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

TL;DR

This paper introduces a hierarchical additive modeling approach combining MART and CAR models to analyze complex, spatially correlated data on assault rates and alcohol outlet density, addressing missing data and covariate interactions.

Contribution

The paper develops a novel two-stage hierarchical additive model integrating MART and CAR to handle complex nonlinear, spatial, and correlated data in crime analysis.

Findings

Model effectively captures nonlinear effects of covariates.

Incorporates spatial correlations to improve accuracy.

Outperforms traditional methods in real data application.

Abstract

Previous studies have suggested a link between alcohol outlets and assaultive violence. In this paper, we explore the effects of alcohol availability on assault crimes at the census tract level over time. The statistical analysis is challenged by several features of the data: (1) the effects of possible covariates (for example, the alcohol outlet density of each census tract) on the assaultive crime rates may be complex; (2) the covariates may be highly correlated 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. We propose a hierarchical additive model, where the nonlinear correlations and the complex interaction effects are modeled using the multiple additive regression trees (MART) and the spatial variances in the assaultive rates that cannot be explained by the specified covariates are smoothed trough the Conditional Autoregressive (CAR) model. We develop a two-stage algorithm that connect the non-parametric trees with CAR to look for important variables covariates associated with the assaultive crime rates, while taking account of the spatial correlations among adjacent census tracts. The proposed methods are applied to the Los Angeles assaultive data (1990-1999) and compared with traditional method.