Mixed Generalized Akaike Information Criterion for Small Area Models
提出并验证了一种新的混合广义赤池信息准则xGAIC，用于小区域模型选择，通过模拟和两个实际应用（就业估计和吸烟率）展示了其良好性能。
Summary A mixed generalized Akaike information criterion xGAIC is introduced and validated. It is derived from a quasi-log-likelihood that focuses on the random effect and the variability between the areas, and from a generalized degree-of-freedom measure, as a model complexity penalty, which is calculated by the bootstrap. To study the performance of xGAIC, we consider three popular mixed models in small area inference: a Fay–Herriot model, a monotone model and a penalized spline model. A simulation study shows the good performance of xGAIC. Besides, we show its relevance in practice, with two real applications: the estimation of employed people by economic activity and the prevalence of smokers in Galician counties. In the second case, where it is unclear which explanatory variables should be included in the model, the problem of selection between these explanatory variables is solved simultaneously with the problem of the specification of the functional form between the linear, monotone or spline options.