Associational and causal inference in spatial hierarchical settings: Theory and applications.

In social sciences, data structures are often hierarchical. When these data also arise in spatial settings, dependence between clusters occurs. This three-paper dissertation considers statistical issues arising in spatial hierarchical settings: modeling, measurement, and causal inference. Modeling. In paper 1, I propose a hierarchical linear model (HLM) with spatially dependent random effects (SHLM) and compare it to the standard HLM that assumes independence between clusters. SHLM parameters are estimated using maximum likelihood (ML) approach via the expectation-maximization (EM) algorithm with an embedded Fisher scoring. The theoretical results indicate that, under SHLM assumptions, HLM estimators of the fixed effects and within-cluster variance are unbiased. However, the between-cluster variance estimator is biased. The sensitivity of the results to model specifications is examined using data from the Project on Human Development in Chicago Neighborhoods (PHDCN). Furthermore, the empirical results indicate that HLM underestimates the standard errors for the fixed effects, resulting in incorrect statistical inferences. Measurement. In paper 2, I propose an empirical Bayes (EB) estimator, which exploits the spatial dependence in the data (EBS). I demonstrate that EBS dominates standard EB (EBE) and sample mean (OLS) estimators with respect to mean squared error loss under SHLM assumptions. The empirical results approximate these theoretical results: EBS dominates EBE and OLS, especially when neighborhood sample sizes are small. Using PHDCN data, I also demonstrate that the EBS estimator is better at estimating the true neighborhood means, predicting future neighborhood means, relating to theoretically-linked demographic covariates, and predicting future crime rates than EBE and OLS. Causal Inference. In paper 3, I use 1990's Chicago's personal and property crime data to evaluate the effectiveness of the community policing program (CAPS). To answer the causal questions I extend Rubin's causal framework by relaxing Cox's no interference between different units assumption. I redefine causal effects and discuss assumptions that make this framework tractable. No statistically significant effect of beat's own treatment on crime was detected. However, I found that increasing the number of contiguous neighbors assigned to CAPS leads to a moderate reduction in personal crime rates for a beat in a CAPS district.PhDPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126846/2/3276319.pd