Hierarchical additive modeling of nonlinear association with spatial correlations--an application to relate alcohol outlet density and neighborhood assault rates.
Previous studies have suggested a link between alcohol outlets and assaults. In this paper, we explore the effects of alcohol availability on assaults at the census tract level over time. In addition, we use a natural experiment to check whether a sudden loss of alcohol outlets is associated with deeper decreasing in assault violence. Several features of the data raise statistical challenges: (1) the association between covariates (for example, the alcohol outlet density of each census tract) and the assault rates may be complex and therefore cannot be described using a linear model without covariates transformation, (2) the covariates may be highly correlated with each other, (3) there are a number of observations that have missing inputs, and (4) there is spatial association in assault rates at the census tract level. We propose a hierarchical additive model, where the nonlinear correlations and the complex interaction effects are modeled using the multiple additive regression trees and the residual spatial association in the assault rates that cannot be explained in the model are smoothed using a conditional autoregressive (CAR) method. We develop a two-stage algorithm that connects the nonparametric trees with CAR to look for important covariates associated with the assault rates, while taking into account the spatial association of assault rates in adjacent census tracts. The proposed method is applied to the Los Angeles assault data (1990-1999). To assess the efficiency of the method, the results are compared with those obtained from a hierarchical linear model.
Yu
Qingzhao
Q
Biostatistics Program, School of Public Health, LSU Health Science Center, 1615 Poydras Street, New Orleans, LA 70112, U.S.A. qyu@lsuhsc.edu
Li
Bin
B
Scribner
Richard Allen
RA
D000293:Adolescent; D000328:Adult; D000367:Age Factors; D000428:Alcohol Drinking / Q000453:epidemiology; D000434:Alcoholic Beverages / Q000600:supply & distribution*; D000465:Algorithms; D003132:Commerce / Q000706:statistics & numerical data*; D003710:Demography; D006801:Humans; D015141:Los Angeles; D008297:Male; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011203:Poverty / Q000706:statistics & numerical data; D044469:Racial Groups / Q000706:statistics & numerical data; D012044:Regression Analysis; D012111:Residence Characteristics / Q000706:statistics & numerical data*; D012737:Sex Factors; D018709:Statistics, Nonparametric; D014754:Violence / Q000706:statistics & numerical data*; D055815:Young Adult