Natalya Verbitsky Savitz & Stephen W. Raudenbush
Savitz, N. V. & Raudenbush, S. W. (1). 5. Exploiting Spatial Dependence to Improve Measurement of Neighborhood Social Processes. Sociological Methodology, 39(1), 151–183. http://dx.doi.org/10.1111/j.1467-9531.2009.01221.x
A number of recent studies have used surveys of neighborhood informants and direct observation of city streets to assess aspects of community life such as collective efficacy, the density of kin networks, and social disorder. Raudenbush and Sampson (1999a) have coined the term “ecometrics” to denote the study of the reliability and validity of such assessments. Random errors of measurement will attenuate the associations between these assessments and key outcomes. To address this problem, some studies have used empirical Bayes methods to reduce such biases, while assuming that neighborhood random effects are statistically independent. In this paper we show that the precision and validity of ecometric measures can be considerably improved by exploiting the spatial dependence of neighborhood social processes within the framework of empirical Bayes shrinkage. We compare three estimators of a neighborhood social process: the ordinary least squares estimator (OLS), an empirical Bayes estimator based on the independence assumption (EBE), and an empirical Bayes estimator that exploits spatial dependence (EBS). Under our model assumptions, EBS performs better than EBE and OLS in terms of expected mean squared error loss. The benefits of EBS relative to EBE and OLS depend on the magnitude of spatial dependence, the degree of neighborhood heterogeneity, as well as neighborhood's sample size. A cross-validation study using the original 1995 data from the Project on Human Development in Chicago Neighborhoods and a replication of that survey in 2002 show that the empirical benefits of EBS approximate those expected under our model assumptions; EBS is more internally consistent and temporally stable and demonstrates higher concurrent and predictive validity. A fully Bayes approach has the same properties as does the empirical Bayes approach, but it is preferable when the number of neighborhoods is small.
Methodological attempts to limit accumulated random errors when measuring neighborhood social and physical environments are better handled by empirical Bayes estimators that exploit spatial dependence than by the typical Bayes methods. Typical Bayes estimators assume that the variables of interest are independently distributed across neighborhoods, but this is implausible given the spatial contiguity of neighborhoods. Three estimators of a neighborhood social process are tested using a theoretical model, the ordinary least squares estimator (OLS), an empirical Bayes estimator using the independence assumption (EBE), and an empirical Bayes estimator which exploits spatial dependence between neighborhoods (EBS). The proposed EBS shows greater precision and predictive validity of the true parameter than the other two estimators, performing better in the expected mean-squared error loss. A cross-validation study on collective efficacy in Chicago neighborhoods then verified these results with real data. Compared to the other two estimators, measures based on EBS were less vulnerable to inconsistency in small sample sizes and had higher temporal instability, construct validity, and predictive validity. The superiority of EBS to the other estimators was found to be largest when spatial dependence is large, and within-neighborhood sample sizes are small. This methodology could be useful when studying social processes impacted by neighborhood public space, e.g., collective efficacy or social and physical disorder.
Description of method used in the article
A first-order Markov model within a linear model with normal-theory random effects was created to test the performance in reducing accumulated errors of three estimators of a neighborhood social process. When estimating a neighborhood's latent variable, the proposed empirical Bayes estimator exploits spatial dependence in borrowing strength, the more typical empirical Bayes estimator assumes neighborhoods to be exchangeable in borrowing strength, and the ordinary least squares estimator relies solely on the information from each neighborhood. The theoretical tests of these estimators compared the expected mean-squared error of measurement. The empirical evidence comes from a cross-validation study using two waves of data on collective efficacy from the Project on Human Development in Chicago Neighborhoods (PHDCN) collected in 1995 and 2002. The three estimators were tested on their performance with respect to squared error loss when within-neighborhood sample sizes are small, for temporal stability between waves, for estimating correlations between collective efficacy and concurrently measured census data, and for predicting future crime in the neighborhoods with collective efficacy measures.
Of some practical use if combined with other research