Abstract

The spatial random effects model is popular in analyzing spatially referenced data sets. The model includes spatially observed covariates and unobserved spatial random effects. If spatial confounding between covariates and random effects is ignored, parameter estimation and spatial prediction would be inaccurate. In this research, we focus on discussing the estimation of regression coefficients and the selection of covariates for spatial regression when existing unmeasured confounders. First, we introduce an adjusted estimation method for regression coefficients and the consequent spatial predictor in the presence of spatial confounding. From a prediction point of view, we then propose a generalized conditional Akaike information criterion to select a subset of covariates, resulting in satisfactory variable selection and spatial prediction. Statistical inferences of the proposed methodology are justified theoretically and numerically.

摘要

空间随机效应模型在分析空间参考数据集时很流行。该模型包括空间观察到的协变量和未观察到的空间随机效应。如果忽略协变量和随机效应之间的空间混杂，参数估计和空间预测将不准确。在本研究中，我们重点讨论存在未测量混杂因素时回归系数的估计和空间回归协变量的选择。首先，我们介绍了回归系数的调整估计方法以及空间混杂情况下的空间预测因子。从预测的角度来看，我们随后提出了一个广义条件 Akaike 信息准则来选择协变量的子集，从而实现令人满意的变量选择和空间预测。