[R-sig-ME] conditional AIC (cAIC) for lmer

Corey Sparks corey.sparks at utsa.edu
Wed May 7 16:14:47 CEST 2014

Hi John,
in the arm library, the display() function will give you a DIC for lmer models. The DIC is usually for fully bayesian models, but the models in lmer are just using approximations to the posterior distributions of the random effects, instead of MCMC sampling, so it’s still a valid method for model comparison and won’t make the assumptions about model degrees of freedom like the AIC reported in lme4:::summary.merMod.


Subject: [R-sig-ME] conditional AIC (cAIC) for lmer
	<2547E22D246F3945BB491BDD8257C2E77F03ACCF at exmbx06-cdc.nexus.csiro.au>
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I would like to calculate the conditional AIC (cAIC) to compare a series of mixed models with different random effects structures for the purpose of ecological inference (method as per Vaida and Blanchard 2005 & Greven and Kneib 2010). I am using lme4 1.1-6 in R 3.1.0. Greven and Kneib provide a package for nlme; I got in touch with them directly and an lme4 version will likely be available later this year. I do, however, have a little bit more of a finite deadline and I was wondering if anyone else has developed a function to do this that works in the latest version of lme4? 

Kyle Edwards posted a function in 2008 (http://r.789695.n4.nabble.com/Using-Conditional-AIC-with-lmer-td847899.html) but this no longer works as the function 'hatTrace' is no longer available (http://r.789695.n4.nabble.com/Function-hatTrace-in-package-lme4-td4646071.html). In the package 'phmm' there is a 'cAIC' function but this doesn't work for lmer models.

Doing sequential likelihood ratio tests is another option, and I have seen some papers using DIC (which I thought was a Bayesian technique so not really applicable to a lmer model). I guess I could report AIC values and note that they are biased in this case due to issues around calculating degrees of freedom, but if there is a better option (e.g. cAIC) I'd prefer to go with that. 

Thanks for your time


Corey Sparks
Assistant Professor
Department of Demography
The University of Texas at San Antonio
501 West Cesar E Chavez Blvd
corey.sparks 'at' utsa.edu
210 458 3166

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