The glmer function from the lme4 package in R is capable of (mixed) modeling for Gaussian, Poisson, Beta, Gamma, and other distributions.

Check out this FAQ page for GLMMs (lme4): https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#introduction

Tricky!

Multiple outcomes modeled simultaneously through a multilevel models. This is not commonly done. Both nlme and lme4 cannot do this at the moment according to Scott A. Baldwin et al., 2014. They do recommend to use MCMCglmm. Please refer to that work (pay attention to the supplementary materials where code is provided for SPSS, SAS, Stata and R).

Baldwin, S. A., Imel, Z. E., Braithwaite, S. R., & Atkins, D. C. (2014). Analyzing multiple outcomes in clinical research using multivariate multilevel models. Journal of Consulting and Clinical Psychology, 82(5), 920–930. https://doi.org/10.1037/a0035628

Orvalho Augusto ,I hope you got my question. Beside to this, what are the assumptions given to MCMCglmm? May i have more clarification. I appreciate your help.

Well, there is one particular form of the co-variance matrix of the residuals errors from the multiple outcomes required for this to work. Both packages at the moment do not support that form. So the recommendation according to that manuscript is to implement the model in a Bayesian methods.

What do you mean by "more than"? Outcomes other than binary? Then "glmer()" or maybe the glmmTMB-package might be what you are looking for.

If you mean "multiple response" or "multivariate response" models, I suggest looking at the "brms"-package, which is highly flexible and allows to fit many types of (mixed effects) models, including multivariate response models (see e.g. https://cran.r-project.org/web/packages/brms/vignettes/brms_multivariate.html). Note that brms is fully Bayesian, interfacing "Stan" from R. The syntax is very similar to lme4, but knowing at least some Bayesian basics is helpful if you use brms.

Thank you Daniel Lüdecke, brms and MCMCglmm would it. In fact, the link you provided for brms is using the same example as on MCMCglmm vignette.

Mollalign Yizengaw,

Daniel Lüdecke ask a question to which I am now curious...

'What do you mean by "more than"?'

Orvalho Augusto replies as if you are asking "Is there an R package available which would allow for modeling of multiple responses with differing (error) distributions?" I understood your question to be "Can the glmer function, within the R package lme4, model responses other than binary?"

Can you provide some clarity? It would likely improve the responses, or at least their focus.

Caleb A. Aldridge , Daniel Lüdecke , Orvalho Augusto

Thank you for your active participation.

For the question" more than binary response" means just focusing on multiple response with different error distributions. Let me explain more.

In travel mode choice survey, people can have many opportunities to choose the travel mode like bicycle, motorcycle, private car, public bus..and so on. In this case, the response variable for the mode they choose is multiple response. I was asking you on how to do generalized linear mixed effect models with such multiple response with different error distribution in R and what kind of packages will be employed?

But, as we know, binary response is either 0 or 1 for the case of specified question with two responses only.

I Hope, it is clear now.

maybe the following link can be helpful:

https://stats.stackexchange.com/questions/319427/mixed-model-with-categorical-response-variable