Conditional Akaike information under generalized linear and proportional hazards mixed models

We 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...

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Bibliographic Details
Published in:Biometrika 2011-09, Vol.98 (3), p.685-700
Main Authors: DONOHUE, M. C., OVERHOLSER, R., XU, R., VAIDA, F.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic methods
Bootstrap method
Cancer
Cluster analysis
Data processing
Degrees of freedom
Inference
Linear programming
Mathematical models
Maximum likelihood estimation
Maximum likelihood estimators
Modeling
Multilevel models
Simulations
Skin cancers
Statistical variance
Studies
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Summary:We 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 cluster-specific inference is of interest.
ISSN:0006-3444
1464-3510
1464-3510
0006-3444
DOI:10.1093/biomet/asr023