# Interpretation of mixed-effects versus GEE poisson/logit regression parameters

What's the difference in the interpretation of the model parameters (intercept +slope) in the mixed-effects model and GEE model for poisson and logistic regression?

In models with nonlinear link functions there is indeed a difference in the interpretation of the regression coefficients in GEEs and mixed-effects models. In short,

• GEEs give you the more usual interpretation of comparing groups of subjects. E.g., for dichotomous outcomes and the logit link you get the log-odds ratio between the group of males and the group of females.
• Mixed-effects models give an interpretation conditional on the random effects. E.g., again for dichotomous outcomes and the logit link you get the log-odds ratio if a particular subject would changed sex and from a male he/she became a female.

Because of this more strange interpretation of mixed models with categorical outcomes, people have been suggesting that GEEs are more practical. Nonetheless, GEEs suffer more when you have missing data.

Recently, there has been a solution proposed to bridge the two worlds. Namely, from a mixed model to get coefficients with a marginal interpretation as in GEEs. This is available in the function marginal_coefs() in the GLMMadaptive package; for more information check here.

Additional discussion on this point available also here and here.

• Is GLMMadaptive good for inference? That is, unbiased estimation? How are parameters estimated? Maximum likelihood or REML or score? – user271077 Jan 19 '20 at 11:41
• Yes, it is unbiased. – Dimitris Rizopoulos Jan 19 '20 at 11:51
• For which parameters and models can GLMMadaptive provide unbiased estimates? – JTH Jan 19 '20 at 14:30
• @JTH to be more precise, GLMMadaptive as other packages that fit mixed models in R (e.g., lme4 and glmmTMB) uses maximum likelihood. This procedure provides asymptotically unbiased estimates for all model parameters. For small samples, you will have some bias. For example, this is the case even for simple logistic regression. GLMMadaptive uses by default the adaptive Gaussian quadrature approach, which is more accurate than the Laplace approximation provided in the other packages. – Dimitris Rizopoulos Jan 19 '20 at 14:56
• Here's a link to the free PubMedCentral version of the Hedeker et al. article @DimitrisRizopoulos referred to. ncbi.nlm.nih.gov/pmc/articles/PMC5650580 – Erik Ruzek Jan 19 '20 at 22:30