A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models

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Abstract

The conditional Akaike information criterion, AIC, has been frequently used for model selection in linear mixed models. We develop a general framework for the calculation of the conditional AIC for different exponential family distributions. This unified framework incorporates the conditional AIC for the Gaussian case, gives a new justification for Poisson distributed data and yields a new conditional AIC for exponentially dis- tributed responses but cannot be applied to the binomial and gamma distri- butions. The proposed conditional Akaike information criteria are unbiased for finite samples, do not rely on a particular estimation method and do not assume that the variance-covariance matrix of the random effects is known. The theoretical results are investigated in a simulation study. The practical use of the method is illustrated by application to a data set on tree growth.

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Saefken, B., Kneib, T., van Waveren, C. S., & Greven, S. (2014). A unifying approach to the estimation of the conditional Akaike information in generalized linear mixed models. Electronic Journal of Statistics, 8(1), 201–225. https://doi.org/10.1214/14-EJS881

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