具空间相关性之非线性关联之阶层加性模式-应用于酒品出口密度与邻近攻击率之关联
Hierarchical Additive Modeling of Nonlinear Association with Spatial Correlations-An Application to Relate Alcohol Outlet Density and Neighborhood Assault Rates
摘要：
以前的研究表明，酒精出口和攻击性暴力之间存在联系。在本文中，我们探讨了随着时间的推移，在人口普查区一级的酒精供应对攻击性犯罪的影响。统计分析受到数据的几个特征的挑战：（1）可能的协变量（例如，每个人口普查区的酒精出口密度）对攻击性犯罪率的影响可能是复杂的;（2）协变量可能彼此高度相关;（3）数据中有很多缺失的输入;（4）结果攻击性犯罪率存在空间相关性。我们提出了一个分层加性模型，其中的非线性相关性和复杂的相互作用的影响建模使用的多重加性回归树（MART）和空间方差的攻击率，不能解释指定的协变量是平滑槽的条件自回归（CAR）模型。我们开发了一个两阶段的算法，将非参数树与CAR连接起来，寻找与攻击性犯罪率相关的重要变量协变量，同时考虑到相邻人口普查区域之间的空间相关性。利用1990-1999年洛杉矶市的实际数据进行了验证，并与传统方法进行了比较。
英文摘要：
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.
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