2000115-Strengthening-Communities-with-Neighborhood-Data

380 Strengthening Communities with Neighborhood Data
that has started to connect spatial statistical methods and program evaluation
leverages spatial Bayesian approaches (Banerjee, Carlin, and Gelfand
2004; Cressie and Wikle 2011). For instance, Verbitsky (2007) 13 uses
spatial Bayesian hierarchical modeling to evaluate whether Chicago’s
community policing programs displaced crime to neighboring areas. 14
Verbitsky Savitz and Raudenbush (2009) test the performance of a spatial
empirical Bayesian estimator in an application related to neighborhood
collective efficacy, which is central to research on neighborhood
effects (Sampson 2012). The spBayes package in R and WinBUGS can be
used to estimate spatial Bayesian models.
Spatial autocorrelation as discussed above (e.g., in the form of spillover
effects) can be associated with the dependent variable (Wy), independent
variables (Wx), and the error term (We) of a model. Spatial
estimators are not required when the values of an area and its neighbors
are correlated for the independent variables. However, the presence of
spatial autocorrelation in the dependent variable or error term violates
standard assumptions in classic statistics and can thus result in inconsistent
and/or biased estimates. Hence the correction of these problems
requires specialized techniques beyond traditional nonspatial methods.
Two standard linear spatial regression models that account for such spatial
dependence are called spatial lag and spatial error models in the spatial
econometrics literature (Anselin 1988).
To determine if spatial effects are present, spatial diagnostic tests
can be applied (e.g., spatial Lagrange multiplier tests to the residuals
of a standard nonspatial OLS model). These tests suggest if spatial lag
and spatial error models are a better fit for a given dataset. In spatial lag
model specifications, the dependent variable is not only a function of the
independent variables and the error term, but also of the average value
of the dependent variable of the neighboring observations of any given
observation. This model can be consistent with spatial multiplier effects.
In spatial error models, the error term is spatially correlated, which can,
for example, be related to a mismatch in scales (e.g., between the spatial
extent of concentrated poverty and the administrative boundary for
which data are available). Recent advances in the estimators of spatial lag
and error models also control for nonconstant error variance (so-called
heteroskedasticity) (Arraiz et al. 2010) or adjust OLS estimates for spatial
correlation and heteroskedasticity (Kelejian and Prucha 2007). Versions
of these methods have recently been implemented in Stata (spivreg package),
R (sphet package), PySAL 1.3, and GeoDaSpace. The Arc_Mat tool-