Performance of Information Criteria for Spatial Models.

Model choice is one of the most crucial aspect in any statistical data analysis. It is well known that most models are just an approximation to the true data generating process but among such model approximations it is our goal to select the "best" one. Researchers typically consider a finite number of plausible models in statistical applications and the related statistical inference depends on the chosen model. Hence model comparison is required to identify the "best" model among several such candidate models. This article considers the problem of model selection for spatial data. The issue of model selection for spatial models has been addressed in the literature by the use of traditional information criteria based methods, even though such criteria have been developed based on the assumption of independent observations. We evaluate the performance of some of the popular model selection critera via Monte Carlo simulation experiments using small to moderate samples. In particular, we compare the performance of some of the most popular information criteria such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected AIC (AICc) in selecting the true model. The ability of these criteria to select the correct model is evaluated under several scenarios. This comparison is made using various spatial covariance models ranging from stationary isotropic to nonstationary models.