoreticalexplanation lags behind the empirical finding on urban density patterns In contrast,following the rural land use theory by von Thünen (1966, English version), economicmodels for the regional density pattern by Beckmann (1971) and Webber (1973)were developed before the work of empirical models for regional population densityfunctions by Parr (1985), Parr et al (1988), and Parr and O’Neill (1989) The citycenter used in the urban density models remains as the center in regional densitymodels The declining regional density pattern has a different explanation Inessence, rural residents farther away from a city pay higher transportation costs forthe shipment of agricultural products to the urban market and for gaining access toindustrial goods and urban services in the city, and are compensated by occupyingcheaper, and hence more, land See Wang and Guldmann (1997) for a recent model.Similarly, empirical studies of regional density patterns can be based on amonocentric or a polycentric structure Obviously, as the territory for a region ismuch larger than a city, it is less likely for physical environments (e.g., topography,weather, and land use suitability) to be uniform across a region than a city Therefore,population density patterns in a region tend to exhibit less regularity than in a city

An ideal study area for empirical studies of regional density functions would be anarea with uniform physical environments, like the “isolated state” in the von Thünenmodel (Wang, 2001a, p 233)

Analyzing the function change over time has important implications for bothurban and regional structures For urban areas, we can examine the trend of urban polarization vs suburbanization The former represents an increasing percentage

of population in the urban core relative to its suburbia, and the latter refers to areverse trend, with an increasing portion in the suburbia For regions, we canidentify the process of centralization vs decentralization Similarly, the former

100 Quantitative Methods and Applications in GIS

refers to the migration trend from peripheral rural to central urban areas, and the

latter is the reverse Both can be synthesized into a framework of core vs periphery

According to Gaile (1980), economic development in the core (city) impacts the

surrounding (suburban and rural) region through a complex set of dynamic spatial

processes (i.e., intraregional flows of capital, goods and services, information and

technology, and residents) If the processes result in an increase in activity (e.g.,

population) in the periphery, the impact is spread If the activity in the periphery

declines while the core expands, the effect is backwash Such concepts help us

understand core–hinterland interdependencies and various relationships between

them (Barkley et al., 1996) If the exponential function is a good fit for regional

density patterns, the changes can be illustrated as in Figure 6.1, where t + 1

represents a more recent time than t In a monocentric model, we can see the relative

importance of the city center; in a polycentric model, we can understand the

strengthening or weakening of various centers

FIGURE 6.1 Regional growth patterns by the density function approach.

r

t

t + 1

Backwash (centralization) (a) (b)

lnDr

r

t Spread (decentralization)

Function Fittings by Regressions and Application in Analyzing Density Patterns 101

In the reminder of this chapter, the discussion focuses on urban density patterns

However, similar techniques can be applied to studies of regional density patterns

6.2 FUNCTION FITTINGS FOR MONOCENTRIC MODELS

6.2.1 F OUR S IMPLE B IVARIATE F UNCTIONS

In addition to the exponential function (Equation 6.1) introduced earlier, three other

simple bivariate functions for the monocentric structure have often been used:

Equation 6.2 is a linear function, Equation 6.3 is a logarithmic function, and

Equation 6.4 is a power function Parameter b in all the above four functions is

expected to be negative, indicating declining densities with distances from the city

center

Equation 6.2 and 6.3 can be easily estimated by ordinary least squares (OLS)

linear regressions Equations 6.1 and 6.4 can be transformed to linear functions by

taking the logarithms on both sides, such as

lnD r = A + blnr (6.6)

Equation 6.5 is the log-transform of exponential Equation 6.1, and Equation 6.6

is the log-transform of power Equation 6.4 The intercept A in both Equations 6.5

and 6.6 is just the log-transform of constant a (i.e., A = lna) in Equations 6.1 and 6.4

The value of a can be easily recovered by taking the reverse of logarithm, i.e., a = e A

Equations 6.5 and 6.6 can also be estimated by linear OLS regressions In regressions

for Equations 6.3 and 6.6 containing the term lnr, samples should not include

observations where r = 0 (exactly the city center), to avoid taking logarithms of

zero Similarly, in Equations 6.5 and 6.6 containing the term lnDr, samples should

not include those where D r = 0 (with zero population)

Take the log-transform of exponential function in Equation 6.5 for an example

The two parameters, intercept A and gradient b, characterize the density pattern in

a city A lower value of A indicates declining densities around the central city; a

lower value of b (in terms of absolute value) represents a flatter density pattern

Many cities have experienced lower intercept A and flatter gradient b over time,

representing a common trend of urban sprawl and suburbanization The changing

pattern is similar to Figure 6.1a, which also depicts decentralization in the context

of regional growth patterns

102 Quantitative Methods and Applications in GIS

In addition to the four simple bivariate functions discussed above, three other

functions are also used widely in the literature One was proposed by Tanner (1961)

and Sherratt (1960) independently, commonly referred to as the Tanner–Sherratt

model The model is written as

(6.7)

where the density D r declines exponentially with distance squared, r2

Newling (1969) incorporated both Clark’s model and the Tanner–Sherratt model

and suggested the following model:

(6.8)

where the constant term b1 is most likely to be positive and b2 negative, and other

notations remain the same In Newling’s model, a positive b1 represents a density

crater around the CBD, where population density is comparatively low due to the

presence of commercial and other nonresidential land uses According to Newling’s

model, the highest population density does not occur at the city center, but rather

at a certain distance away from the city center

The third model is the cubic spline function used by some researchers (e.g.,

Anderson, 1985; Zheng, 1991) in order to capture the complexity of urban density

pattern The function is written as

(6.9)

where x is the distance from the city center, D x is the density there, x0 is the distance

of the first density peak from the city center, x i is the distance of the ith knot from

the city center (defined by either the second, third, etc., density peak or simply even

intervals across the whole region), and Z i * is a dummy variable (= 0, if x is inside

the knot; = 1, if x is outside of the knot).

The cubic spline function intends to capture more fluctuations of the density

pattern (e.g., local peaks in suburban areas), and thus cannot be strictly defined as

a monocentric model However, it is still limited to examining density variations

related to distance from the city center regardless of directions, and thus assumes a

concentric density pattern.

6.2.3 GIS AND R EGRESSION I MPLEMENTATIONS

The density function analysis only uses two variables: one is Euclidean distance r

from the city center, and the other is the corresponding population density D r

=

∑

Euclidean distances from the city center can be obtained using the techniquesexplained in Section 2.1 Identifying the city center requires knowledge of the studyarea and is often defined as a commonly recognized landmark site by the public Inthe absence of a commonly recognized city center, one may use the local governmentcenter2 or the location with the highest level of job concentration to define it, or

follow Alperovich (1982) to identify it as the point producing the highest R2 indensity function fittings Density is simply computed as population divided by areasize Area size is a default item in any ArcGIS polygon coverage and can be added

in a shapefile (see step 3 in Section 1.2) Once the two variables are obtained inGIS, the dataset can be exported to an external file for regression analysis.Linear OLS regressions are available in many software packages For example,one may use the widely available Microsoft Excel Make sure that the AnalysisToolPak is installed in Excel Open the distance and density data as an Excelworkbook, add two new columns to the workbook (e.g., lnr and lnDr), andcompute them as the logarithms of distance and density, respectively Select Toolsfrom the main menu bar > Data Analysis > Regression to activate the regressiondialog window shown in Figure 6.2 By defining the appropriate data ranges for

X and Y variables, Equations 6.2, 6.3, 6.5, and 6.6 can be all fitted by OLS linear

regressions in Excel Note that Equations 6.5 and 6.6 are the log-transformations ofexponential Equation 6.1 and power Equation 6.4, respectively Based on the results,

Equation 6.1 or 6.4 can be easily recovered by computing the coefficient a = e A and

the coefficient b unchanged.

Alternatively, one may use the Chart Wizard in Excel to obtain the regressionresults for all four bivariate functions directly First, use the Chart Wizard to draw

a graph depicting how density varies with distance Then click the graph and chooseChart from the main menu > Add Trendline to activate the dialog window shown

in Figure 6.3 Under the menu Type, all four functions (linear, logarithmic, nential, and power) are available for selection Under the menu Options, choose

expo-“Display equation on chart” and expo-“Display R-squared value on chart” to have sion results shown on the graph The Add Trendline tool outputs the regression

regres-FIGURE 6.2 Excel dialog window for regression.

results for the four original bivariate functions without log-transformations, but doesnot report as many statistics as the Regression tool The regression results reported

here are based on linear OLS regressions by using the log-transform Equations 6.5

and 6.6 (though the computation is done internally) This is different from nonlinearregressions, which will be discussed in the next section

Both the Tanner–Sherratt model (Equation 6.7) and Newling’s model (Equation6.8) can be estimated by linear OLS regression on their log-transformed forms See

Table 6.1 In the Tanner–Sherratt model, the X variable is distance squared (r2), and

in Newling’s model, there are two X variables (r and r2) Newling’s model has one

more explanatory variable (r2) than Clark’s model (exponential function), and thus

always generates a higher R2 regardless of the significance of the term r2 In thissense, these two models are not comparable in terms of fitting power Table 6.1summarizes the models

FIGURE 6.3 Excel dialog window for adding trend lines.

D r=ae br2

D r=ae b r b r1 + 2

Fitting the cubic spline function (Equation 6.9) is similar to that of other centric functions, with some extra work in preparing the data First, sort the data by

mono-the variable distance in an ascending order Second, define mono-the constant x0 and

calculate the terms (x – x0), (x – x0)2, and (x – x0)3 Third, define the constants x i (i.e., x1, x2, …) and compute the terms Take one term, , as

an example: (1) set the values = 0 for those records with x ≤ x1, and (2) compute thevalues = for those records with x > x1 Finally, run a multivariate regression,

where the Y variable is density D x and the X variables are (x – x0), (x – x0)2, (x – x0)3,

, , and so on The cubic spline function contains multiple X variables, and thus its regression R2 tends to be higher than other models

6.3 NONLINEAR AND WEIGHTED REGRESSIONS IN

FUNCTION FITTINGS

In function fittings for the monocentric structure, two statistical issues deserve morediscussion One is the choice between nonlinear regressions directly on the expo-nential and power functions vs linear regressions on their log-transformations (asdiscussed in Section 6.2) Generally they yield different results since the two have

different dependent variables (D r in nonlinear regressions vs lnD r in linear sions) and imply different assumptions of error terms (Greene and Barnbrock, 1978)

regres-We use the exponential function (Equation 6.1) and its log-transformation(Equation 6.5) to explain the differences The linear regression on Equation 6.5

assumes multiplicative errors and weights equal percentage errors equally, such as

The nonlinear regression on the original function (Equation 6.1) assumes that

additive errors and weights all equal absolute errors equally, such as

D r = ae br + ε (6.11)

The ordinary least squares (OLS) linear regression seeks the optimal values of

a and b so that residual sum of squares (RSS) is minimized See Appendix 6B on

how the parameters in a bivariate linear function are estimated by the OLS regression.Nonlinear least squares regression has the same objective of minimizing the RSS.For the model in Equation 6.11, it is to minimize

where i indexes individual observations There are several ways to estimate the

parameters in nonlinear regression (Griffith and Amrhein, 1997, p 265), and all

methods use iterations to gradually improve guesses For example, the modified Gauss–Newton method uses linear approximations to estimate how RSS changes with

(x−x i)3Z i*

(x−x1) Z*

3 1(x−x1)

br i

i

small shifts from the present set of parameter estimates Good initial estimates (i.e.,those close to the correct parameter values) are critical in finding a successful non-linear fit The initialization of parameters is often guided by experience and knowledge

of similar studies

Which is a better method for estimating density functions, linear or nonlinearregression? The answer depends on the emphasis and objective of a study The linear

regression is based on the log-transformation By weighting equal percentage errors

equally, the errors generated by high-density observations are scaled down (in terms

of percentage) However, the differences between the estimated and observed values

in those high-density areas tend to be much greater than those in low-density areas(in terms of absolute value) As a result, the total estimated population in the citycan be off by a large margin On the contrary, the nonlinear regression is to minimizethe residual sum of squares directly based on densities instead of their logarithms

By weighting all equal absolute errors equally, the regression limits the errors

(in terms of absolute value) contributed by high-density samples As a result, thetotal estimated population in the city is often closer to the actual value than the onebased on linear regression, but the estimated densities in low-density areas may beoff by high percentages

Another issue in estimating urban density functions concerns randomness of sample (Frankena, 1978) A common problem for census data (not only in the U.S.)

is that high-density observations are many and are clustered in a small area near thecity center, whereas low-density ones are fewer and spread in remote areas In otherwords, high-density samples may be overrepresented, as they are concentrated within

a short distance from the city center, and low-density samples may be sented, as they spread across a wide distance range from the city center A plot ofdensity vs distance will show many observations in short distances and fewer in

underrepre-long distances This is referred to as nonrandomness of sample and causes biased

(usually upward) estimators A weighted regression can be used to mitigate theproblem Frankena (1978) suggests weighting observations in proportion to theirareas In the regression, the objective is to minimize the weighted residual sum of

squares (RSS) Note that R2 in a weighted regression can no longer be interpreted

as a measure of goodness of fit and is called pseudo-R2 See Wang and Zhou (1999)for an example Some researchers favor samples with uniform area sizes In casestudy 6 (Section 6.5.3 in particular), we will also analyze population density func-tions based on survey townships of approximately same area sizes

Estimating the nonlinear regression or weighted regression requires the use ofadvanced statistical software For example, in SAS, if the DATA step uses DEN torepresent density, DIST to represent distance, and AREA to represent area size, thefollowing SAS statements implement the nonlinear regression for the exponentialEquation 6.1:

proc MODEL; /* procedure for nonlinear regression */PARMS a 1000 b -0.1; /*initialize parameters */DEN = a * exp(b * DIST); /* code the fitting function */fit DEN; /* define the dependent variable */

The statement PARMS assigns initial values for parameters a and b in the iteration

process If the model does not converge, experiment with different initial valuesuntil a solution is reached

The weighted regression is run by adding the following statement to theabove program:

weight AREA; /* define the weight variable */

SAS also has a procedure REG to run OLS linear regressions See the sampleSAS program monocent.sas included in the CD for details

6.4 FUNCTION FITTINGS FOR POLYCENTRIC MODELS

Monocentric density functions simply assume that densities are uniform at the samedistance from the city center regardless of directions Urban density patterns in somecities may be better captured by a polycentric structure In a polycentric city,residents and businesses value access to multiple centers, and therefore populationdensities are functions of distances to these centers (Small and Song, 1994, p 294).Centers other than the primary or major center at the CBD are called subcenters

6.4.1 P OLYCENTRIC A SSUMPTIONS AND C ORRESPONDING F UNCTIONS

A polycentric density function can be established under several alternative assumptions:

1 If the influences from different centers are perfectly substitutable so thatonly the nearest center matters, the city is composed of multiple mono-centric subregions Each subregion is the proximal area for a center(see Section 4.1), within which various monocentric density functions can

be estimated Taking the exponential function as an example, the model

for the subregion around the ith center (CBD or subcenter) is

(6.12)

where D is the density of an area, r i is the distance between the area and

its nearest center, i, and a i and b i (i = 1, 2, …) are parameters to be estimated.

2 If the influences are complementary so that some access to all centers isnecessary, then the polycentric density is the product of those monocentricfunctions (McDonald and Prather, 1994) For example, the log-transformedpolycentric exponential function is written as

(6.13)

where D is the density of an area, n is the number of centers, r i is the

distance between the area and center i, and a and b i (i = 1, 2, …) are

3 Most researchers (Griffith, 1981; Small and Song, 1994) believe that therelationship among the influences of various centers is between assump-tions 1 and 2, and the polycentric density is the sum of center-specificfunctions For example, a polycentric model based on the exponentialfunction is expressed as

(6.14)

The above three assumptions are based on Heikkila et al (1989)

4 According to the central place theory, the major center at the CBD andthe subcenters play different roles All residents in a city need access tothe major center for higher-order services; for other lower-order services,residents only need to use the nearest subcenter (Wang, 2000) In otherwords, everyone values access to the major center and access to the nearestcenter (either the CBD or a subcenter) Using the exponential function as

an example, the corresponding model is

(6.15)

where r1 is the distance from the major center, r2 is the distance from the

nearest center, and a, b1, and b2 are parameters to be estimated

Figure 6.4 illustrates the different assumptions for a polycentric city Residentsneed access to all centers under assumption 2 or 3, but effects are multiplicative in 2and additive in 3 Table 6.2 summarizes the above discussion

FIGURE 6.4 Illustrations of polycentric assumptions.

D a e i b r i

Linkage

1 Only access to the nearest

center is needed

Distances r i from the nearest center i

(1 variable)

Areas in a subregion i Linear regression a

2 Access to all centers is

necessary (multiplicative effects)

Distances from each center

(n variables r i)

All areas Linear regression

3 Access to all centers is

necessary (additive effects)

Distances from each center

(n variables r i)

All areas Nonlinear regression

4 Access to CBD and the

nearest center is needed

Distances from the major and nearest center (2 variables)

All areas Linear regression b

a This assumption may be also estimated by nonlinear regression on

b This assumption may be also estimated by nonlinear regression on

6.4.2 GIS AND R EGRESSION I MPLEMENTATIONS

Analysis of polycentric models requires the identification of multiple centers first.Ideally, these centers should be based on the distribution of employment (e.g.,Gordon et al., 1986; Giuliano and Small, 1991; Forstall and Greene, 1998) Inaddition to traditional choropleth maps, Wang (2000) used surface modeling tech-niques to generate isolines (contours) of employment density3 and identified employ-ment centers based on both the contour value (measuring the threshold employmentdensity) and the size of area enclosed by the contour line (measuring the base value

of total employment) With the absence of employment distribution data, one mayuse surface modeling of population density to guide the selection of centers.4 SeeChapter 3 for various surface modeling techniques Surface modeling is descriptive

in nature Only rigorous statistical analysis of density functions can answer whetherthe potential centers identified from surface modeling indeed exert influence onsurrounding areas and how the influences interact with each other

Once the centers are identified, GIS prepares the data of distances and densitiesfor analysis of polycentric models For assumption 1, only the distances from thenearest centers (including the major center) need to be computed by using the Neartool in ArcGIS For assumption 2 or 3, the distance between each area and everycenter needs to be obtained by the Point Distance tool in ArcGIS For assumption

4, two distances are required: the distance between each area and the major centerand the distance between each area and its nearest center The two distances areobtained by using the Near tool in ArcGIS twice See Section 6.5.2 for details.Based on assumption 1, the polycentric model is degraded to monocentricfunctions (Equation 6.12) within each center’s proximal area, which can be estimated

by the techniques explained in Sections 6.2 and 6.3 Equation 6.13 for assumption

2 and Equation 6.15 for assumption 4 can also be estimated by simple multivariatelinear regressions However, Equation 6.14, based on assumption 3, needs to beestimated by a nonlinear regression, as shown below

Assuming a model of two centers with DIST1 and DIST2 representing thedistances from the two centers, respectively, a sample SAS program for estimatingEquation 6.14 is similar to the program for estimating Equation 6.4, such as

proc model;

parms a1 1000 b1 -0.1 a2 1000 b2 -0.1;

DEN = a1*exp(b1*DIST1)+ a2*exp(b2*DIST2);

fit DEN;

6.5 CASE STUDY 6: ANALYZING URBAN DENSITY PATTERNS

IN THE CHICAGO REGION

Chicago has been an important study site for urban studies The classic urbanconcentric model by Burgess (1925) was based on Chicago and led to a series ofstudies on urban structure, forming the so-called Chicago School This case study