Conditional Akaike information under generalized linear and proportional hazards mixed models

Abstract

SUMMARYWe study model selection for clustered data, when the focus is on cluster specific inference. Such data are often modelled using random effects, and conditional Akaike information was proposed in Vaida & Blanchard (2005) and used to derive an information criterion under linear mixed models. Here we extend the approach to generalized linear and proportional hazards mixed models. Outside the normal linear mixed models, exact calculations are not available and we resort to asymptotic approximations. In the presence of nuisance parameters, a profile conditional Akaike information is proposed. Bootstrap methods are considered for their potential advantage in finite samples. Simulations show that the performance of the bootstrap and the analytic criteria are comparable, with bootstrap demonstrating some advantages for larger cluster sizes. The proposed criteria are applied to two cancer datasets to select models when the clusterspecific inference is of interest.Some key words: Akaike information; Conditional likelihood; Effective degrees of freedom.

Choice of generalized linear mixed models using predictive crossvalidation

“…They note, however, that their asymptotic approximation may not be reliable in certain settings and propose using bootstrap methods instead. An asymptotically unbiased estimator of the cAIC for use with generalized linear mixed models is presented ( [42]), which seems to be quite similar to the above mentioned approximation ( [13]). Another unbiased estimator of the cAIC to be used for Poisson regression models is proposed, which involves a high number of model fits and might thus be unsuitable for large data sets ( [25]) .…”

“…For each model we calculated the mean LS and the mean BS or DSS, respectively. For comparison, the conditional AIC (cAIC, [13]) was calculated. Note that in some cases the estimated covariance matrix of the random effects was singular and thus not invertible.…”

“…An analytic deduction of the cAIC is impossible ( [13]), but the authors suggest an asymptotic approximation which includes the effective degrees of freedom ( [27]). They note, however, that their asymptotic approximation may not be reliable in certain settings and propose using bootstrap methods instead.…”

Bayesian adaptive lasso with variational Bayes for variable selection in high-dimensional generalized linear mixed models

“…Donohue et al (2011) argue that treament is not significant and consider 5 different Poisson mixed models with different inclusion of the rest 5 covariates. By using an AIC-type model selection criterion, Donohue et al (2011) We consider the variable selection problem for this Poisson mixed regression model with a random intercept. We consider all the 6 potential covariates age, skin, gender, exposure, treament and year.…”

“…We consider all the 6 potential covariates age, skin, gender, exposure, treament and year. Our method selects the same model as selected by Donohue et al (2011). The estimate of vector β is (−24.609, 0.008, 0.350, 1.579, 0.854, 0, 0), and the estimate of the random effect standard deviation σ is 102.7.…”