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.