Effective transformation-based variable selection under two-fold subarea models in small area estimation

We present a simple yet effective variable selection method for the two-fold nested subarea model, which generalizes the widely-used Fay-Herriot area model. The twofold subarea model consists of a sampling model and a linking model, which has a nested-error model structure but with unobserved responses. To select variables under the two-fold subarea model, we first transform the linking model into a model with the structure of a regular regression model and unobserved responses. We then estimate an information criterion based on the transformed linking model and use the estimated information criterion for variable selection. The proposed method is motivated by the variable selection method of Lahiri and Suntornchost (2015) for the Fay-Herriot model and the variable selection method of Li and Lahiri (2019) for the unit-level nested-error regression model. Simulation results show that the proposed variable selection method performs significantly better than some naive competitors, especially when the variance of the area-level random effect in the linking model is large.