Spatial Dynamics of the Local Built Environment in the City of Chicago: An Investigation of Data Sources and Methods

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2 Spatial Dynamics of the Local Built Environment in the City of Chicago: An Investigation of Data Sources and Methods Michael D. Bader Jennifer A. Ailshire Department of Sociology and Population Studies Center University of Michigan Population Studies Center Research Report November 2008 Corresponding author: Michael D. Bader, Department of Sociology and Population Studies Center, University of Michigan, 426 Thompson Street, Ann Arbor, MI An earlier version of this paper was presented at the 2008 annual meetings of the Population Association of America in New Orleans, LA. The authors would like to express their gratitude for the very helpful suggestions Filiz Garip provided at those meetings as well as the valuable feedback provided by Sean Reardon and Gina Lovasi on an earlier draft.

3 Spatial Dynamics of the Local Built Environment 2 ABSTRACT Recent studies have demonstrated the importance of the local built environment on individual health outcomes. Further investigation of key theoretical issues, namely improved conceptualization of potential causal mechanisms and the definition of neighborhood boundaries, is hindered by issues of measurement. Using innovative data collected from systematic social observations of a sample (N=1,663) blocks in the city of Chicago, we adapt the geostatistical method of kriging used in environmental and material sciences to demonstrate how the spatial autocorrelation of observations in the social environment can be used to create both nuanced and geographically comprehensive measures the built environment. We validate kriging as a method of estimating the physical condition of buildings on city blocks and use measured based on this estimation to investigate the association between the physical conditions of buildings on selfrated health. We discuss the implications for data collection and analysis of neighborhood effects on health and suggest possible extensions using other innovative methods of measurement.

4 Spatial Dynamics of the Local Built Environment 3 INTRODUCTION A growing body of research has demonstrated associations between individual health outcomes and the individual s neighborhood of residence (Diez-Roux 2000; Robert 1999; Sampson, Morenoff, and Gannon-Rowley 2002). Despite consistent findings that individuals living in more economically disadvantaged neighborhoods have higher levels of health risks than those living in more economically advantaged areas, net of individual demographic traits, socioeconomic characteristics and risk-factors, little is known about the mechanisms through which neighborhood disadvantage affects individuals health. One of the most promising avenues of research investigates how particular characteristics of the built environment might exert an independent influence on health at the individual level. Innovative methods in data collection, particularly through detailed observation of neighborhoods and using non-routine (Cummins et al. 2005) forms of data, have advanced empirical research of the mechanisms linking the built environment to individual health. Investigators have explored the importance of the neighborhood built environment in two ways. The first attempts to capture the highly nuanced characteristics of the built environment through direct observation of the social and built environment (Sampson and Raudenbush 1999; Sastry et al. 2006). The second way that investigators have considered the role of the built environment is through the use of data sources that reveal the types of establishments available at particular locations (Kirtland et al. 2003; Moore 2005; Morland, Wing, and Diez Roux 2002). These have highlighted the importance of investigating the spatial scale and definition of neighborhood boundaries. Fully exploring the association between neighborhoods and individual health requires that measures of the built environment be developed that are both detailed enough to provide an adequately nuanced depiction of the complexity of the built environment and sufficiently comprehensive geographically such that different spatial constructions of neighborhoods can be tested. Underlying the theoretical understanding of the way the built environment influences individual health is the notion of distance. Specifically, spatially proximate attributes of a resident s neighborhood are likely to influence their behavior in that setting. However, investigations have often relied on an implicit assumption of spatial relationships rather than explicitly modeling those relationships. In this paper, we introduce an analytic method of

5 Spatial Dynamics of the Local Built Environment 4 measurement that enables both nuance and spatial coverage of the entire study region that can overcome the limitations of prior research. Kriging is a family of methodological tools used widely in environmental and material sciences to estimate the presence of a physical process at a given location based on the spatial autocorrelation structure between sampled measurement locations. We describe how this method can be adapted for use in spatially dependent social and population sciences and specifically apply this method to develop measures of the physical condition of buildings that are used to explain differences in self-reported rated health among residents in the city of Chicago. THEORY AND MEASUREMENT OF NEIGHBORHOOD BUILT ENVIRONMENT Role of Neighborhoods on Individual Well-Being Neighborhoods have long been thought to play a fundamental role in social life and, accordingly, have been a centerpiece of sociological analysis (Park et al. 1925; Suttles 1972; Zorbaugh 1929). Conceptualized as the smallest form of social organization outside of the family, neighborhoods represent an important location for understanding the role of modern society and its influence on individuals. The influence of neighborhoods on residents is highlighted by Wilson s (1996; 1987) work exploring the consequences of structural disinvestment on low-skilled, predominantly African American residents of inner city neighborhoods. Wilson countered the dominant analytic lens that tended to explain the causes and consequences of poverty in terms of individual experiences or cultural deficiencies, arguing instead that socioeconomic opportunities are shaped by the local resources one can access (e.g. jobs, education, housing, etc.). Economically disadvantaged neighborhoods tend to have fewer resources than more privileged neighborhoods, thereby constraining the ability of residents from socially disadvantaged neighborhoods to succeed in the modern economy. A great deal of research followed and expanded Wilson s original theoretical formulation of the role of neighborhoods on individual well-being to investigate the links between neighborhoods and various social and behavioral outcomes including educational attainment, crime, substance use, sexual activity, childbearing, income, labor force participation (for reviews, see Ellen, Mijanovich, and Dillman 2001; Leventhal and Brooks-Gunn 2000; Riva, Gauvin, and Barnett 2007; Sampson, Morenoff, and Gannon-Rowley 2002). By taking the notion seriously that social and material context matters for individual health, social scientists

6 Spatial Dynamics of the Local Built Environment 5 challenge the long-held tradition of medical science that understands individual health experiences as primarily the result of individual attributes and specific pathologies. Understanding health, something assumed to be highly individualized, as the product at least in part of one s social surrounding can reveal a great deal about the structural role of the social on individual s lives. Furthermore, population-based interventions have the potential for higher returns in population health than individual-based programs. While this substantial body of research has demonstrated that individuals living in disadvantaged neighborhoods suffer disproportionately from negative health outcomes, less attention has been devoted to understanding how living in a disadvantaged neighborhood might matter. Indeed, a recent review of the literature highlighted the predominant role that concentrated socioeconomic disadvantage has in the investigation of neighborhood effects on health (Entwisle 2007). To understand the specific ways in which neighborhoods might influence the health of the individuals, it is important to develop instruments and measures that capture the nuanced environments found in neighborhoods. Furthermore, determining how characteristics of the environment might mediate or moderate poverty is also a priority for understanding how context might affect health. Another important aspect of understanding how neighborhoods affect the health of residents is determining what, exactly, a neighborhood is. Although this is a question that has vexed social scientists for decades (Galster 2001; Park et al. 1925; Suttles 1972), advances in geographic information systems (GIS) have increased the ability of social scientists to empirically examine both the scale and definition of neighborhood boundaries that influence individual behavior (Downey 2006; Mohai and Saha 2006). While Census tracts or other administrative boundaries still serve as the predominant practical definitions of neighborhoods, innovative investigations of neighborhood definitions have been probed. These include egocentric neighborhoods which are formed by drawing a buffer around an individual s residence (Chaix et al. 2005; Wendel-Vos and Schuit 2004), t-communities that are bounded by major ecological barriers and major streets (Grannis 1998; 2005), and network-based communities. Understanding the relationship between neighborhood of residence and individual well being requires constant attention to advancing the theory and methods involved in neighborhood effects research. Further investigations into the specific pathways through which neighborhoods exert influence on individual health outcomes will benefit from improved measures of

7 Spatial Dynamics of the Local Built Environment 6 neighborhood characteristics. This will require the use of data that is both sufficiently nuanced, representing the complexity and detail of the surrounding environment, as well as geographically comprehensive enough to capture the maximum amount of spatial variation. Independent Measurement of the Neighborhood Environment Addressing the role of neighborhoods in determining individual health requires that measures developed from independent evaluations of the neighborhood be created. Respondent perceptions have been used to account for the role of the built environment on health (Balfour and Kaplan 2002; Kirtland et al. 2003); however, because a respondent s report of their surroundings could be correlated in unobservable ways with the outcome researchers are interested in investigating, any effects of measures based on a respondent s report of their surrounding might be statistically biased (Kirtland et al. 2003; Sampson and Raudenbush 2004). 1 Two innovative methods of data collection from non-routine sources (Cummins et al. 2005) have been used to investigate the role of neighborhoods on health, systematic social observation of the built environment and collection of neighborhood data from proprietary or administrative data sources. These innovative methods have begun to address the issues of measurement of the built environment, though each has tended to focus on one of the two areas needed for improvement nuanced data or geographic comprehensiveness but have not addressed both. Systematic social observation and ecometric measurement. Systematic social observation (SSO) is a method of audit study that uses trained observers to indicate and measure specific items in a sampled area, typically in the neighborhoods surrounding respondents. Using a standard instrument designed by investigators, the trained staff observes properties of the physical environment and records their observations on the instrument. Because the responses are systematically collected and raters are trained to observe the same items in different neighborhoods, investigators are able to collect a variety of nuanced measurements of the physical and social attributes of neighborhoods independently of the 1 We are not arguing that respondent perceptions are unimportant to uncovering links between the neighborhood environment and respondent health. In fact, we would argue that understanding how a person perceives their environment is related to health critical to uncovering the ways that the environment affects individuals (Ross and Mirowsky 2001); however, being able to distinguish between the physical characteristics of the environment and the ways that residents perceive those characteristics requires that we be able to accurately measure the physical environment surrounding a resident.

8 Spatial Dynamics of the Local Built Environment 7 respondents themselves (Sampson and Raudenbush 1999; Reiss 1971). The instruments are designed by investigators which permits a great deal of latitude to determine which measures to obtain based on theoretically driven research hypotheses (Pikora et al. 2003). Collecting such rich data, however, is a resource-intensive process that requires sampling and necessarily limits the number of places within the study s geographic region that a researcher is able to observe and collect these nuanced measures. In response to this type of data collection, the ecometric measurement approach was developed to distinguish relevant attributes of the physical environment and permit comparisons across discrete geographic entities (e.g. neighborhoods). While this approach represents an important advancement in the measurement of physical surroundings, it also has some serious drawbacks. First, the reliabilities of ecometric measures are proportional to the number of observations obtained in each geographic entity (Raudenbush and Bryk 2002; Raudenbush and Sampson 1999). Because it is unfeasible to canvass all of the street fronts in the study region, sample designs must be created to obtain sufficient numbers of observations. Optimizing these sample designs in order to maximize the number of observations requires defining the geographic entities before entering the field, thereby compelling researchers to determine, a priori, the scale of analysis. The second issue arising from this approach is that it does not account for the spatial nature of variations in the built environment. While the ecometric approach can account for the clustering of observations within geographic entities, the measurement within these entities is assumed to capture a spatially constant process (Chaix et al. 2005). In other words, a resident at one side of the neighborhood is assumed to have the same level of the physical attribute as one on the opposite side. This is not a problem if the neighborhood definitions are relatively small; however, given the fact that neighborhoods are designed as relatively large entities to maximize observations, this is problematic. Proprietary or administrative data. The second form of data collection used by investigators to develop independent measures of the built environment is obtaining data from proprietary or governmental agencies. For example, researchers have purchased the address listings of commercial food providers to determine the availability of particular types of establishments where one can purchase food products in neighborhoods (Moore and Diez Roux 2006; Powell et al. 2007; Wang et al. 2007). Databases maintained by government agencies

9 Spatial Dynamics of the Local Built Environment 8 containing the locations of parks, crimes, pedestrian accidents and a host of other pertinent information can be obtained by investigators to analytically describe the local environments surrounding residents, particularly if the study area falls within a single jurisdiction. These databases, both proprietary and governmental, are intended to maintain complete records and are, therefore, valuable to investigators. Advances in geographic information systems (GIS) technology have facilitated the geocoding finding the spatial locations from address information of address lists and permitted alternate constructions of neighborhoods to be created (Kirtland et al. 2003). In particular, such geographically comprehensive data has allowed investigators to conceptualize alternate forms of neighborhood boundaries beyond arbitrary administrative boundaries such as census tracts or postal codes that are often used, and criticized, in the research on the built environment. Of course, the problem with such data is that it is often collected for purposes other than research. Therefore, while the data is geographically comprehensive, it often lacks the nuance and detail that are desirable for investigators. Developing Measures of the Built Environment In order to empirically address the conceptual hypotheses regarding how neighborhoods surrounding an individual might influence that individual s well-being, the measurements used by investigators must both capture the nuance of the built environment as well as be comprehensive enough to permit flexibility in neighborhood definitions. Collecting nuanced SSO data on all streets within a study area is virtually impossible if the study region is of even moderate size, which makes flexible neighborhood definitions difficult to construct. Conversely, the proprietary and administrative data, while allowing flexible constructions of neighborhood boundaries, is often collected by organizations independent of the investigators for purposes other than the analysis of the built environment on health. Combining the strengths of these two methodological innovations requires the development of new tools that can support the nuanced measurement at a large geographic scale. USING KRIGING TO MEASURE THE BUILT ENVIRONMENT A family of methodological tools, known as kriging, can help solve this problem. Kriging is a geostatistical method that uses values measured at locations sampled across space to interpolate unknown values at un-sampled locations. It is based on a two-step process. In the

10 Spatial Dynamics of the Local Built Environment 9 first step, we determine if and how sampled data co-vary across space. In the second step, we use the spatial covariance structure determined in the first step to assign a weight to each sampled location and then take the sum of the product of the sampled value and its corresponding weight at each sampled location. This can be depicted schematically as: (Interpolated Value) = [(Value Measured at Sampled Location i ) * (Weight for Location i )] In practice, a separate set of weights is applied for each un-sampled location being estimated. As we will show later, the weight applied to each sampled location is directly proportional to the proximity of that sampled location to the point being estimated and inversely proportional to the proximity of that sampled location to other sampled locations. Using this method, any point in the study region can be estimated based on the weights applied to the sampled values and, if many points across the study region are estimated, we can create a smoothed surface of attribute values across the entire study region. In the current analysis, we are interested in examining the effect of the physical condition of buildings on respondents self rated health; however, we are only able to observe the physical condition of buildings on 1,663 of the over 20,000 blocks in the city of Chicago. Kriging was developed to handle a similar problem in natural resource exploration 2 and has been used to investigate problems in epidemiology (Jerrett et al. 2005) and real estate (Basu and Thibodeau 1998). It s use in problems investigating the way the built environment affects health, however, has been left mostly unexplored (for exception, see Auchincloss et al. 2007). In the sections that follow, we describe the properties of kriging that make it attractive for application for studying the role of the built environment on health followed by a brief introduction and overview of the method. Properties of the Kriging Method Kriging has several properties which make it particularly useful for measuring the built environment. The first property that makes kriging attractive for interpolating values at 2 Because of the expense of digging mines to extract resources, operators would sample locations across a field determining the amount of the desired resource could be found at each of the sampled locations. Based on these samples, operators would then determine a spatially continuous surface estimating the amount of the resource at each point on the field in order to minimize the cost and maximize the amount of the resource where they dug (Matheron 1963).

11 Spatial Dynamics of the Local Built Environment 10 unknown locations is that the spatial structure used to interpolate those values is derived from the data itself. This means that one uses the empirical data from the sampled locations to estimate the spatial correlation or spatial decay function. This data derived method stands in contrast to other spatial interpolation methods that weight observations by an assumed decay function, such as inverse distance, inverse distance squared, or Gaussian decays. In fact, as we have mentioned and is described in more detail below, the first step to implement kriging is to evaluate the covariance of sampled locations as a function of the distance separating those observations. The second attractive property of kriging is that it is an exact interpolator, meaning that the estimated value of a sampled point is exactly equal to the observed value at that point. Again, this stands in contrast to methods such as inverse distance weighting where the value at a sampled point is undefined (because one cannot divide by a separation distance of zero); although this can be solved by substituting the measured value for the estimate, this can create a disjuncture in the smoothing surface. Beyond the theoretical value of having a single function that can describe the entire study surface, having an exact interpolator has the added practical benefit that it is not necessary to add this additional step of substituting measured values at the end of the interpolation process. The third beneficial property of kriging is that it provides both an estimate of the value at any location in the study region, as well as an estimate of the error surrounding the estimated value. These errors provide a considerable advantage over other methods of spatial interpolation. Because analysts can determine the confidence with which they predict a value at any given point in the study region, they can target areas where they can either collect more data (if the survey is still in the field) or to interpret results more cautiously because there is more measurement error at those particular locations. How Kriging Works In order to describe how this method can be usefully applied to research on the built environment, we provide a brief introduction to the concepts and calculations used in this method. 3 This introduction is not intended to be comprehensive, but is instead intended to 3 For a more comprehensive treatment, see Chiles and Delfiner (1999) or Isaaks and Srivastava (1989); and for social science applications see Bailey and Gatrell (1995)

12 Spatial Dynamics of the Local Built Environment 11 provide enough of the background to understand its particular application to the measurement of the built environment. As we have mentioned, kriging can be understood as a two-step process. The first step determines if and how the sampled data co-vary across space. Determining this spatial covariance is necessary to first determine if kriging is a useful methodological tool for a particular problem and, second, uncover the functional form of the spatial covariance structure among the sampled locations. The second step interpolating the values is accomplished through weighting the measured observations at each of the sampled locations to generate estimates of the attribute at non-sampled locations. Determining if and how the sampled data co-vary across space. To examine if and how the data co-vary across space, we use an instrument called a variogram. A variogram visually depicts the amount of variation between the values measured at two sampled points as a function of their separation distance. Formally, for any point, x, separated by another point by separation distance h, the variogram function can be estimated as where E[.] is the expectation operator, (h) is the value of the variogram for any two points separated by a distance, h; Z x is the measurement of the attribute at point x; and Z x+h is the value of the measurement separated from point x by the distance, h. In order to assess the spatial dependence in the sampled data, we calculate this variogram value for all n*(n-1) pairs of sampled locations and then plot the value by the distance that separates the two points. The resulting n*n(-1) pairs of points are plotted in a variogram cloud; however, with so many data points, it is difficult to assess whether and how the values at sampled locations are spatially dependent. Therefore, in order to determine the functional form of the variogram, we average the variogram values within bins defined as equal intervals of separation distance, also known as the lag distance. The averaged values within bins are then plotted at the midpoint of the separation distance to provide an empirical or sample variogram function. 4 After creating 4 There is no reason why other smoothing techniques, like lowess estimators or kernel smoothers cannot perform the same function; however, binning across lag distances tends to provide reasonable estimates of the variogram value, particularly if multiple lag distances are attempted and the functional form remains similar across the various lag distances.

13 Spatial Dynamics of the Local Built Environment 12 this empirical variogram, a functional form of the variogram, γ(h), can be estimated that fits the form of the empirical variogram well. Interpolating values. As we mentioned previously, the values of the physical attribute are estimated at any location by assigning a weight to each of the sampled locations. The weights are based on the spatial structure and are determined through the creation of the variogram in the previous step. The particular value at any location is simply the summed products of the measured value at the sample location and the sampled locations corresponding weight. In matrix form, this can be expressed as where z 0 * is the estimated value at a particular location; is a vector of weights for each sampled location, = { 1, 2,, N } and z is a vector of measured values at each on N sampled location, z = {z 1, z 2,,z N }. Calculating the weights. The weights used to calculate the interpolated value are based on the function estimated from the variogram determined in the first step. More precisely, the weights are based on the spatial covariance, σ (h), which, for a stationary process can be calculated by where σ (0) is the covariance at a separation distance of zero and γ(h) is the variogram function calculated in Equation (1). Simply, a stationary process is one where the covariance between two points varies only as a function of the separation distance between two points. This implies that the attribute has a spatially constant variance around a constant, if unknown, mean. Using this covariance function, the vector of weights is calculated for every location at which a value of the attribute is being interpolated. It can be shown that the interpolated value, z 0 *, from Equation (2) is the best linear unbiased estimate based on the spatial covariance using the following system of equations:

14 Spatial Dynamics of the Local Built Environment 13 In the matrix, A, the values σ ij in each cell equal the value of the covariance function determined in Equation 3 above, σ (h), at the separation distance, h, between sampled points, i and j while the values of σ 0i equal the value of the covariance function for the separation distance between the point being estimated and the sampled point, i. Since the values of i and υ the weight assigned to sample location, i, and a Lagrange multiplier to constrain the sum of the i s to one, respectively are the only unknowns in the system, one can simply solve for the vector, X, to obtain the weights and constraint. The first N elements of the vector X comprise the vector of weights,, introduced in Equation (2) and which can now be used to calculate the interpolated value. From the system of equations above, one further beneficial property unique to kriging bears mentioning now that the process of estimation has been described. In order to solve for the matrix, X, we multiply the inverse of matrix A by matrix B, i.e. X = A -1 B. Remembering that the value of the covariance function, σ (h), is larger as separation distance decreases, one will notice that the kriging weights are based on two pieces of information. First, the weights are directly proportional to the proximity of a sampled location, i, to the location for which values are being interpolated. This can be seen because the value of σ(h) in the elements of matrix B are larger the closer they are to the sampled location, i, and the matrix B is proportional to the value of element i in vector X. Second, taking the inverse of matrix A indicates that the weights are inversely proportional to the proximity of sampled locations with each other since the value of element ij in matrix A is larger the closer the two sampled values are to each other and value of the matrix A is inversely proportional to the value of X. This means that kriging not only accounts for the spatial proximity of the point being estimated to the sampled points, but that it also weights spatially clustered sample locations less heavily so that the interpolated value is not inflated by assuming that each sampled point provides independent information to be used in the

15 Spatial Dynamics of the Local Built Environment 14 interpolation. In other words, the weight assigned to each sampled location is penalized not only for its distance from the point being estimated, but it is also penalized for providing less unique spatial information if it is close to other points that are sampled. Assumptions. This type of estimation is formally known as ordinary kriging and is used for the estimation of stationary random functions. As mentioned previously, stationarity implies that there is a constant mean throughout the study region (i.e. first-order stationarity) assuming that the measured values of the attribute at the sampled locations are independently and identically distributed. Ordinary kriging also assumes that the variance of the attribute is constant throughout the entire study region (i.e. second-order stationarity). Based on these assumptions, the variance of the estimates (i.e. the estimation error) can be estimated as where σ 00 is the value of the covariance function at a separation distance of zero. Methods have been developed that relax assumptions about a constant mean, constant variance and normality, though they are beyond the scope of this paper. Using Kriging to Measure the Built Environment As a methodological tool, kriging can be used to develop nuanced measures of the built environment across a geographically expansive space. To demonstrate how kriging can be applied to this problem, we use data collected by the SSO method on a sample of city blocks to develop a kriged measure of the physical condition of buildings in the city of Chicago. One of the key shortcomings towards understanding the role of neighborhoods on health has been the lack of validation of measures used in analysis. Therefore, we begin our analysis by demonstrating the validity of the kriged measures. After doing this, we employ the measures obtained using kriging to evaluate whether there is a significant effect of the neighborhood built environment on self-rated health.

16 Spatial Dynamics of the Local Built Environment 15 DATA AND METHODS Data Respondent data. The data used in this analysis come from the Chicago Community and Adult Health Study (CCAHS). The CCAHS is a multi-stage area probability sample of 3,105 adults living in the city of Chicago, IL interviewed between May, 2001 and March, The sample was stratified into 343 neighborhood clusters (NCs) defined in the Project on Human Development in Chicago Neighborhoods (PHDCN) as one or more geographically contiguous census tracts which were joined based on the demographic characteristics of the population, local knowledge of the city s neighborhoods and major ecological boundaries (Sampson, Raudenbush, and Earls 1997). One adult aged eighteen years or older was interviewed from each sampled household with an overall response rate of 71.82%. Residents were also over-sampled from the 80 focal neighborhoods defined in the PHCDN. The sample contains an average of 9.1 subjects per NC. Individual-level descriptive statistics are presented in Table 1. The outcome used in the analysis is self-reported health. Self-reported health is derived from the respondent's subjective assessment of his or her general health as (1) poor, (2) fair, (3), good, (4) very good, and (5) excellent. All models include individual covariates representing respondent's sex, age, race/ethnicity, immigrant status, education, and income. Sex is treated as a dummy variable where the reference is males. Age is categorized into 6 groups (18-29, 30-39, 40-49, 50-59, 60-69, 70 and over) with the youngest age group used as the omitted category. Race/ethnicity is dummy coded such that the reference, Non-Hispanic whites, is compared to Non-Hispanic blacks, Hispanics, and Non-Hispanic Others. Immigrant status is a 3 category distinction between first generation, second generation, and third generation and higher, with the last category treated as the reference. Education is measured using dummy variables representing less than 12 years of education, years of education, and 16+ years of education, with the highest education category used as the omitted category. Finally, a measure of income is included that divides income into 5 categories representing less than $10,000, $10,000-29,999, $30,000-49,999, and $50,000+ with the highest income category used as the reference. Because there was significant missing data on income we include an additional category for missing on income to retain those individuals in the analysis.

17 Spatial Dynamics of the Local Built Environment 16 Built environment data. The CCAHS also developed an SSO instrument based on a similar instrument used in the PHDCN. Trained raters walked around the perimeter of blocks where a respondent was sampled. The raters observed particular items listed on the instrument and rated the condition of those items on both sides of the streets enclosing the block. In total, 1,663 blocks were observed containing 13,251 block faces. Because respondents were oversampled in the 80 focal neighborhoods and the SSO ratings were conducted on blocks containing sampled respondents, naturally there is also an over-sample of SSO ratings in the 80 focal neighborhoods. For this analysis, we use an average of three items from the SSO measuring the condition of the physical structures on the block face. These items are the condition of industrial and commercial buildings, the condition of residential buildings and the condition of recreational facilities. Each item was rated on a scale of one ( very well kept/good condition ) to four ( poor/badly deteriorated condition ) for each block face. The block face level observations were averaged across the block to develop a block-face level score of physical condition for each of the 1,663 blocks. Neighborhood demographic data. Measures of the neighborhood structural characteristics are derived from variables available in Summary File 3 of the 2000 Census of Population and Housing. A neighborhood disadvantage scale was created using the following variables from the 2000 Census: level of education and income of individuals, proportion of individuals employed as professionals, proportion of families living below the poverty threshold, proportion of families on public assistance, proportion of female headed families, and proportion of owner occupied housing. Standardized neighborhood disadvantage scales were created at the neighborhood cluster level (alpha=0.92) and the tract level (alpha=0.90). Neighborhood-level descriptive statistics are presented in Table 2 for each definition of neighborhood: neighborhood cluster, tract, and block group. Strategy and Methods Validation of kriging. In order to have confidence in using kriging to measure the built environment generally, and the physical condition of structures in particular, it is important to determine the validity of measures derived from the method. To do this, we divide the SSO data into two subsets by randomly placing two-thirds of the blocks (N=1108) into the first subset and

18 Spatial Dynamics of the Local Built Environment 17 reserving the final third (N=555) in the second subset. Using the coordinates at the centroids of each of the blocks in the first subset of the data as the sampled locations, we calculate the variogram and kriged estimates of physical condition at the location of each of the block centroids for the reserved third of SSO blocks. We then compare the estimates calculated by kriging to the measured values at the reserved locations to determine how well kriging estimates the value of physical condition at unsampled locations. Determining the influence of physical condition on health. We use multilevel regression to estimate models of neighborhood effects on self-rated health. The analysis proceeds in two steps. First, in order to assess the behavior of the kriged measure, we compare the effect of the kriged physical conditions measure on the outcome to the effect of an averaged measure. We do this at the level of neighborhood cluster, tract, and block group. Then we analyze the independent and joint effects of disadvantage and physical conditions (kriged measure) on selfreported health at the neighborhood cluster and tract levels. Statistical analyses are conducted using the HLM software (Version 6, Scientific Software International, Raudenbush et al. 2004). Data in all analyses are weighted to account for the differential probability of selection and nonresponse rates, and to adjust the sample representativeness to the 2000 age/race/sex/ specific Census population estimates for the city of Chicago. The sample weight also adjusts for the oversampling of individuals in the focal areas. ANALYSIS AND RESULTS Validation of Kriging The descriptive statistics of the physical condition variable for both the full sample of 1,663 blocks as well as the subset of two-thirds of the blocks are presented in Table 1. One can see from these statistics that the subset of data is very similar to the full sample of blocks in Chicago. Histograms of the physical condition variable (not shown) also reveal that the variable is approximately normally distributed, though there is a large clustering of observations occurring at the value of two. We use the geographic coordinates at the block centroid as our location of measurement on the larger subset and as the location of estimation on the smaller subset. Using the block centroids does introduce some level of imprecision into the measurement; however, we feel it is justified for two reasons. First, blocks are an appropriate

19 Spatial Dynamics of the Local Built Environment 18 basic human ecological level from which to build measurements in an urban setting. Second, developing estimates at any smaller level (e.g. streets) quickly increases the number of calculations and, given that blocks are created by the street grid, it does not significantly improve the spatial precision of measurement. Plots of the variogram can be viewed in Figures 1(a) and 1(b). Figure 1(a) plots the variogram cloud as well as the empirical variogram at a lag distance of 1000 meters on the vertical axis and separation distance on the horizontal axis. The variogram cloud is the raw value of the variogram calculated from Equation 1 for all 1.2 million pairs of points (i.e. 1,108 observations squared). One can tell that it is very difficult to summarize such information without use of the empirical variogram which simply averages the values of the variogram cloud within each lag distance. For clarity, Figure 1(b) displays the same empirical variogram at a magnified scale and without the variogram cloud. Figure 1(b) also includes the following estimate of the variogram function for separation distance, h, based on the empirical variogram that approximates an exponential function and has a nugget effect 5, b 0, at the intercept which accounts for small-scale variability of the outcome: In this function, the value of the sill, c, is the asymptotic limit of the function minus the nugget effect, b 0, and approximately reflects the total variation in the attribute. The value of a is approximately equal to one-third of the practical-range, or the distance at which the function so closely equals zero that no spatial variation practically exists beyond that distance. We estimated the values of the function to be: b 0 = , c = , and a = Kriged estimates are then calculated at the centroids of each of the 555 blocks in the reserved subset. Using the variogram function estimated in the previous step, we calculated the covariance function using Equation 3. Based on this covariance function, we estimated the 5 This effect is called a nugget effect because, in its original geophysical use, it represented finding some small nugget of ore that did not actually indicate finding a larger deposit of the ore. 6 This estimate is based simply on fitting the exponential function by eye to the empirical variogram. This process can also be accomplished through restricted maximum likelihood estimation (Chiles and Delfiner 1999).

20 Spatial Dynamics of the Local Built Environment 19 values at the location of each of the 555 reserved blocks using the subset of 1,108 as our sampled locations. To assess how closely the kriged estimates reproduced the values at the 555 reserve locations we subtracted the estimated value of the physical condition from the measured value of the physical conditions to obtain the errors. A histogram of these errors is shown in Figure 2 along with a line demonstrating a normal distribution. One will notice that the errors very closely approximate a normal distribution around a mean of In addition to the estimate, we obtained the variance of each estimate based on Equation (5). Using this value, we calculated the 95% confidence intervals for each location and found that 533 of the 555 measured values (96.0%) fell within the 95% confidence interval of the estimate. These statistics indicate that kriging performs excellently at estimating the value of block-level physical condition. Influence of the Built Environment on Individual Health Creation of the kriged physical condition measure. While we have demonstrated that kriging generates valid measures, these measures are only captured at the block level. Modeling these estimates requires that other substantively significant levels of aggregation, i.e. neighborhoods, be created. The ideal solution to create these estimates would be to integrate the value of the kriging system over the entire area of the neighborhood. Practically, this is impossible; therefore, the area over which measures are to be aggregated are divided into a grid where the value of the attribute is estimated by the kriging system. The arithmetic mean of the values estimated on this grid can be used as the block level estimate (Isaaks and Srivastava 1989). This form of estimation is formally known as block kriging, though to avoid confusion between city blocks and the specific methodological tool, we will call this procedure area kriging. In an urban setting, the street grid conveniently divides the city into smaller units that can be used as the grid to create area kriged measures at different areal units of interest such as neighborhood clusters, census tracts or radial buffers around respondents. Of course, it is also true that blocks can vary substantially in size. To account for this, we weight the estimate of each city block by the proportion of the total area in the neighborhood areal unit that city block comprises. For the current analyses, we compute area kriged measures at the census blockgroup, census tract and neighborhood cluster levels.

21 Spatial Dynamics of the Local Built Environment 20 Results of analysis. In the first step of the analysis we compared the kriged physical condition measure to the average physical condition measure. Those results are shown in Table 3. At each level of aggregation, the affect of the kriged measure is in the same direction and of a similar magnitude to the average measure. The kriged measures have a larger effect on self-rated health at each level of aggregation. The difference between the two measures is most pronounced at the tract level, a difference of The deviance statistics indicate that the kriged measures yield better model fit, though the differences are not statistically significant. Results from the multilevel analysis of the effects of neighborhood disadvantage and physical conditions on self-reported health are presented in Table 4 for both the NC and tract level. Models 1 and 2 for both NCs and tracts show that disadvantage and physical conditions are both significant predictors of self-reported health. The effect size of either variables is larger at the tract level than it is at the NC level, with the largest independent effect found for physical conditions at the tract level (0.179). The joint effect of disadvantage and physical conditions is shown in model 3. The effect of disadvantaged is reduced by 3.5% at the NC-level and 21.3% at the tract-level by including physical conditions. The effect of physical conditions is reduced to non-significance by including disadvantage. It is difficult to disentangle the joint effects of disadvantage and physical conditions because they are highly correlated (NC-level, ρ=0.77; tract-level, ρ =0.73). However, these models indicate that physical conditions at least explain some of the relationship between disadvantage and self-reported health. Importantly, while the disadvantage variable is a more comprehensive measure of the neighborhood environment, the physical conditions variable actually measures physical characteristics of the neighborhood environment. CONCLUSIONS In this paper, we have demonstrated how kriging can be used to develop valid measures of the built environment and how those measures can be utilized in analysis of the effect of neighborhood attributes on health. The use of kriging with existing innovative methods of data collection, such as systematic social observation, allows for analysis of the built environment that responds to theoretically driven concerns requiring both detailed and geographically comprehensive measurements. Based on the results in this analysis, we draw some preliminary conclusions about the use of kriging to further measure the built environment.

22 Spatial Dynamics of the Local Built Environment 21 The validation of kriged estimates compared to the measured values at the same location shows how well kriging performs at estimating the physical condition of buildings. Indeed, the mean error between the estimates and measured attributes was virtually zero. While kriging did not perfectly predict the measured values, only four percent of our estimates fell outside of the 95% confidence intervals of the estimates. Just as importantly, the normality in the distribution of errors around the mean indicates that any errors in measurement are unbiased. Of course, the validity test was only conducted on the single attribute measuring the physical condition of buildings. This validation cannot be extrapolated to other attributes of the neighborhood environment. Using kriging to develop additional measures of the built environment will require similar validation. This analysis provides a framework for future investigators to follow in order to determine the validity of their measures. In fact, based on our results modeling the effect of the physical condition of buildings on self-rated health, it is apparent that other measures must be explored. The neighborhood level measures using kriging behave similarly to the simple mean of observations aggregated within neighborhoods for the three scales of analysis. Although the coefficients for the kriged measures are higher for all three neighborhood definitions, they are not significant. The similarity in these measures and effects might be partially explained by the fact that the correlation length of the spatial correlation of the physical condition is very long, meaning that observations even at large separation distances are correlated. The practical range, or distance at which observations can be found to be spatially correlated, is almost 8.5 kilometers. If the attribute varies at a much smaller spatial correlation length, larger differences between the simple aggregated measure and the kriged measure might be found. The need to find other contextual attributes is supported by the fact that the effect of physical conditions is not significant after controlling for socioeconomic disadvantage. As we noted, this might be simply due to the high correlation between disadvantage and the physical condition of buildings resulting in collinearity of the variables. At the same time, however, this measure captures a very specific attribute of the built environment which might not independently contribute to self rated health. This could indicate that measures of the physical environment must capture more dimensions of the built environment in order to observe an effect of the built environment.

23 Spatial Dynamics of the Local Built Environment 22 This highlights one of the areas where this analysis could be significantly improved. While ecometric measurement at the neighborhood level might underestimate the spatial correlation of neighborhood processes, we believe that ecometric analysis at the block-level creates an excellent measurement instrument. The data collected through systematic social observation provide a rich source of information about the variation in the built environment that ecometric tools are uniquely adept at capturing. Therefore, creating kriged measures from tested ecometric scales such as physical disorder and developing new scales to capture unique attributes of the built environment is a logical next step. Another area in need of development is formulating different conceptions of neighborhoods. Although we have highlighted the theoretical importance of testing different constructions of neighborhoods, we use traditional Census administrative boundaries for this analysis. Obviously, creating measures based on different definitional boundaries of neighborhoods and testing whether those measures have a significant association with health is a priority. Despite these limitations, we believe that the present analysis represents a non-trivial step towards developing measures of the built environment that reveal the possibilities of small scale analysis of the built environment. As more attention is devoted to understanding how specific attributes of the built environment influence individual health and well being, theoretical and methodological advances in neighborhood effects research will become increasingly important.

24 Spatial Dynamics of the Local Built Environment 23 REFERENCES Auchincloss, Amy H., Diez Roux, Ana V., Daniel G. Brown, Trivellore E. Raghunathan and Christine A. Erdmann "Filling the Gaps: Spatial Interpolation of Residential Survey Data in the Estimation of Neighborhood Characteristics." Epidemiology 18: Bailey, Trevor C., and Anthony C. Gatrell Interactive Spatial Data Analysis. Harlow Essex, England: Longman Scientific & Technical ; J. Wiley. Balfour, Jennifer L. and George A. Kaplan "Neighborhood Environment and Loss of Physical Function in Older Adults: Evidence from the Alameda County Study." American Journal of Epidemiology 155: Basu, Sabyasachi and Thomas G. Thibodeau "Analysis of Spatial Autocorrelation in House Prices." The Journal of Real Estate Finance and Economics 17: Chaix, Basile, Juan Merlo, S. V. Subramanian, John Lynch and Pierre Chauvin "Comparison of a Spatial Perspective with the Multilevel Analytical Approach in Neighborhood Studies: The Case of Mental and Behavioral Disorders due to Psychoactive Substance use in Malmo, Sweden, 2001." American Journal of Epidemiology 162: Chiles, Jean-Paul and Pierre Delfiner Geostatistics : Modeling Spatial Uncertainty. New York : Wiley. Cummins, Steven, Sally Macintyre, Sharon Davidson and Anne Ellaway "Measuring Neighbourhood Social and Material Context: Generation and Interpretation of Ecological Data from Routine and Non-Routine Sources." Health & Place, 11: Diez-Roux, Ana V "Multilevel Analysis in Public Health Research." Annual Review of Public Health 21: Downey, Liam "Using Geographic Information Systems to Reconceptualize Spatial Relationships and Ecological Context." American Journal of Sociology 112: Ellen, Ingrid G., Tod Mijanovich and Keri-Nicole Dillman "Neighborhood Effects on Health: Exploring the Links and Assessing the Evidence." Journal of Urban Affairs 23: Entwisle, Barbara "Putting People into Place." Demography 44: Galster, George "On the Nature of Neighbourhood." Urban Studies 38: Grannis, Rick "The Importance of Trivial Streets: Residential Streets and Residential Segregation." American Journal of Sociology 103: "T-Communities: Pedestrian Street Networks and Residential Segregation in Chicago, Los Angeles, and New York." City & Community 4: Isaaks, Edward H. and R. M. Srivastava "Applied Geostatistics.":xix, 561. Jerrett, Michael, Richard T. Burnett, Renjun Ma, C. A. Pope III, Daniel Krewski, K. B. Newbold, George Thurston, Yuanli Shi, Norm Finkelstein, Eugenia E. Calle and Michael J. Thun "Spatial Analysis of Air Pollution and Mortality in Los Angeles." Epidemiology 16: Kirtland, Karen A., Dwayne E. Porter, Cheryl L. Addy, Matthew J. Neet, Joel E. Williams, Patricia A. Sharpe, Linda J. Neff, C. D. Kimsey and Barbara E. Ainsworth "Environmental Measures of Physical Activity Supports: Perception Versus Reality." American Journal of Preventive Medicine 24: Leventhal, Tama and Jeanne Brooks-Gunn "The Neighborhoods they Live in: The Effects of Neighborhood Residence on Child and Adolescent Outcomes." Psychological Bulletin 126: Matheron, G "Principles of Geostatistics." Economic Geology 58:

25 Spatial Dynamics of the Local Built Environment 24 Mohai, Paul and Robin Saha "Reassessing Racial and Socioeconomic Disparities in Environmental Justice Research*." Demography 43:383. Moore, K. S "What's Class Got to do with it? Community Development and Racial Identity." Journal of Urban Affairs 27: Moore, L. V. and A. V. Diez Roux "Associations of Neighborhood Characteristics with the Location and Type of Food Stores." American Journal of Public Health 96: Morland, Kimberly, Steve Wing and Ana V. Diez Roux "The Contextual Effect of the Local Food Environment on Residents' Diets: The Atherosclerosis Risk in Communities Study." Am J Public Health 92: Park, Robert E., Ernest W. Burgess, Roderick D. McKenzie and Louis Wirth The City. Chicago, IL: University of Chicago Press. Pikora, Terri, Billie Giles-Corti, Fiona Bull, Konrad Jamrozik and Rob Donovan "Developing a Framework for Assessment of the Environmental Determinants of Walking and Cycling." Social Science & Medicine 56: Powell, L. M., S. Slater, D. Mirtcheva, Y. Bao and F. J. Chaloupka "Food Store Availability and Neighborhood Characteristics in the United States." Preventive Medicine 44: Raudenbush, Stephen W. and Anthony S. Bryk Hierarchical Linear Models : Applications and Data Analysis Methods. Thousand Oaks : Sage Publications. Raudenbush, Stephen W., Anthony S. Bryk, Yuk F. Cheong, Richard Congdon and Mathilda du Tolt HLM 6 : Hierarchical Linear and Nonlinear Modeling. Lincolnwood, Ill.: Scientific Software Int. Inc. Raudenbush, Stephen W. and Robert J. Sampson "Ecometrics: Toward a Science of Assessing Ecological Settings, with Application to the Systematic Social Observation of Neighborhoods." Sociological Methodology 29:1-41. Reiss, Albert J "Systematic Observation of Natural Social Phenomena." Sociological Methodology 3:3-33. Riva, Mylene, Lise Gauvin and Tracie A. Barnett "Toward the Next Generation of Research into Small Area Effects on Health: A Synthesis of Multilevel Investigations Published since July 1998." Journal of Epidemiology and Community Health 61: Robert, Stephanie A "Socioeconomic Position and Health: The Independent Contribution of Community Socioeconomic Context." Annual Review of Sociology 25: Ross, Catherine and John Mirowsky Neighborhood disadvantage, disorder and health. Journal of Health and Social Behavior 42(3): Sampson, Robert J., Jeffery Morenoff and Thomas Gannon-Rowley "Assessing Neighborhood Effects: Social Processes and New Directions in Research." Annual Review of Sociology 28: Sampson, Robert J. and Stephen W. Raudenbush "Systematic Social Observation of Public Spaces: A New Look at Disorder in Urban Neighborhoods." The American Journal of Sociology 105: "Seeing Disorder: Neighborhood Stigma and the Social Construction of "Broken Windows"." Social Psychology Quarterly 67: Sampson, Robert J., Stephen W. Raudenbush and Felton Earls "Neighborhoods and Violent Crime: A Multilevel Study of Collective Efficacy." Science 277: Sastry, Narayan, Bonnie Ghosh-Dastidar, John Adams and Anne R. Pebley "The Design of a Multilevel Survey of Children, Families, and Communities: The Los Angeles Family and Neighborhood Survey." Social Science Research, 35: Suttles, Gerald D The Social Construction of Communities. Chicago: University of Chicago Press.

26 Spatial Dynamics of the Local Built Environment 25 Wang, M. C., S. Kim, A. A. Gonzalez, K. E. MacLeod and M. A. Winkleby "Socioeconomic and Food-Related Physical Characteristics of the Neighbourhood Environment are Associated with Body Mass Index." Journal of Epidemiology and Community Health 61: Wendel-Vos, G. C. W. and A. J. Schuit "Factors of the Physical Environment Associated with Walking and Bicycling." Medicine and Science in Sports and Exercise 36: Wilson, William J The Truly Disadvantaged : The Inner City, the Underclass, and Public Policy. Chicago: University of Chicago Press. Wilson, William J., When Work Disappears : The World of the New Urban Poor. New York : Knopf : Distributed by Random House, Inc. Zorbaugh, Harvey W The Gold Coast and the Slum; a Sociological Study of Chicago's Near North Side. Chicago,: University of Chicago Press.

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28 Table 3. Multilevel Regression ofself Rated Health on Physical Conidtions (Kriged vs. Average Measures) Neighborhood Cluster Level Tract Level Block Group Level Kriged Average Kriged Average Kriged Average Coef (SE) Coef (SE) Coef (SE) Coef (SE) Coef (SE) Coef (SE) Neighborhood Characteristics Physical Conditions 0.165** (0.062) 0.116** (0.045) 0.179** (0.057) 0.112** (0.039) 0.171** (0.053) 0.114** (0.035) Individual Characteristics Female 0.095** (0.034) 0.096** (0.034) 0.095** (0.034) 0.096** (0.034) 0.098** (0.034) 0.099** (0.034) Age (ref=age 18-29) Age *** (0.050) 0.185*** (0.050) 0.191*** (0.050) 0.192*** (0.050) 0.187*** (0.050) 0.186*** (0.050) Age *** (0.053) 0.340*** (0.053) 0.340*** (0.053) 0.340*** (0.053) 0.327*** (0.053) 0.327*** (0.053) Age *** (0.059) 0.549*** (0.059) 0.543*** (0.059) 0.545*** (0.060) 0.532*** (0.060) 0.535*** (0.060) Age *** (0.068) 0.534*** (0.068) 0.545*** (0.068) 0.545*** (0.068) 0.540*** (0.068) 0.540*** (0.068) Age *** (0.068) 0.480*** (0.068) 0.476*** (0.068) 0.477*** (0.068) 0.475*** (0.068) 0.478*** (0.068) Race/Ethnicity (ref=non-hisp White) Non-Hisp Black 0.136* (0.054) 0.151** (0.052) 0.121* (0.054) 0.144** (0.052) 0.124* (0.052) 0.145** (0.050) Hispanic 0.124* (0.058) 0.131* (0.057) 0.113* (0.058) 0.126* (0.057) 0.124* (0.058) 0.138* (0.057) Non-Hisp Other (0.097) (0.097) (0.097) 0.02 (0.097) (0.097) (0.097) Immigrant Status (ref=3rd+ generation) 1st Generation Immigrant (0.055) (0.055) (0.055) (0.055) (0.055) (0.055) 2nd Generation Immigrant (0.059) (0.059) (0.060) (0.060) (0.060) (0.060) Education (ref=16+ years) <12 years of education 0.492*** (0.058) 0.496*** (0.058) 0.494*** (0.058) 0.500*** (0.058) 0.490*** (0.058) 0.492*** (0.058) years of education 0.270*** (0.044) 0.272*** (0.044) 0.270*** (0.044) 0.272*** (0.044) 0.272*** (0.044) 0.273*** (0.044) Income (ref=$50,000+) Income < $10, *** (0.069) 0.393*** (0.069) 0.370*** (0.069) 0.375*** (0.069) 0.360*** (0.070) 0.364*** (0.070) Income $10,000-$29, *** (0.052) 0.316*** (0.052) 0.313*** (0.053) 0.314*** (0.053) 0.306*** (0.053) 0.306*** (0.053) Income $30,000-$49, (0.053) (0.053) (0.053) (0.053) (0.053) 0.05 (0.053) Missing data on income 0.132* (0.054) 0.133* (0.054) 0.132* (0.055) 0.134* (0.055) 0.125* (0.054) 0.126* (0.054) Intercept 1.281*** (0.128) 1.377*** (0.100) 1.248*** (0.119) 1.376*** (0.090) 1.279*** (0.111) 1.388*** (0.083) Deviance p<0.10,* p<0.05, ** p<0.01, ***p<

29 Table 4. Multilevel Regression of Self Rated Health on Neighborhood Disadvantage and Physical Conidtions (Kriged Measures) Neighborhood Cluster Level Tract Level Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Coef (SE) Coef (SE) Coef (SE) Coef (SE) Coef (SE) Coef (SE) Neighborhood Characteristics Neighborhood Disadvantage 0.143*** (0.037) 0.138** (0.050) 0.160*** (0.042) 0.126* (0.054) Physical Conditions 0.165** (0.062) (0.083) 0.179** (0.057) (0.073) Individual Characteristics Female 0.087* (0.034) 0.087* (0.034) 0.086* (0.034) 0.096** (0.034) 0.095** (0.034) 0.095** (0.034) Age (ref=age 18-29) Age *** (0.050) 0.186*** (0.050) 0.178*** (0.050) 0.183*** (0.050) 0.191*** (0.050) 0.184*** (0.050) Age *** (0.053) 0.340*** (0.053) 0.332*** (0.053) 0.332*** (0.053) 0.340*** (0.053) 0.334*** (0.053) Age *** (0.059) 0.547*** (0.059) 0.542*** (0.059) 0.536*** (0.059) 0.543*** (0.059) 0.538*** (0.059) Age *** (0.067) 0.533*** (0.068) 0.529*** (0.067) 0.542*** (0.068) 0.545*** (0.068) 0.544*** (0.068) Age *** (0.068) 0.479*** (0.068) 0.480*** (0.068) 0.481*** (0.068) 0.476*** (0.068) 0.479*** (0.068) Race/Ethnicity (ref=non-hisp White) Non-Hisp Black 0.09 (0.057) 0.136* (0.054) (0.057) (0.055) 0.121* (0.054) (0.056) Hispanic 0.118* (0.057) 0.124* (0.058) 0.117* (0.058) 0.116* (0.057) 0.113* (0.058) (0.058) Non-Hisp Other (0.097) (0.097) (0.097) (0.097) (0.097) (0.097) Immigrant Status (ref=3rd+ generation) 1st Generation Immigrant (0.055) (0.055) (0.055) (0.055) (0.055) (0.055) 2nd Generation Immigrant (0.059) (0.059) (0.059) (0.060) (0.060) (0.060) Education (ref=16+ years) <12 years of education 0.467*** (0.059) 0.492*** (0.058) 0.467*** (0.059) 0.471*** (0.059) 0.494*** (0.058) 0.470*** (0.059) years of education 0.248*** (0.045) 0.270*** (0.044) 0.248*** (0.045) 0.248*** (0.045) 0.270*** (0.044) 0.251*** (0.045) Income (ref=$50,000+) Income < $10, *** (0.069) 0.390*** (0.069) 0.379*** (0.069) 0.360*** (0.069) 0.370*** (0.069) 0.357*** (0.069) Income $10,000-$29, *** (0.052) 0.314*** (0.052) 0.303*** (0.052) 0.300*** (0.053) 0.313*** (0.053) 0.300*** (0.053) Income $30,000-$49, (0.053) (0.053) (0.053) (0.053) (0.053) (0.053) Missing data on income 0.125* (0.054) 0.132* (0.054) 0.124* (0.054) 0.127* (0.055) 0.132* (0.055) 0.126* (0.055) Intercept 1.707*** (0.065) 1.281*** (0.128) 1.682*** (0.194) 1.686*** (0.064) 1.248*** (0.119) 1.527*** (0.168) Deviance + p<0.10,* p<0.05, ** p<0.01, ***p<0.001

30 Spatial Dynamics of the Local Built Environment 2 Figure 1(a). Variogram cloud of spatial variation in physical conditions Figure 1(b). Empirical and estimated variogram function of spatial variation in physical conditions

31 Spatial Dynamics of the Local Built Environment Figure 2. Histogram of errors in kriged estimates from measured values in physical condition

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