Conditional Model Selection in Mixed-Effects Models with cAIC4

Abstract

Model selection in mixed models based on the conditional distribution is appropriate for many practical applications and has been a focus of recent statistical research. In this paper we introduce the R package cAIC4 that allows for the computation of the conditional Akaike information criterion (cAIC). Computation of the conditional AIC needs to take into account the uncertainty of the random effects variance and is therefore not straightforward. We introduce a fast and stable implementation for the calculation of the cAIC for (generalized) linear mixed models estimated with lme4 and (generalized) additive mixed models estimated with gamm4. Furthermore, cAIC4 offers a stepwise function that allows for an automated stepwise selection scheme for mixed models based on the cAIC. Examples of many possible applications are presented to illustrate the practical impact and easy handling of the package.

Keywords

• conditional AIC
• lme4
• mixed-effects models
• penalized splines