# Citation for deviance on generalized linear mixed-effects models

All examples I've found on deviance tests being performed are on generalized linear models. Is there something I can cite validating the use of deviance tests for generalized linear mixed-effects models with normal random effects, ideally outlining what the procedure looks like?

This is for submission for a peer-reviewed journal whose primary audience is MDs who are not statistically inclined. I am trying to justify my model selection method for inference. You can find my writeup of the situation here, except there is an additional term $$b_2\beta_{it}$$ in the model, as well as the possibility of an interation term $$b_3\alpha_{it}\beta_{it}$$. I used deviance testing to compare nested models which all contained the two random effects in that model, to justify which fixed effects to use, and whether or not to use the interaction term.

• What is your purpose for performing such a procedure ? Many things that are well defined for linear and generalised linear models do not carry across to mixed models. Oct 15, 2020 at 8:58
• @RobertLong Good question. Keep in mind this is for submission for a peer-reviewed journal whose primary audience is MDs who are not statistically inclined. I am trying to justify my model selection method for inference. You can find my writeup of the situation here, except there is an additional term $b_2\beta_{it}$. I used deviance testing to compare nested models which all contained the two random effects in that writeup, and to justify which fixed effects to use. Oct 15, 2020 at 13:25
• @RobertLong I've clarified this in the original question. Thanks. Oct 15, 2020 at 13:29
• OK I've read your other post (+1 for both btw). So, exams and students are partially crossed ? And if I've understood correctly you want to justify the inclusion of fixed effects based on some test ? Maybe I'm mising something, but why not just use a likelihood ratio test ? Oct 15, 2020 at 14:05
• That's a likelihood ratio test :) Oct 15, 2020 at 14:41