Variable Selection for Linear Mixed Models with Applications in Small Area Estimation

Abstract

In small area estimation, linear mixed models are frequently used. Variable selection methods for linear mixed models are available. However, in many applications such as small area estimation data users often apply variable selection methods that ignore the random effects. In this paper, we first evaluate the accuracy of such variable selection method for the Fay-Herriot model, a regression model when dependent variable is subject to sampling error variability. We show that the approximation error, that is, the difference between the standard variable selection criterion and the corresponding ideal variable selection criterion without any sampling error variability, does not converge to zero in probability even for a large sample size. In our simulation, we notice that standard variable selection criterion could severely underestimate the ideal adjusted R ² and BIC variable selection criteria in presence of high sampling error variability. We propose a simple adjustment to the standard variable selection method for the Fay-Herriot model that reduces the approximation errors. In particular, we show that the approximation error for our new variable selection criteria converge to zero in probability for large sample size. Using a Monte Carlo simulation, we demonstrate that our proposed variable selection criterion tracks the corresponding ideal variable selection criterion very well compared to the standard variable selection method.