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Previous studies have suggested a link between alcohol outlets and assaultiveviolence. In this paper, we explore the effects of alcohol availability onassault crimes at the census tract level over time. The statistical analysis ischallenged by several features of the data: (1) the effects of possiblecovariates (for example, the alcohol outlet density of each census tract) onthe assaultive crime rates may be complex; (2) the covariates may be highlycorrelated with each other; (3) there are a lot of missing inputs in the data;and (4) spatial correlations exist in the outcome assaultive crime rates. Wepropose a hierarchical additive model, where the nonlinear correlations and thecomplex interaction effects are modeled using the multiple additive regressiontrees (MART) and the spatial variances in the assaultive rates that cannot beexplained by the specified covariates are smoothed trough the ConditionalAutoregressive (CAR) model. We develop a two-stage algorithm that connect thenon-parametric trees with CAR to look for important variables covariatesassociated with the assaultive crime rates, while taking account of the spatialcorrelations among adjacent census tracts. The proposed methods are applied tothe Los Angeles assaultive data (1990-1999) and compared with traditionalmethod.

Hierarchical Additive Modeling of Nonlinear Association with Spatial  Correlations-An Application to Relate Alcohol Outlet Density and Neighborhood  Assault Rates