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.