Mixed Generalized Akaike Information Criterion for Small Area Models

Abstract

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.

Model selection in linear mixed-effect models

“…found that both the McAIC and a model averaging procedure (which has more appropriate weights) depending on McAIC, work better than cAIC in terms of prediction errors. They prove empirically the same results in the case of small area prediction, which is the topic on which and Lombardía et al (2017) focus on. They show, therefore, a prediction error improvement of CScAIC with respect to cAIC.…”

“…when σ 2 is unknown and estimated by its ML estimator and B * c is the bias correction. Lombardía et al (2017) introduce a mixed generalized Akaike information criterion, xGAIC, for SAE models. One typical model used in the field of SAE is the Fay-Herriot model, which is a particular type of LMMs containing only one random effect, the intercept.…”

“…These results constitute empirical evidence of the consistency property of the EBIC. Lombardía et al (2017), instead, compared the extended generalized AIC they defined (20) with the conditional AIC defined by Vaida and Blanchard (2005). They discovered that the xGAIC for the Fay-Herriot model presents better performances in terms of correct classification rates of the true model.…”

“…The main purpose of the study was to analyze which proteins had a significant influence on the longitudinal trajectory of renal function measured by glomerular filtration rate (GFR) of the patients. Lombardía et al (2017) analyzed a dataset about surveys conducted from the behavioral risk factors information system in Galicia (2010-2011). The sample design applied in the survey was a stratified random sampling, allocating with equal proportions by sex and age group.…”

Artificial Intelligence Based Commercial Risk Management Framework for SMEs

“…The prediction quality could be measured using various criteria, for instance, Akaike's Information Criterion (AIC)-"in general terms, the value of AIC for a model M is defined as AIC(M) = −2 log {l(M)} + 2D, where l(M) is the model likelihood and D is a penalty term, which was originally equal to the number of parameters in the model, p" [75]. Another alternative is Corrected Akaike's Information Criterion (CAIC)-a bias-corrected version of AIC for a small number of observations used for estimation [74].…”