Conditional Akaike information criterion in the Fay-Herriot model

The Fay-Herriot model, a popular approach in small area estimation, uses relevant covariates to improve the inference for quantities of interest in small sub-populations. The conditional Akaike information (AI) (Vaida and Blanchard, 2005 [23]) in linear mixed-effect models with i.i.d. errors can be extended to the Fay-Herriot model for measuring prediction performance. In this paper, we derive the unbiased conditional AIC (cAIC) for three popular approaches to fitting the Fay-Herriot model. The three cAIC have closed forms and are convenient to implement. We conduct a simulation study to demonstrate their accuracy in estimating the conditional AI and superior performance in model selection than the classic AIC. We also apply the cAIC in estimating county-level prevalence rates of obesity for working-age Hispanic females in California. (C) 2012 Elsevier B.V. All rights reserved.