[R] mixed-effects models with (g)lmer in R and model selection

[Don McKenzie]

This is a complicated and subtle statistical issue, not an R question, the latter being the purpose of this list.  There are people on the list who could give you literate answers,
to be sure, but a statistically oriented list would be a better match.

e.g., 

http://stats.stackexchange.com/


> On Feb 19, 2016, at 5:01 AM, Wilbert Heeringa <wjheeringa at gmail.com> wrote:
> 
> Dear all,
> 
> Mixed-effects models are wonderful for analyzing data, but it is always a
> hassle to find the best model, i.e. the model with the lowest AIC,
> especially when the number of predictor variables is large.
> 
> Presently when trying to find the right model, I perform the following
> steps:
> 
>   1.
> 
>   Start with a model containing all predictors. Assuming dependent
>   variable X and predictors A, B, C, D, E, I start with: X~A+B+C+D+E
>   2.
> 
>   Lmer warns that is has dropped columns/coefficients. These are variables
>   which have a *perfect* correlation with any of the other variables or
>   with a combination of variables. With summary() it can be found which
>   columns have been dropped. Assume predictor D has been dropped, I continue
>   with this model: X~A+B+C+E
>   3.
> 
>   Subsequently I need to check whether there are variables (or groups of
>   variables) which *strongly* corrrelate to each other. I included the
>   function vif.mer (developed by Austin F. Frank and available at:
>   https://raw.github.com/aufrank/R-hacks/master/mer-utils.R) in my script,
>   and when applying this function to my reduced model, I got vif values for
>   each of the variables. When vif>5 for a predictor, it probably should be
>   removed. In case multiple variables have a vif>5, I first remove the
>   predictor with the highest vif, then re-run lmer en vif.mer. I remove again
>   the predictor with highest vif (if one or more predictors have still a
>   vif>5), and I repeat this until none of the remaining predictors has a
>   vif>5. In case I got a warning "Model failed to converge" in the larger
>   model(s), this warning does not appear any longer in the 'cleaned' model.
>   4.
> 
>   Assume the following predictors have survived: A, B en E. Now I want to
>   find the combination of predictors that gives the smallest AIC. For three
>   predictors it is easy to try all combinations, but if it would have been 10
>   predictors, manually trying all combinations would be time-consuming. So I
>   used the function fitLMER.fnc from the LMERConvenienceFunctions package.
>   This function back fit fixed effects, forward fit random effects, and
>   re-back fit fixed effects. I consider the model given by fitLMER.fnc as the
>   right one.
> 
> I am not an expert in mixed-effects models and have struggled with model
> selection. I found the procedure which I decribed working, but I would
> really be appreciate to hear whether the procedure is sound, or whether
> there are better alternatives.
> 
> Best,
> 
> Wilbert
> 
> 	[[alternative HTML version deleted]]
> 
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