Spatial regression models have a variety of applications in several fields ranging from economics to public health. Typically, it is of interest to select important exogenous predictors of the spatially autocorrelated response variable. In this paper, we propose variable selection in linear spatial lag models by means of the focussed information criterion (FIC). The FIC-based variable selection involves the minimization of the asymptotic risk in the estimation of a certain parametric focus function of interest under potential model misspecification. We systematically investigate the key asymptotics of the maximum likelihood estimators under the sequence of locally perturbed mutually contiguous probability models. Using these results, we obtain the expressions for the bias and the variance of the estimated focus leading to the desired FIC formula. We provide practically useful focus functions that account for various spatial characteristics such as mean response, variability in the estimation and spatial spillover effects. Furthermore, we develop an averaged version of the FIC that incorporates varying covariate levels while evaluating the models. The empirical performance of the proposed methodology is demonstrated through simulations and real data analysis.

翻译：空间回归模型在经济学、公共卫生等多个领域具有广泛应用。通常，研究者关注如何从空间自相关响应变量中筛选重要的外生预测因子。本文提出通过聚焦信息准则（FIC）实现线性空间滞后模型的变量选择。基于FIC的变量选择旨在最小化在可能模型误设情况下，对特定关注的参数聚焦函数进行估计时的渐近风险。我们系统研究了在局部扰动且相互邻接的概率模型序列下，最大似然估计量的关键渐近性质。利用这些结果，推导出估计聚焦函数的偏差与方差表达式，进而得到所需的FIC公式。我们提供了具有实践价值的聚焦函数，这些函数能够综合考虑均值响应、估计变异性和空间溢出效应等多种空间特征。此外，我们发展了FIC的加权平均版本，该版本在模型评估时融入了不同协变量水平的影响。通过模拟实验与真实数据分析，验证了所提方法的实证性能。