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I have database with missing values (NA) so that it is theoretically not possible to use AIC (or AICc) to weight models with different sample size.

Would using Bayesian Information Criterion (BIC) account for this problem?

Alternatively I am thinking of using the "full-information maximum likelihood", but I cannot find a library in R that runs linear mixed models with this method.

Yet another alternative could be to use an imputation model such as MICE to "fill up" missing values (NAs).

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You have mixed a couple of different topics and it is not clear what you mean by it not being theoretically possible to use AIC/AICc in your situation (it is not clear what exactly the issue is). So, let me try to split this up into the three main topics:

Firstly, AIC, AICc and BIC are all unsuitable for comparing models that are run on different datasets (whether they have different sample sizes or not). They are only relative measures that can be compared on the exact same data.

Secondly, missing data are not per-se a reason for why AIC, AICc or BIC could not be used. You already point out one of the approaches that would allow that on the very next paragraph (using some form of generalized linear mixed effects model (GLMM)). And the approach of using multiple imputation in some form is typically equivalent (assuming the GLMM exactly matches the imputation model and enough imputations are done). For how to get AIC or similar measures after multiple imputation, you really just need to google something like +"Model selection" +"model averaging" +"after multiple imputation".

Thirdly, regarding software implementation there are a lot of options for fitting GLMMs. Since you asked about R, the lme4 package would be an option and there are almost certainly other ones, while in SAS you could use PROC MIXED.

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  • $\begingroup$ Sorry if I didn't make it clear enough, I am not familiar dealing with modelling issues. I do have only a dataset, but some of the variables have missing values. Say we have two variables (A and B) potentially explaining X, the whole dataset is 100 lines, but B has 25 missing values. So when I try different models, say "model1<-lmer(X ~ A)" and "model2<-lmer(X ~ A+B)", model1 sample size is 100, but that of model2 is 75, I understand from you answer that the models are not comparable using AIC or BIC, so the only solution for comparison is to use imputation first, correct? $\endgroup$
    – Chagalapoli
    Aug 18, 2017 at 2:15

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