We study model selection for clustered data, when the focus is on the cluster specific inference. Such data can be modeled using random effects, and the concept of onditional Akaike information (cAI) has been proposed and used to derive a conditional Akaike information criterion (cAIC) under the linear mixed models (LMM). Here we extend the approach to the generalized linear mixed models (GLMM) and the proportional hazards mixed models (PHMM). While the derivation under the LMM used exact calculation, outside the normal linear models we have to resort to asymptotic approximations, and we believe that this approach is more generally applicable. In the presence of nuisance parameters, a profile conditional Akaike information is proposed. Resampling methods are also considered which
have been shown in the past to have good small sample properties. The proposed criteria are studied under simulation, and applied to cancer data sets fitted with these models.