# Alternatives to stepwise regression for generalized linear mixed models

Are there any easy to use alternatives to stepwise variable selection for GLMMs? I have seen implementations of e.g. LASSO for linear regression, but so far not seen anything for mixed models. Mixed models seem non-trivial in general, so I am wondering if any of the fancy new methods have been adapted from them (and possibly implemented in R). Using whatever selection procedure you like and then validating the results seems a sensible way to go in the meantime.

To give some context: in my current project, I am looking at approximately 700 variables and 5000 binary observations. Stepwise selection takes about 1 day; many variables have about 10% missingness.

Edit: Thank you for the very interesting answers so far! Two concerns that I have are: do these new methods have longer runtimes than stepwise selection and can they deal with missing data (if each variable has different missingness, than for hundreds of variables it is very easy to loose all observations in a complete case analysis - something that stepwise selection can deal with by only using small subsets of the available variables at the same time).

• Look a bit closer: glmmLasso exists. – usεr11852 Sep 30 '15 at 23:51
• Thank you @usεr11852 . It is great to know this method exists. It seems to be very fast (compared to stepwise selection). However, unlike stepwise selection it limits us to a complete case analysis, which can be a problem when using a large number of variables with different missingness. I did get a "Fisher matrix not invertible" error, but my design matrix might be rank-deficient. If you do have suggestions to avoid a complete case analysis (by only looking at small subsets of the variables at the same time), please let me know. Also, please feel free to convert this to an answer. – Rob Hall Oct 1 '15 at 18:47
• To solve the missing data problem, consider multiple imputation. This paper provides a way to combine multiple imputation with LASSO; on first glance it seems that it should work with glmmLasso as well but may take some effort to implement. Alternatively, see if you can combine your 700 variables into a smaller set based on subject-matter knowledge, to minimize the missing-data problem. – EdM Oct 1 '15 at 19:09
• @EdM thank you for the very interesting article. I have so far avoided MI as my particular goal is prediction rather than inference (and stakeholders have some concerns about a large amount of imputation). At first glance, the paper seems to involve imputing in the usual fashion, then doing LASSO in the usual fashion and then aggregating results in a novel fashion, so it might be compatible with existing implementations. This looks like it might enable me to solve my problem if I can get it all to work. – Rob Hall Oct 1 '15 at 19:17