Using Geographic Information Systems to Reconceptualize Spatial Relationships and Ecological Context

Abstract

In this article, the author demonstrates how geographic information system (GIS) software can be used to reconceptualize spatial relationships and ecological context and address the modifiable areal unit problem. In order to do this, the author uses GIS to (1) test an important category of spatial hypotheses (spatial proximity hypotheses), (2) overcome methodological problems that arise when data sets are not spatially comparable, and (3) measure ecological context. The author introduces a set of GIS variable construction techniques that are designed to accomplish these tasks, illustrates these techniques empirically by using them to test spatial proximity hypotheses drawn from the literature on environmental inequality, and demonstrates that results obtained using these techniques are methodologically superior to and substantively different from results obtained using traditional techniques. Finally, the author demonstrates that these techniques are the product of an alternative conceptualization of physical space that allows sociologists to develop new ways to think about and measure spatial relationships, ecological context, and place-based social inequality and that gives them the ability to reconceptualize spatially based methodological problems that have confronted them for years.

INTRODUCTION

In recent years, sociology has taken a significant spatial turn. Whether studying geographic access to abortion providers, urban poverty, corporate board interlocks, social capital, collective efficacy, or environmental inequality, sociologists are asking increasingly sophisticated substantive questions about space and ecological context (Anderton et al. 1994a; Kasarda 1989; Kono et al. 1998; Lichter, McLaughlin, and Ribar 1998; Mouw 2000; Sampson, Morenoff, and Earls 1999; Wilson 1987). This renewed interest in space and ecological context emerged simultaneously with the development of geographic information systems (GIS): mapping and database management software explicitly designed to analyze spatial data and test spatial hypotheses. However, sociologists have been slow to integrate GIS into their research. This is unfortunate, not only because GIS can improve our ability to test spatial hypotheses accurately, but just as importantly because GIS allows researchers to think about the spatial relationships that exist between social groups, social goods, objects, and events in a more sophisticated manner than is otherwise possible. This, in turn, allows researchers to (a) develop new ways to think about and measure ecological context and place-based social inequality and (b) devise new solutions for methodological problems that arise when data are spatially referenced—that is, when data contain observations tied to specific geographic coordinates.

In order to demonstrate the important role GIS can play in advancing these areas of sociological thinking and research, I will show how GIS can be used to (1) test an important category of spatial hypotheses (spatial proximity hypotheses), (2) overcome an important set of methodological problems (those that arise when the data sets researchers use are not spatially comparable), and (3) measure ecological context. In addition, I will demonstrate that the techniques researchers generally use to do these things produce inaccurate findings and that more accurate findings can be obtained using the GIS techniques introduced here.

In demonstrating the methodological advantages of these GIS techniques, I hope to convince researchers not only of the superiority of these techniques, but just as importantly, I hope to demonstrate that using GIS will change the way researchers think about spatial relationships, ecological context, and place-based social inequality, and that this, in turn, will have a substantive impact on the results researchers obtain and the conclusions researchers draw.

Thus, in the following section, I provide a general discussion of how GIS can help researchers to reconceptualize spatial relationships, ecological context, and place-based social inequality. This is followed by a more technical discussion of the methodological advantages of using GIS to construct ecological indicators, merge spatially incomparable data sets, and test spatial proximity hypotheses.

Because my goal is to demonstrate the advantages of using GIS to as broad an array of sociologists as possible, I have chosen to present more general and elementary GIS techniques than I otherwise would. On the one hand, this allows me to present these techniques in the most transparent and straightforward way possible, making them more accessible to a general sociological audience. On the other hand, in presenting these techniques without complicating twists that make sense for some research problems but not others, I will avoid giving the impression that these techniques can only be used in a very limited number of situations.

Clearly, there are many situations in which, and many research problems for which, using GIS makes little sense. Nevertheless, giving the impression that these techniques can only be used in a limited number of situations would be a serious mistake since these techniques can be used to solve a variety of research problems.

RECONCEPTUALIZING SPATIAL RELATIONSHIPS

GIS can help researchers reconceptualize spatial relationships and ecological context in several ways. For example, by making it relatively easy to map out the spatial distribution of social groups, social goods, and events in specific study areas, it becomes possible to examine visually where residentially segregated social groups live in relation to various social goods and ills. This allows researchers to think more clearly about questions such as Under what conditions are residentially segregated minority groups most likely to live near socially undesirable goods such as factory pollution? This is not the type of question researchers generally pose because the global measures of segregation that researchers generally use, such as the dissimilarity, isolation, and concentration indices, tell us the degree to which segregation exists in specific metropolitan areas, but not where segregated minority groups live within these metropolitan areas. However, knowing exactly where segregated minority groups live is important because the spatial distribution of socially desirable and undesirable goods varies across metropolitan areas and minorities are no longer confined solely to the inner city.²

For example, maps and analyses not presented here demonstrate that residential segregation in the urban core places minority groups near polluting manufacturing facilities in some metropolitan areas but not others. In addition, in some metropolitan areas, relatively low levels of residential segregation and concentration in the urban core actually increase minority group representation in polluted neighborhoods (maps and analyses available upon request).

GIS also allows researchers to map out changes in the spatial distributions of social groups, social goods, and events over time, giving researchers the ability to visually test hypotheses that make predictions about these changing spatial distributions. For example, I have generated maps (not presented here) that demonstrate that between 1920 and 1990, black neighborhoods in the Detroit metropolitan area expanded at their edges rather than into or along the region’s highly polluted industrial corridors. This contradicts the environmental inequality hypothesis that blacks move into environmentally hazardous neighborhoods in disproportionate numbers due to residential segregation and black/white income inequality (maps available upon request).

But perhaps the most important way in which GIS can help researchers to reconceptualize spatial relationships and ecological context is in allowing researchers to move back and forth between alternate representations of physical space. Quantitative sociologists typically think about physical space, and objects and events in physical space, as a set of discrete and bounded spatial units such as street addresses (points) and census tracts (polygons). This conception of physical space makes sense for many research questions, and its widespread use is understandable given the type of data and data manipulation tools generally available to sociologists. However, it does a poor job of representing many of the factors and processes that interest sociologists because people do not live in a world that is defined solely in discrete spatial terms.

Instead, people live in a world in which physical space is simultaneously discrete and continuous: a world in which space is divided into discrete and bounded spatial units for many purposes, but in which distance between points also matters because (a) the social impact of goods, objects, and events often declines continuously as distance from these goods, objects, and events increases, (b) the spheres of influence exerted by specific goods, objects, and events often fail to coincide with the boundaries of discrete and bounded units of analysis such as census tracts, and (c) ecological context tends to vary within discrete and bounded units of analysis.

Thus, in order to accurately measure ecological context, researchers must be able to model physical space as a continuous, unbounded surface in which variable values can vary continuously rather than being tied to specific analysis units. However, because people live in a world in which physical space is simultaneously discrete and continuous, and in which data are often collected for discrete units of analysis, researchers must also be able to move back and forth between continuous and discrete representations of the physical world. GIS allows researchers to do this.

Figures 1 and 2, which examine the spatial distribution of a subset of manufacturing facilities and manufacturing facility jobs in the Detroit metropolitan area, compare a continuous model of physical space to the discrete and bounded model of physical space that quantitative sociologists typically employ. The Detroit metropolitan area is defined here as the city of Detroit and the cities and townships immediately surrounding Detroit, and manufacturing facility location and employment data are drawn from the Environmental Protection Agency’s (EPA) 1990 Toxics Release Inventory (TRI) and the 1990 Michigan Manufacturers Directory (Pick Publications 1990). These data sets are described in more detail in a subsequent section of the article; however, it is important to note that the TRI does not provide data on all manufacturing facilities in the Detroit metropolitan area. Thus, figures 1 and 2 present information on a small, but important, subset of Detroit metropolitan area manufacturing facilities.

Fig. 1.

Discrete representations of physical space, the Detroit metropolitan area, 1990

Fig. 2.

Continuous representations of physical space, the Detroit metropolitan area, 1990

In figure 1, map (a) is a discrete representation of the Detroit metropolitan area in which each polygon represents a census tract and each dot represents a single manufacturing facility; map (b) is a discrete representation of the Detroit metropolitan area in which census tracts are categorized according to the number of TRI facility manufacturing jobs located in each tract. Researchers interested in metropolitan area residents’ access to manufacturing jobs could draw circles with a fixed radius around the center of each census tract and for each tract, count the number of manufacturing jobs that fall inside that tract’s circle or the number of manufacturing jobs that are located in tracts that are partially or completely encompassed by that tract’s circle (Mouw 2000). Researchers could also calculate the distance between each pair of census tracts in the metropolitan area and calculate, for each tract, the weighted sum of all the manufacturing jobs in the metropolitan area, using weights that decline from one to zero as the distance between tracts increases. Finally, researchers could determine the average distance from each tract to all the manufacturing jobs in the metropolitan area, using distance between tracts and the number of jobs in each tract to determine average distance (Boardman and Field 2002).

Maps (c) and (d) in figure 2 are continuous representations of the distribution of TRI facility manufacturing jobs in the Detroit metropolitan area. Map (c) was created by laying a 25 meter resolution grid—a rectangular grid with 25 meter square grid cells—on top of map (a) in figure 1 and calculating the number of TRI facility manufacturing jobs located within a one-kilometer radius of each grid cell. Map (d) was created by laying a 25 meter resolution grid on top of map (a) in figure 1 and calculating the number of manufacturing jobs located within a three-kilometer radius of each grid cell. The result for map (c) is a continuous surface with grid cell values ranging from 0 to 14,200. The result for map (d) is a continuous surface with grid cell values ranging from 0 to 26,036.

Maps (c) and (d) can be interpreted as describing the overlapping employment opportunity areas of each TRI facility in the Detroit metropolitan area, weighted by the number of manufacturing jobs in each TRI facility.³ A more realistic representation of these overlapping employment opportunity areas would use a larger radius to delineate the geographic extent of these areas as well as a distance decay function to account for the fact that as distance to a job increases, an individual’s ability to commute to that job decreases. Nevertheless, these maps are sufficient for illustrating how discrete and continuous representations of physical space shape the way we view spatial relationships and ecological context.

One of the first things we notice when we examine maps (c) and (d) is that continuous representations of physical space allow us to delineate the actual areas that are potentially impacted by the presence or absence of manufacturing jobs. Continuous representations allow us to do this because they treat map features, such as the TRI facilities in map (a), as objects with specific and measurable spheres of influence rather than as discrete points to be counted. Treating them as such allows us to model their joint sphere of influence in such a way as to accurately represent their spatial relationships to each other and precisely measure ecological context.

Of course, continuous representations of physical space can be used to model the spheres of influence of many ecological characteristics, including criminal activity, visible signs of social disorder, environmental amenities and disamenities, abortion clinic access, and built environment characteristics such as industrial activity and highways. Continuous representations can also be used to model individuals’ cognitive maps of their neighborhoods, including their perceptions of the boundaries of their neighborhoods and the positive and negative attributes of their neighborhoods and surrounding communities.⁴

Thus, continuous representations of physical space can be used to compare the spheres of influence of multiple social goods, objects, and events, both to each other and to the distribution of various social groups. Continuous representations of physical space can also be used to compare the spheres of influence of multiple attributes of the same social good. For example, as illustrated in a subsequent section of this article, continuous representations of physical space can be used to model factories’ positive (jobs) and negative (pollution) spheres of influence at the same time, allowing us to answer research questions that we might not otherwise be able to answer satisfactorily, such as, Is factory employment or factory pollution a better predictor of a neighborhood’s demographic characteristics?

As I will demonstrate below, GIS provides us with the tools to model these spheres of influence much more accurately than is possible using traditional methodological techniques, giving us the ability to construct more accurate ecological indicators than is otherwise possible. However, the point I want to make here is that because continuous representations of physical space allow us to think about social goods, objects, and events in terms of their nonbounded spheres of influence, such representations allow us to consider spatial relationships in a new light, giving us new ways to think about ecological context and place-based social inequality.

In addition, because GIS allows us to move back and forth between discrete and continuous representations of physical space, while simultaneously helping us to reconsider spatial relationships and ecological context, GIS also allows us to rethink the methods we use to construct ecological indicators, merge spatially incomparable data sets, and test spatial proximity hypotheses. Thus, the remainder of the article focuses on the methodological advantages of using GIS to do these things.

SPATIAL PROXIMITY HYPOTHESES AND SPATIALLY INCOMPARABLE DATA SETS

Spatial proximity hypotheses can be defined as hypotheses that include geographic distance as a predictor or outcome of some social process. Accurately measuring proximity can be difficult to do because researchers are either unable to obtain coordinate-specific location data or are forced to aggregate coordinate-specific location data to make that data comparable with aggregated data sets collected by others.

Spatially incomparable data sets can be defined as data sets that contain spatially referenced observations gathered from nonidentical, but geographically overlapping, units of analysis: units whose geographic boundaries change over time, such as census tracts, or units that overlap geographically but are based on different geographic coordinates, such as street addresses (points) and census tracts (polygons/areal units). Methodological problems arise when researchers alter spatially incomparable data sets to make them comparable. For example, when researchers merge dual-decade census tract data (census tract data drawn from two different decades) without using GIS-based application tools, they are generally forced to either (a) drop from their analyses all census tracts whose boundaries have changed or (b) merge census tract observations in each of the original data sets until the two data sets are spatially comparable (Bergesen and Herman 1998; Marchand 1986). In either case, the end result is the loss of a significant number of observations, and in the latter case the result is a significant increase in the size of many of the analysis units.

Methodological problems also arise when researchers aggregate address-specific data to make that data comparable with census tract data or use address-specific data to create tract-level dummy variables indicators (Anderton et al. 1994a, 1994b; Bergesen and Herman 1998; Bowen et al. 1995). In each of these cases, researchers lose important spatial information, and as a result they are generally forced to assume that their address-specific observations, or at least the impacts of these observations, are distributed evenly within their polygon-based units of analysis. They are also forced to assume that their address-specific observations do not affect adjacent areal units of analysis or that the effect of address-specific observations in one areal unit of analysis on outcomes in other areal units of analysis is equal to the sum of these observations’ independent effects divided by, or in some other way adjusted for, the distance between the host unit and the other analysis units.⁵

For example, spatial diffusion and spatial exposure correction models, such as those found in Myers (1997), Soule and Zylan (1997), Strang and Tuma (1993), and Tolnay, Deane, and Beck (1996), model the effect of events in one analysis unit on the presence of events in other analysis units, adjusting the magnitude of this effect to account for the distance between analysis units.

However, in making these adjustments, these models ignore the spatial distribution of events within host units and, therefore, the actual distance between specific events and specific nonhost analysis units. This is clearly appropriate in many cases. However, as figure 3 demonstrates, it is not appropriate in all cases.

Fig. 3.

The distribution of TRI facilities within census tracts, the Detroit metropolitan area, 1990

Figure 3 provides a close-up view of a subset of Detroit metropolitan area census tracts in 1990. Each polygon in the figure represents a census tract and each dot a TRI facility. In map (a), the four solid black dots are all located inside the boundaries of the same tract (this tract is approximately 4,800 meters long and the greatest distance between any two of the four highlighted facilities is approximately 2,200 meters; however, it is not the only large tract in the metropolitan area). Map (b) displays the TRI facilities’ overlapping one-kilometer-radius employment opportunity areas, and map (c) displays the TRI facilities’ overlapping three-kilometer-radius employment opportunity areas.

These maps show that facilities, events, and objects that are located in the same tract do not necessarily impact the same nonhost tracts and that even when they do impact the same nonhost tracts, they do not necessarily impact the same areas within these tracts. These maps also show that because TRI facilities’ individual employment opportunity areas partially overlap, their joint employment opportunity area can take on multiple values within a single tract (this is especially the case when distance decay functions are used to calculate individual and joint employment opportunity areas).⁶ Thus, ignoring the spatial distribution of events and objects within host units is problematic in cases where the distance between specific events and objects and specific analysis units, or between specific events and objects and specific points in space, is theoretically important, as is the case in many spatial proximity hypotheses.

Despite the methodological difficulties inherent in merging spatially incomparable data sets and testing spatial proximity hypotheses, a wide variety of sociologists have done one or both of these things. For example, Lichter et al. (1998) hypothesize that in the 1980s, decreased geographic access to abortion providers led to an increase in the proportion of households headed by women; Kono et al. (1998) hypothesize that geographic proximity plays an important role in shaping corporate board interlocks; spatial mismatch theorists hypothesize that the spatial disjuncture that exists between inner-city black neighborhoods and manufacturing facility employment opportunities has played an important role in the development of a black, urban underclass (Kasarda 1989; Wilson 1987); and environmental inequality researchers hypothesize that poor people and minorities live closer to environmental hazards than do wealthier individuals and whites (Anderton et al. 1994a, 1994b; Bryant and Mohai 1992).

In addition, Bergesen and Herman (1998), in their study of the 1992 Los Angeles race riot, merge street-intersection-specific riot fatality data with merged 1980/1990 census tract data; Mouw (2000), in his study of spatial mismatch in Detroit and Chicago, merges 1980 and 1990 census tract data for both metropolitan areas; South and Crowder (1998), in their study of black and white residential mobility, link individual-level Panel Study of Income Dynamics (PSID) data to 1980 census data using PSID respondent street addresses; McCarthy et al. (1988), in their study of social movement organization founding rates, merge address-specific car crash fatality data with county-level census data; and Anderton et al. (1994a), in their national study of environmental inequality, merge address-specific hazardous waste site data with 1980 census tract data.

Given the broad and varied use of spatial proximity hypotheses and spatially incomparable data sets within the discipline, it is important that we devise methodological techniques that overcome or minimize the problems that arise from both these activities. Thus, in the sections that follow, I set forth two GIS-based variable construction techniques that minimize these problems and illustrate these techniques empirically by using them to test four spatial proximity hypotheses drawn from the literature on environmental inequality. I compare results obtained using the variable construction techniques described in this article with results obtained using more traditional methodological approaches, and demonstrate that results obtained using these techniques are methodologically superior to and substantively different from results obtained using traditional techniques.

The remainder of the article is organized as follows. First, I demonstrate that the techniques researchers generally use to merge dual-decade census data and point and polygon data are methodologically problematic. I then describe the two GIS variable construction techniques noted above and use them to test the four spatial proximity hypotheses noted above.

Before proceeding, I should note that the techniques described below are not the only GIS techniques sociologists can use to overcome or minimize the methodological problems that arise when testing spatial proximity hypotheses, merging spatially incomparable data sets, and constructing ecological indicators. I should also note that although the following discussion is fairly technical, the GIS techniques described below are not merely technical fixes or neat methodological tools. They also represent an alternative approach to conceptualizing spatial relationships, ecological context, and place-based social inequality that allows researchers to develop new solutions to old methodological problems.

In other words, the solutions presented below are possible not only because GIS provides researchers with a new set of technical tools, but also because GIS provides researchers with a new way of thinking about physical space that allows them to reconceptualize many spatially based methodological problems. Thus, the following discussion not only provides researchers with new solutions to an important set of methodological problems, it also provides researchers with examples of how GIS can be used to solve similar spatially based methodological problems. It thereby demonstrates the potentially important role GIS can play in advancing sociological research.

THE MODIFIABLE AREAL UNIT PROBLEM

The methodological problems described in the previous section are specific instances of a more general methodological problem associated with spatially aggregated data sets, the modifiable areal unit problem (MAUP), which arises when the boundaries used to define areal-unit observations are modifiable and arbitrary, at least in relation to the underlying population distribution (Fotheringham and Wong 1991; Martin 1996; Openshaw and Taylor 1981).⁷

The MAUP consists of two related problems, a scale problem and a zoning problem. The scale problem refers to the fact that as the size of areal units of analysis increases, variable variation tends to decrease and covariation between different variable pairs tends to vary, sometimes quite drastically and not in a predictable fashion (Fotheringham and Wong 1991; Wong 1996).⁸

Equations (1), (2), and (3), which are used to calculate Pearson’s correlation coefficient (r_xy), b̂ in a bivariate ordinary least squares (OLS) regression, and β̂₂ in a trivariate OLS regression, demonstrate why decreasing variation and unstable covariation affect correlation coefficient and regression parameter estimates. In these equations S_x and S_y are the standard deviations of x and y respectively, var(x_i) is the variance of x_i, cov(x₁, x₂) is the covariance of the two independent variables, and cov(x_i, y) is the covariance of x_i and the dependent variable.

$$r_{xy}=cov(xy)/S_x{S}_y,$$ (1)

$$\widehat{b}=r_{xy}(S_y/S_x),$$ (2)

$${\widehat{\beta }}_2=[var(x_1)cov(x_{2}y)-cov(x_{1}y)cov(x_1{x}_2)]/[var(x_1)var(x_2)-cov{(x_1{x}_2)}^2].$$ (3)

Looking first at equation (1), we see that as the variation in x and y decreases, the denominator in equation (1) also decreases. If cov(xy) remains stable, increases, or decreases at a slower rate than the denominator decreases, r_xy will increase, which is, in fact, what generally happens (Arbia 1989; Openshaw and Taylor 1979). Turning our attention to equation (2), we see that the bivariate slope estimate, b̂, is derived by multiplying the correlation coefficient, r_xy, by the ratio of the standard deviation of y to the standard deviation of x. Thus, variation in bivariate slope estimates due to data aggregation will differ from variation in correlation coefficient estimates due to data aggregation if the variances of x and y change at different rates as the data become increasingly aggregated (data aggregation refers here to the merging of census observations). For example, if the variance of x decreases at a faster rate than the variance of y as the data are increasingly aggregated, then b̂ will increase at a faster rate than r_xy (assuming, of course, that r_xy increases as the data are aggregated).

Finally, turning our attention to equation (3), we see that it quickly becomes very difficult to predict how data aggregation will affect regression slope estimates. For example, we know β̂₂ will decrease if, holding the other terms in the equation constant, the covariance of x₂ and y decreases at a faster rate than the covariance of x₁ and y as the data are increasingly aggregated. Similarly, we know β̂₂ will increase if, holding the other terms in the equation constant, the variance of x₂ decreases as the data are increasingly aggregated (this does not hold true if the denominator switches from positive to negative as x₂ decreases). However, because (a) variances and covariances do not remain constant as data are increasingly aggregated, (b) the variances of different variables do not decrease at the same rate as data are increasingly aggregated, and (c) it is impossible to predict how covariances will vary when data are aggregated (see n. 8), it is virtually impossible to predict how data aggregation will affect regression slope estimates (Fotheringham and Wong 1991).

Given the great difficulty inherent in trying to predict how data aggregation will affect bivariate and multivariate parameter estimates, many researchers have turned to data simulations to gain a better understanding of the problem. For example, Openshaw (1978), merging county-level data from the 1970 U.S. census to create ever-larger units of analysis, shows that in a bivariate regression, the slope coefficient tends to increase as the data become increasingly aggregated. Similarly, Fotheringham and Wong (1991) examine the effect that analysis unit size has on multivariate estimates by aggregating 1980 census block group data to create increasingly large units of analysis. Randomly aggregating contiguous block groups to create 120 different zoning systems at six levels of aggregation, and running OLS and logit regression models with four independent variables each, they found systematic variation in most, but not all, of their slope coefficient estimates as the data became increasingly aggregated.

However, the direction of this variation was not constant across independent variables. For example, in their logit models, the coefficients for two of their independent variables tended to increase, and the coefficients for one of their independent variables tended to decrease, as the data became increasingly aggregated; and in their OLS models, the coefficients for two of their independent variables tended to decrease, and the coefficients for one of their independent variables tended to increase, as the data became increasingly aggregated.

Finally, Fotheringham and Wong (1991) also found that R² values and the standard errors of their parameter estimates tended to increase as analysis units became larger and fewer in number. Thus, merging census tract observations to make dual-decade census tract data sets comparable is a highly problematic endeavor, made more problematic by the fact that it is exceedingly difficult, if not impossible, to predict how data aggregation will affect regression results.⁹

The zoning problem

The zoning problem refers to the fact that if we hold the number of polygon-based analysis units in a study area constant, but change the boundaries used to define the analysis units, we can dramatically affect correlation coefficient and regression parameter estimates (Arbia 1989; Flowerdew, Geddes, and Green 2001; Fotheringham and Wong 1991; Openshaw and Taylor 1979). This has implications for the merging of point and polygon data—which is typically done by summing together point-specific data values in each polygon unit or creating polygon-level dummy variables to record the presence or absence of point-level observations in each polygon unit—because even if the boundaries used to define the polygons were not designed arbitrarily, they are very likely to be arbitrary in relation to the spatial distribution of the point-level data.

For example, although census tracts are “designed to be relatively homogeneous units with respect to population characteristics, economic status, and living conditions” (U.S. Census Bureau 2004), their boundaries are relatively arbitrary with respect to the spatial distribution of point-specific observations such as polluting manufacturing facilities, riot fatalities, and violent crimes.

Figure 4 illustrates the arbitrary nature of census tract boundaries in relation to the distribution of Detroit metropolitan area manufacturing facilities in 1990. As in the previous figures, the Detroit metropolitan area is defined as the city of Detroit and the cities and townships immediately surrounding Detroit (this definition will be used throughout the remainder of the article). However, the manufacturing facilities shown in figure 4 are drawn from the region’s four most highly polluting industrial sectors—transportation equipment, chemicals, primary metals, and fabricated metal products—rather than from the TRI. These facilities were selected because they represent a larger sample than do TRI facilities and because a similar data set is used later in the article.

Fig. 4.

Factory location and census tract boundaries, the Detroit metropolitan area, 1990

As is true in many urban areas, Detroit metropolitan area manufacturing facilities are generally located along major transportation routes that often serve as census tract boundaries. The result, illustrated in figure 4, is not only that the size and shape of Detroit’s industrial neighborhoods and corridors fail to match the size and shape of the region’s census tracts (see the highlighted areas), but also that many manufacturing facilities are located near the boundaries of multiple census tracts.

The fact that so many of the factories shown in figure 4 are located near census tract boundaries means that they are likely to affect people in multiple censustracts.¹⁰ Moreover, because a facility’s host census tract can be relatively large, pollution from that facility, or positive or negative perceptions of that facility, may have a greater impact on people in adjacent tracts than on people located at the far end of the host tract. However, when we sum together the number of facilities, pounds of pollution, or number of factory jobs in each census tract, or create a dummy variable to indicate the presence or absence of manufacturing facilities in a census tract, we ignore the possibility that facilities in one tract may affect people in adjacent tracts, perhaps to a greater degree than they affect people in the host tract. We also ignore the possibility that facilities may not affect every square inch of their host tract or adjacent tracts equally.¹¹

Moreover, it is likely that these considerations hold for at least some other point-specific data. For example, it is not unreasonable to assume that violent crime and drug dealing can influence perceptions of neighborhood order and disorder across tract boundaries and unevenly within tract boundaries or that the effect of abortion clinics on out-of-wedlock births is poorly captured by county, zip code, or census tract boundaries. As a result, it is likely that aggregating point data to the polygon level will, in many cases, produce results that are more highly dependent on the zoning scheme used to define researchers’ aerial unit boundaries than on the underlying relationships researchers wish to investigate.

Given the serious methodological problems that arise when researchers aggregate point data to the polygon level or merge census tract observations to make dual-decade census tract data sets spatially comparable, it is imperative that researchers devise new methodological techniques for doing both of these things. Thus, in the sections that follow, I describe two GIS variable construction techniques that minimize the methodological problems associated with merging point and polygon data and dual-decade census data, use these techniques to test four hypotheses drawn from the literature on environmental inequality, and compare the results of these tests to results obtained using more traditional data merging techniques. I begin with a brief discussion of the four environmental inequality hypotheses.

ENVIRONMENTAL INEQUALITY HYPOTHESES

Environmental inequality is a relatively new field of study that attempts to evaluate the claim that the poor, the working class, and people of color are disproportionately burdened by environmental hazards (Anderton et al. 1994a, 1994b; Bowen et al. 1995; Bryant and Mohai 1992; Szasz and Meuser 1997). In order to ascertain the validity of this claim, environmental inequality researchers have set forth several spatial proximity hypotheses, four of which will be tested in this article.

• Hypothesis 1.—

  Neighborhood proximity to environmental hazards is positively associated with the percentage of blacks in a neighborhood (Mohai and Bryant 1992; Sadd et al. 1999).

• Hypothesis 2.—

  Neighborhood proximity to environmental hazards is negatively associated with neighborhood income levels (Hamilton 1995; Mohai and Bryant 1992; Szasz and Meuser 1997).

• Hypothesis 3.—

  Neighborhood proximity to industrial pollution is a stronger predictor than neighborhood proximity to industrial employment of neighborhood racial composition (Bullard 1992).¹²

• Hypothesis 4.—

  Blacks move into environmentally hazardous neighborhoods in disproportionate numbers (Godsil 1991; Hamilton 1995; Mohai and Bryant 1992).

These hypotheses raise unique methodological challenges. The first and second force us to measure proximity, the third to compare the predictive power of variables—employment opportunities and pollution—that operate at different spatial scales, and the fourth to measure change over time. However, what unites them conceptually and makes testing them especially challenging is that the data sets sociologists use to evaluate them typically contain spatially noncomparable units of analysis. Thus, these hypotheses provide an ideal platform for demonstrating the methodological advantages of using the GIS techniques introduced in this article.

A VERY BRIEF INTRODUCTION TO GIS

A GIS is a software package that unites spatial data, such as the location of factories and census tracts, with data about the features making up the spatial database, such as the number of people living in each census tract or the number of employees in each factory.¹³ In a GIS, data are stored as map layers that can be precisely positioned on top of each other.¹⁴ There are two basic types of map layers in a GIS, vector map layers and raster map layers. A vector map uses points, lines, and polygons to represent physical features (vector maps are what most people think of when they think of maps). A raster map stores and displays spatially referenced numeric data in rectangular grids composed of square cells that are described in terms of resolution.

The procedures described in this article convert vector-based census tract maps and vector-based manufacturing facility maps into raster grids, mathematically manipulate these grids, and then convert them back into vector-based census tract maps, using tract boundaries to aggregate the manipulated raster data.¹⁵ In the examples presented below, the raster data is aggregated either by summing together the cell values that fall inside each vector-based census tract or by calculating the mean or median cell value in each vector-based census tract.¹⁶

As we shall see, these procedures minimize the problems associated with merging point and polygon data by allowing researchers to mathematically manipulate grid cells without regard to census tract boundaries, thereby allowing point-specific data in one census tract to affect grid cells located in other census tracts, to have an uneven effect on cells located in the host tract, and to have an uneven effect on cells located in nonhost tracts.

These procedures also minimize the problems associated with merging dual-decade census tract data. They do this by allowing researchers to reallocate grid cells from one set of census tract boundaries to another, thereby allowing researchers to easily reapportion data from one set of census tract boundaries to another.

MEASURING POLLUTION PROXIMITY IN DETROIT

In this section, I test the hypothesis that neighborhood proximity to environmental hazards is positively associated with the percentage of blacks in a neighborhood (%black) and negatively associated with neighborhood income levels, comparing results obtained using a traditional environmental hazard indicator (the total pounds of factory emissions in a census tract) to results obtained using two GIS-based environmental hazard indicators (defined below). Data are drawn from the Detroit metropolitan area. Tract-level demographic data were obtained from the 1990 U.S. census, and facility-level pollution data were obtained from the Environmental Protection Agency’s 1990 Toxics Release Inventory (TRI). The TRI records the number of pounds of specified toxic chemicals released into the environment each year by manufacturing facilities that employ the equivalent of 10 or more full-time workers and manufacture, process, or otherwise use specified chemicals in specified quantities. In 1990, the specified quantities were 25,000 pounds for facilities that manufactured or processed TRI chemicals and 10,000 pounds for facilities that otherwise used TRI chemicals.¹⁷

In order to test the black proximity and income proximity hypotheses, environmental inequality researchers generally aggregate site-specific environmental hazard data to create variables such as the total pounds of TRI emissions in a census tract or the number of hazardous waste facilities in a zip code. They then correlate these aggregated indicators with demographic variables such as median household income and %black.¹⁸ In most studies, only people who live in analysis units containing hazards or emissions (hazardous analysis units) are considered to be living in proximity to hazards and emissions. However, in some studies, people living in analysis units adjacent to hazardous units are also considered to be living in proximity to hazards and emissions.

As noted above, this methodological approach is problematic in a number of respects. First, it forces us to assume that environmental hazards (or at least their negative effects) are distributed evenly within analysis units. However, manufacturing facilities tend to cluster along major transportation routes (Northam 1979) that often serve as census tract boundaries. Second, it forces us to assume that environmental hazards affect every square inch of their host unit equally. Third, it forces us to assume that environmental hazards do not affect people in adjacent units of analysis or that the effect of environmental hazards in one unit of analysis on outcomes in other units of analysis is equal to the sum of the hazards’ independent effects divided by, or in some other way adjusted for, the distance between the host unit and the other analysis units.

Fourth, simple summing fails to take analysis unit size into account. However, analysis units generally become larger as you move away from the urban core. In the Detroit metropolitan area, for example, distance from the central business district is significantly correlated with %black, median household income, and census tract size. As a result, in the Detroit metropolitan area, median household income and %black are both correlated with tract size, a potentially important determinant of the number of facilities and pounds of emissions in a tract.

In order to overcome these problems, I located the TRI facilities on a vector-based 1990 census tract map and then converted this map into two, 25-meter resolution raster maps (maps in which the outer dimensions of each cell are 25 meters × 25 meters in length).¹⁹ Each cell in the first raster map was set equal to the distance from the center of that cell to the nearest TRI facility. Each cell in the second raster map was set equal to the pounds of TRI pollutants emitted within a one-quarter kilometer radius of the center of that cell. I then took the sum of the values of all the cells falling into each 1990 census tract and divided this sum by the number of cells in each tract. This gave me two new tract-level variables: the average minimum distance in a tract, or the distance from the average tract cell to its nearest TRI facility, and the average exposure in a tract, or the pounds of TRI pollutants emitted within a one-quarter kilometer radius of the average tract cell.²⁰

Figure 5 compares average exposure to a traditional pollution proximity indicator, the total pounds of TRI pollutants emitted in each census tract (total emissions). In this figure, tracts A, C, and D each represent a single 16-parcel tract, while tract B represents an 8-parcel tract. For simplicity’s sake, we will assume that the center of each parcel lies within a one-quarter kilometer radius of the center of every parcel it touches but outside a one-quarter kilometer radius of the center of all the other parcels, and that each facility is located in the center of its parcel. Average exposure is calculated by assigning a value to each parcel equal to the pounds of pollutants emitted within a one-quarter kilometer radius of its center point, summing up the parcel values for each tract and dividing each tract total by the number of parcels in that tract. For example, there are 10,500 pounds of pollutants emitted within a one-quarter kilometer radius of the parcel in the top left-hand corner of tract B, and average exposure in that tract equals [(10,500 × 2) + (500 × 4)]/8 = 2,875.

Fig. 5.

Comparing facility presence indicators

Comparing tracts A and B, we see that although total emissions are much greater in tract A than in tract B, average exposure is 15% greater in tract B than in tract A. Comparing tracts C and D, we see that although total emissions in tract C equals total emissions in tract D, average exposure is significantly lower in tract D than it is in tract C due to the spatial distribution of facilities in each tract. It should be clear, then, that average exposure minimizes the problems associated with the MAUP by taking tract size, facility location, and the boundary problem into consideration. The same is true of average minimum distance, which also takes tract size, facility location, and the boundary problem into consideration. As a result, average exposure and average minimum distance are more valid indicators of proximity than is total emissions.

Testing the Hypotheses

In order to test the black proximity and income proximity hypotheses, %black and median household income are correlated with average exposure, average minimum distance, and total emissions (table 1).²¹ I use Kendall correlation coefficients rather than Pearson’s correlation coefficients because the data are not distributed normally, and correlation coefficients rather than multiple regression because I am not testing causal hypotheses.

TABLE 1.

Kendall Tau b Correlation Coefficients for Facility Presence, % black, and Median Household Income, 1990

	% black	Median Houshold Income
Total emissions	−.002	−.115***
Average exposure	.118**	−.233***
Average minimum distance	−.277**	.449***

^*P < .05.

^**P < .01.

^***P < .001.

Table 1 shows that in the Detroit metropolitan area, total emissions is significantly correlated with median household income, but not with %black. Average minimum distance and average exposure, on the other hand, are both significantly correlated with %black and median household income in the expected direction. As average exposure increases, %black increases and median household income decreases, and as the distance from the average tract cell to its nearest facility increases, %black decreases and median household income increases.²²

These results indicate that addressing the MAUP is not simply a methodological concern. It has substantive implications as well. If we were to focus solely on the aggregated proximity indicator, total emissions, we would be forced to conclude that in the Detroit metropolitan area, TRI emissions are distributed inequitably according to income but not race, and that income-based environmental inequality in the region is relatively weak. However, using the GIS-based proximity indicators, we find that Detroit metropolitan area TRI emissions are distributed inequitably according to both income and race, and that income-based environmental inequality in the region is relatively strong. Thus, using GIS to reconceptualize and measure spatial relationships and ecological context has had a statistically significant and substantively important impact on the results reported here.

IS IT JOBS OR POLLUTION?

An interesting problem that arises when studying environmental inequality is that manufacturing facilities produce jobs as well as pollution, forcing researchers to ask whether manufacturing facilities are socially desirable, socially undesirable, or both, and whether the pollution burdens and employment benefits of manufacturing activity are borne by the same individuals, neighborhoods, and social groups (Bullard 1992). Nevertheless, to my knowledge, no environmental inequality researcher has conducted a study that asks whether manufacturing facility employment or pollution is a stronger predictor of neighborhood demographic composition.

One possible explanation for this is that when researchers think about physical space, they tend do so in discrete and bounded terms and, as a result, are unlikely to think about comparing the spheres of influence or relative predictive power of different attributes of the same social good. A more likely explanation for this is that this is a very difficult question to answer. This is because the size of the area affected by facility emissions is likely to be much different than the size of the area affected by facility employment opportunities. Thus, in order to measure accurately manufacturing facilities’ socially desirable and undesirable properties, we must measure characteristics that operate at different spatial scales.

In this section, I demonstrate how the GIS variable construction technique introduced in the preceding section can be used to do this, using data drawn from the Detroit metropolitan area to determine whether manufacturing facility pollution or employment is a stronger predictor of neighborhood racial composition. As in the previous section, I do not employ plume or distance decay modeling techniques to create the pollution and employment indicators used below because I want to simplify the presentation and avoid giving readers the impression that the techniques introduced here can only be used to study environmental inequality and spatial mismatch theory.

In addition, because the emphasis in this article is to illustrate the important role GIS can play in advancing sociological thinking and research, and not to settle substantive debates, I do not attempt to determine the actual scales at which employment and pollution have an impact. Instead, I assume that facility emissions exert a strong negative impact on a relatively small scale (within a one-quarter kilometer radius of each facility) and that manufacturing employment opportunities exert a strong positive impact on a larger, albeit still relatively small, geographic scale (within a one-, three-, or five-kilometer radius of each facility).

While these relatively small radii would make little sense in a plume or distance decay modeling context, their use makes sense here because EPA and census data suggest that as the distance from manufacturing facilities increases, manufacturing facilities’ pollution and employment impacts decline fairly rapidly at first and then more slowly as distance increases further.²³ In addition, these data suggest that pollution impacts decline much more rapidly than employment impacts. Thus, if I were to increase the length of the radii used to create the indicators employed here, it is quite likely that I would overestimate the pollution and employment impacts of the TRI facilities in the database.

The data used in this section were obtained from the following sources: tract-level demographic data were obtained from the 1990 U.S. census, pollution data were obtained from the 1990 Toxics Release Inventory, and employment data were obtained from the 1990 Michigan Manufacturers Directory (Pick Publications, 1990). The Michigan Manufacturers Directory lists the names, addresses, and number of employees of manufacturing facilities throughout the state. Because employee data are not available for every facility in the directory, only those TRI facilities with employee data are included in the analysis.²⁴

In order to determine whether manufacturing facility employment or pollution is a stronger predictor of neighborhood racial composition, I regress %black on two grid-based indicators, average employment and average exposure, controlling for median family income, median family income squared, the percentage of housing units in a tract that are owner occupied, the percentage of housing units built before 1960, the percentage of housing units that are vacant, the median property value of owner-occupied housing, median gross rent, and a set of spatial trend variables that take into account the distance and compass direction from the central business district to each census tract.²⁵

I include the spatial trend variables because the procedures I use to control for spatial autocorrelation assume spatial stationarity, which “implies that the relationships within any subset of points remain the same no matter where the points reside in space” (Kaluzny et al. 1998, p. 6).²⁶ However, because it is not my goal to examine the association between the spatial trend variables and the dependent variable, I do not report the spatial trend coefficients below.

Average exposure and average employment are both calculated at the tract level using 25-meter resolution grid cells and the variable construction technique introduced in the previous section. Average exposure is defined as the pounds of TRI pollutants emitted within a one-kilometer radius of the average tract cell, average employment 1 is defined as the number of TRI facility workers employed within a one-kilometer radius of the average tract cell, average employment 3 is defined as the number of TRI facility workers employed within a three-kilometer radius of the average tract cell, and average employment 5 is defined as the number of TRI facility workers employed within a five-kilometer radius of the average tract cell.

Table 2, models 1–3, show that average employment 1, 3, and 5 are all stronger predictors than average exposure of the percentage of blacks in a tract. Whereas average employment is significantly and negatively associated with %black at all three scales of spatial measurement, average exposure is not significantly associated with the dependent variable even when average employment is dropped from the model (model 4). Thus, the lack of statistical association between average exposure and %black is not the result of multicollinearity between average exposure and average employment.

TABLE 2.

Regression of % black on Average Exposure and Average Employment, 1990

	Model 1 (1-km radius)	Model 2 (3-km radius)	Model 3 (5-km radius)	Model 4	Model 5
Intercept	−118.1770***	−107.8500***	−89.8750***	−119.7085***	−25.1384**
Average exposure	.0120	.0090	.0074	.0004
Average employment 1	−.0053*
Average employment 3		−.0026***
Average employment 5			−.0016***
Total emissions (in 1,000s)					.0044
Total employment (in 1,000s)					−2.0267
Median property value	−.0001	−.0001	−.0001	−.0001	−.0001*
Median gross rent	.0292*	.0258*	.0259*	.0283*	.0308*
% owner occupied	−.1124	−.0958	−.0205	−.1064	−.2083*
% housing built before 1960	.1495**	.1547**	.1180*	.1476*	.1608**
% vacant housing units	.0200	.0192	.0215	.0201	.0011
Median family income	−.0007*	−.0007	−.0009*	−.0007*	−.0003
Median family income squared	.0000*	.0000	.0000*	.0000	.0000
ρ	.1388*	.1388*	.1388*	.1388*	.1390*
Log likelihood	−3,798	−3,778	−3,780	−3,801	−3,791

Note.—N of observations is 594 for all models. Spatial trend variables were utilized in the models but not reported here.

^*P < .05.

^**P < .01.

^***P < .001.

In order to compare these results to results obtained using a traditional variable construction technique, I inserted total emissions and total employment into the regression equation in place of average exposure and average employment. Total emissions is defined as the total pounds of TRI pollutants emitted in each census tract in 1990 divided by 1,000, and total employment is defined as the number of TRI facility workers employed within the boundaries of each census tract in 1990 divided by 1,000. When these variables are inserted into the regression equation (model 5), neither of them is significantly associated with the dependent variable.

These results demonstrate that using GIS to construct ecological indicators and address the MAUP can have a substantive impact not only on correlation results (table 1), but on regression results as well. If we were to focus solely on the results for model 5, we would be forced to conclude that in the Detroit metropolitan area in 1990, neither TRI emissions nor TRI employment was significantly associated with the percentage of blacks in a tract. Our conclusions are quite different, however, when we focus our attention on the results found in models 1–3. These results indicate that in the Detroit metropolitan area in 1990, TRI facility employment was a more important determinant than TRI facility pollution of neighborhood racial composition and that as TRI facility employment increased, the percentage of blacks in a tract decreased.

On the one hand, these findings contradict the environmental inequality argument that net of other factors, manufacturing facility pollution is still an important determinant of neighborhood racial composition (Mohai and Bryant 1992). On the other hand, in showing that in the Detroit metropolitan area, %black is negatively associated with average employment, but insignificantly associated with average exposure, these analyses provide tentative support for the argument that for blacks the burdens of industrial production outweigh its benefits (Bullard 1992).

In order to provide more complete support for this argument, we would need to carefully specify the precise distance decay functions and plume modeling parameters needed to estimate TRI facilities’ employment and pollution impacts. Nevertheless, the findings reported in table 2 demonstrate that GIS can be used to convert point data into substantively meaningful aerial-unit indicators that accurately measure observational characteristics operating at different spatial scales. These indicators minimize the methodological problems associated with merging point and polygon data by taking facility location and the boundary problem into consideration and can be constructed whenever researchers merge spatially referenced point data with spatially referenced aerial-unit data such as that provided by the U.S. census.

USING CENSUS DATA TO EXAMINE CHANGE OVER TIME

As noted above, a major problem confronting researchers who use census data to examine change over time is that census boundaries change from one decade to the next, forcing many researchers to either (a) drop from their analyses all census units whose boundaries have changed or (b) merge census units in each of the original data sets until their observations are comparable over time (Bergesen and Herman 1998; Marchand 1986). This is problematic for at least two reasons. First, regardless of which approach is taken, a large number of observations are lost. Second, even when a study is restricted to two time points, the number of census units that need to be merged can be quite large, resulting in the creation of analysis units that are larger (in some cases much larger) and more heterogeneous than the nonmerged analysis units to which they are being compared. These are serious problems, as my earlier discussion made clear. Not only can data aggregation have a dramatic effect on correlation coefficient and regression parameter estimates, it can also increase R²-values and the standard errors of the parameter estimates.

Thus, in this section, I introduce a GIS procedure that allows researchers to merge census data from different decades without merging or dropping census observations. It does this by reapportioning data from one set of census boundaries to another, using raster maps as a bridge between the different sets of census boundaries.

After describing the procedure, I use it to test the hypothesis that blacks move into environmentally hazardous neighborhoods in disproportionate numbers. I test this hypothesis by regressing the tract-level change in %black from one decade to the next (%black₁₉₉₀ – %black₁₉₈₀) on average exposure₁₉₈₀ and a set of control variables also measured in 1980, comparing regression results obtained using merged observation data to results obtained using the GIS procedure described below.

Before proceeding, I should note that this procedure is not the only GIS procedure that has been developed to reapportion data from one set of census boundaries to another. For example, the University of Missouri’s Office of Social and Economic Data Analysis provides internet users with a free “geographic correspondence engine” called MABLE/Geocorr that allows researchers to convert U.S. census data from one census geography to another (within a single census year or across different censuses); and Geolytics, Inc., sells a data set that allows researchers to, in their words, “normalize” 1970, 1980, and 1990 U.S. census tract data to 2000 census tract boundaries.²⁷

However, neither of these applications allows researchers to reapportion data to or from analysis units not covered by its correspondence engine. Thus, MABLE/Geocorr does not allow researchers to reapportion census data collected prior to 1980, the Geolytics data set does not allow researchers to reapportion census data collected prior to 1970 or to reap-portion 1970, 1980, or 1990 census data to pre-2000 boundaries, and neither application allows researchers to reapportion data to or from non-census analysis units.²⁸

As we shall see, the procedure described below does not limit researchers in these ways. Its only major limitation is one that is common to many GIS applications: researchers must be able to input their analysis unit boundaries into a GIS using a common projection and common datum (see n. 14 for definitions of these terms).

Constructing the New Variables

One of the advantages of GIS is its ability to precisely position raster and vector maps on top of each other and convert these maps from one format to the other. Thus, we can convert a 1990 vector-based census tract map into a series of raster grids—one for each 1990 variable in our analysis—lay a 1980 vector-based census tract map on top of these grids, and for each 1980 census tract calculate (a) the sum of the values of all the cells that fall into that tract and (b) the mean and median cell value in that tract. In other words, we can “rasterize” our 1990 census tract data and then reaggregate it using 1980 census tract boundaries.

When doing this, each grid cell is assigned to the tract that overlaps the center of the cell, and all cells belonging to the same tract are assigned the same value, the value of the variable in that tract. However, when reapportioning count variables (i.e., total population, number of housing units), each count variable observation must be divided by the number of cells in its 1990 tract before it is rasterized and reaggregated. For example, if I want to calculate the number of people in 1990 who live within the boundaries of each 1980 tract, I must first divide “total population₁₉₉₀” by the number of cells in each 1990 tract—which gives me “total population per cell₁₉₉₀”—rasterize this new variable, and then sum the “population per cell₁₉₉₀” cell values that fall in each 1980 tract (Grannis [1998] uses a similar, non-raster-based method to reapportion census data).²⁹

Figure 6 illustrates this process and compares it to tract merging. Object 1 in figure 6 contains three fictitious 1990 census tracts, with total populations of 50, 75, and 100 respectively; object 2 contains their corresponding 1980 census tract boundaries; object 3 contains the boundary and population value obtained through the tract merging process (225 = 100 + 75 + 50); and object 4 is the raster grid created by calculating and rasterizing a “total population per cell” variable. In order to calculate the 1990 population that lives in each 1980 tract and the 1990 population that lives in the merged supertract, object 5 sums the cell values in object 4 that fall into each 1980 tract, and object 6 sums the cell values in object 4 that fall into the merged supertract.

Fig. 6.

Reaggregation and tract merging

Objects 1–6 highlight several important points. First, when converting census maps to raster grids all the cells belonging to the same tract must take on the same value. Second, merged census data provide less precise population distribution information than do reaggregated census data. Third, when we sum the cell values in object 4 to create object 6, we obtain virtually the same population value (224.999) as we do when we use the tract merging process illustrated in object 3 (the cell values in object 6 do not add up to 225 due to rounding errors). Thus, if we are to obtain accurate results when reapportioning count variable data, we must rasterize population-per-cell values rather than total population values.

The opposite is true when rasterizing and reaggregating median value variables. In this case, the actual median values must be rasterized (object 7) and then reaggregated by calculating the mean or median cell value in each 1980 tract (the mean cell value in each 1980 tract can be found in object 8).³⁰ Thus, if the values in object 1 actually represented median tract incomes, we would conclude that the median income in the larger of the two 1980 tracts equals 81.25 (the mean cell value found in tract A, object 8) or 87.5 (the median cell value), and that the median income in the smaller of the two tracts equals 87.5 (the mean and median cell value).

Comparing the Methods

In order to test the hypothesis that blacks move into environmentally hazardous neighborhoods in disproportionate numbers, I regress the change in %black from one decade to the next (%black₁₉₉₀ – %black₁₉₈₀) on average exposure₁₉₈₀, %black₁₉₈₀, and a set of control variables also measured in 1980, comparing results obtained using reaggregated data with results obtained using merged observation data.³¹

As argued earlier, it is extremely difficult, if not impossible, to make specific predictions about how census tract merging (data aggregation) will affect regression results. Nevertheless, prior research demonstrates that data aggregation can increase and decrease slope coefficient estimates within the same regression model and inflate the standard errors of parameter estimates. Prior research also demonstrates that aggregated data set coefficients can be significantly different from nonaggregated data set coefficients and that coefficients can change sign as the data are increasingly aggregated (Fotheringham and Wong 1991; Wong 1996). Thus, it is likely that some of the variable coefficients that are statistically significant in the reaggregated data model will be statistically insignificant in the merged data model, that some coefficient values will increase and others will decrease as we move from one data model to the other, and that these differences will be statistically significant in some cases. Finally, some coefficients may even change sign as we move from one data model to the other.

As in the previous examples, data were drawn from the Detroit metropolitan area. Tract-level demographic data were obtained from the 1980 and 1990 U.S. census, and manufacturing facility data were obtained from the 1980 Directory of Michigan Manufacturers (Pick Publications 1980). Facility data were drawn from the 1980 Directory of Michigan Manufacturers rather than from the TRI database, because the Environmental Protection Agency did not begin collecting TRI data until 1987. Thus, average exposure₁₉₈₀ is defined as the number of manufacturing facilities located within a one-quarter kilometer radius of the average tract cell.

In order to ensure that the manufacturing facilities included in the data set were among the most hazardous in the region, the data set is restricted to facilities in four highly polluting industrial sectors: transportation equipment, chemicals, primary metals, and fabricated metal products. These industries are well represented in Detroit’s industrial economy and according to the TRI were the four most highly polluting industrial sectors in the Detroit metropolitan area in 1992, responsible for approximately 99% of the region’s TRI emissions that year.

The control variables are drawn from the literature on racial succession, which is defined as “the replacement of whites by nonwhites within the boundaries of a given neighborhood” (White 1984, p. 165). Racial succession is generally viewed as a function of white geographic mobility (Steinnes 1977), the age and condition of the housing stock (Wilson 1983), and the proximity of white neighborhoods to nonwhite neighborhoods (Massey and Denton 1993; Steinnes 1977). In the regression models reported below, black neighborhood proximity is measured as “the highest %black in any adjacent tract,” and indicators of geographic mobility include the percentage of housing units that are owner occupied, the percentage of families with children, the percentage of people who lived in the same house five years ago, the percentage of people 25 years old and older who are high school graduates, median family income, and median family income squared (Galster 1990; Steinnes 1977; Vandell 1981). Indicators of housing stock age and condition include median property value, median gross rent, the percentage of housing units built before 1940, and the percentage of housing units built between 1940 and 1949, 1950 and 1959, and 1960 and 1969. Although not reported below, spatial trend variables are also included in the analysis because the autoregressive procedures used to control for spatial autocorrelation assume spatial stationarity.

Finally, because all the independent variables are measured in 1980, only two variables in the reaggregated data set are actually reaggregated: total population₁₉₉₀ and total black population₁₉₉₀. These variables, along with %black₁₉₈₀, are used to calculate the dependent variable, the change in %black from 1980 to 1990.

Table 3 compares the results obtained using the reaggregated and merged observation data sets.³² Although neither data set provides support for the hypothesis that blacks move into environmentally hazardous neighborhoods in disproportionate numbers, results clearly differ across the two models. For example, comparing the two models, we see that the coefficients for “the percentage of housing units that are owner-occupied” are significantly different from each other in the two models, as are the coefficients for “the percentage of families with children” and the coefficients for “the percentage of people who lived in the same house five years ago.” In addition, average exposure, % owner occupied, and “the percentage of housing units built from 1940 to 1949” are significantly associated with the dependent variable when the reaggregated data are used but not when the merged observation data are used.

TABLE 3.

Regression of Change in % black from One Decade to the Next on Test and Control Variables, 1980–90

	Model 1 (Reaggregated)	Model 2 (Merged)
Intercept	−26.5145*	36.5098*
Average exposure	−2.9304*	−1.8254
Highest %black in any adjacent tract	.1854***	.1259***
%black1980	−.2134***	−.1183***
Median property value	−.0001	−.0001
Median gross rent	−.0016	−.0140
% owner occupied	−.0996*	.0531a
% families with children	.1194**	−.1167* a
% housing built before 1940	.0690	.0687
% housing built 1940–49	.1457*	.0582
% housing built 1950–59	.1045	.0586
% housing built 1960–69	.0837	.0880
% same house as five years ago	.0302**	−.3001*** a
% high school graduates	.0752	.0966
Median family income	.0006	−.0002
Median family income squared	.0001	.0001
ρ	.1311*	.1392*
Log likelihood	−3,415	−2,681
N	607	504

^aThis pair of variable coefficients (model 1 and model 2) are significantly different from one another. Spatial trend variables were utilized in the models but not reported here.

^*P < .05.

^**P < .01.

^***P < .001.

Thus, according to the reaggregated data, but not the merged data, as average exposure₁₉₈₀ increases, the change in %black from 1980 to 1990 decreases, a surprising finding that runs counter to much environmental inequality theorizing.³³ Not only does it contradict the hypothesis that blacks move into environmentally hazardous neighborhoods in disproportionate numbers, it also raises the possibility that during the 1980s Detroit metropolitan area blacks moved away from such neighborhoods. In addition, because blacks and whites constituted nearly all of the region’s population in 1980 and 1990, it raises the possibility that whites moved into polluting manufacturing neighborhoods in disproportionate numbers during these years.

A final difference between the two models listed in table 3 is that the coefficient signs for “the percentage of families with children” and “the percentage of people who lived in the same house five years ago” are not stable across the two models despite the fact that these variables are significantly associated with the dependent variable in both models.

This finding is not entirely surprising given what we know about the MAUP (Fotheringham and Wong 1991; Wong 1996). Nevertheless, it merits some explanation. Inspection of the data shows that data merging had a pronounced effect on many of the observations that were located at the tail ends of the reaggregated dependent variable distribution, increasing the value of many of the lowest-value reaggregated dependent variable observations and decreasing the value of several of the highest-value reaggregated dependent variable observations. This effect was particularly pronounced at the low end of the dependent variable distribution because many of the lowest-value dependent variable observations were merged with multiple higher-value observations, producing merged observations with dependent variable values closer to the mean of the distribution than to the lower tail of the distribution (e.g., one low-value dependent variable observation was merged with six higher-value observations, another was merged with five higher-value observations, and several were merged with two-to-four higher-value observations).³⁴

Moreover, it turns out that many of these tail-end, reaggregated, dependent variable observations are also found at or near the tails of the distributions of “the percentage of families with children” and “the percentage of people who lived in the same house five years ago.” Thus, one possible explanation for why the coefficients for these independent variables are so unstable across the two models is that for these two variables, the tail-end dependent variable observations had a high degree of leverage in the reaggregated data set but not in the merged data set.³⁵ However, given the complexity of the equations used to estimate regression coefficients, this explanation is at best tentative and most likely incomplete.

DISCUSSION

The findings reported in this section are the product of two very different approaches to the problem of boundary noncomparability. Tract merging, which is rooted in a discrete conception of physical space, overcomes this problem by merging tracts whose boundaries have changed over time. In the process it creates a whole new set of methodological problems, those associated with the MAUP.

Reaggregation, which is rooted in a continuous conception of physical space, overcomes the boundary problem by reapportioning data from one set of census tract boundaries to another, thereby avoiding tract merging altogether. As a result, reaggregated data contain more precise population distribution information than do merged data (this is true for all the variables in the reaggregated data set, not just those that have been reaggregated). Reaggregated data also contain observations that are smaller and more closely identical to each other in size than are merged observations. Finally, reaggregated data contain a greater number of observations than do merged data: in table 3, for example, the reaggregated data set has 607 observations but the merged observation data set has only 504 observations, despite the fact that the merged observation data set was created in such a way as to maximize the number of observations in the data set.

Most important, in overcoming the boundary problem without merging census observations, reaggregation avoids the methodological problems associated with the MAUP. In doing this, it provides researchers with an important new tool for merging dual-decade census data and other spatially incomparable, polygon-based data sets. Moreover, reaggregation is not merely a technical fix. As I have just demonstrated, reaggregation can also have a theoretically significant impact on research findings.

CONCLUSION

This article makes three important contributions to sociological thinking and research. First, it demonstrates that modeling physical space as a continuous, unbounded surface can change the way sociologists think about spatial relationships and ecological context, allowing sociologists to reconceptualize spatially based methodological problems that have been troubling them for years. Second, because GIS provides researchers with new methodological tools and new ways of conceptualizing physical space, GIS also allows sociologists to answer questions about spatial relationships, ecological context, and social inequality that they might not otherwise ask or be able to answer satisfactorily.

Third, this article introduces sociologists to a set of GIS techniques that minimize the serious methodological problems associated with testing spatial proximity hypotheses and merging spatially incomparable data sets. These techniques do not provide perfect solutions to these methodological problems, nor are they the only GIS techniques that can be used to overcome or minimize them. Nevertheless, they are particularly effective in dealing with these problems and can be used whenever sociologists need to merge spatially referenced point and polygon data or data whose boundaries change over time.

As a result, these techniques can be used to study a wide variety of research topics, including mental health, crime, collective efficacy, neighborhood disorder, social movements, urban poverty, and spatial mismatch. For example, using these techniques, site-specific crime data can be merged with survey and census data to examine the effect of crime on community cohesion, collective efficacy, and social movement activism, site-specific industrial location data can be merged with survey and census data to examine the effect of industrial activity on neighborhood disorder and depression (see Downey and Van Willigen 2005), and site-specific church and synagogue data can be merged with dual-decade census data to examine the effect that the presence of Catholic, Jewish, and Protestant institutions have on neighborhood racial composition and racial succession.

In making these contributions, this article highlights the fact that GIS provides sociologists with a new set of research tools and a new way of thinking about physical space that have the potential to change the way sociologists conduct ecological research and think about spatially based social processes. Thus, if they have not already done so, sociologists who study spatial and ecological processes should seriously consider incorporating GIS into their research.