Conditional Akaike information criterion for generalized linear mixed models

In this study, a model identification instrument to determine the variance component structure for generalized linear mixed models (glmmglmms) is developed based on the conditional Akaike information (caicai). In particular, an asymptotically unbiased estimator of the caicai (denoted as caicccaicc) is derived as the model selection criterion which takes the estimation uncertainty in the variance component parameters into consideration. The relationship between bias correction and generalized degree of freedom for glmmglmms is also explored. Simulation results show that the estimator performs well. The proposed criterion demonstrates a high proportion of correct model identification for glmmglmms. Two sets of real data (epilepsy seizure count data and polio incidence data) are used to illustrate the proposed model identification method.