I know what fixed and random effects in linear models or GLM are. I am using Generalized Linear Mixed Models (GLMM) to handle this. So far, so good.

One point worries me, for months actually. In all textbooks, all websites, etc., GLMM is presented as a method to handle non-independent, correlated data. However, the word "mixed" means that you are handling both fixed and random effects, which is indeed the usual case with non-independent data.

The point is that you can have non-independent data without random effect at all. For example, you want to compare the response between males and females (sex: a fixed factor), before or after (another fixed factor, defining subjects) a treatment.

Reciprocally, you can have non-independent data without fixed effect at all. For example, you might be willing to compare the response of people in a couple of different countries (a random factor) and in a couple of different regions (another random factor) in each country.

In these two (fake) examples, and whatever the distribution of the response variable (and the link function you use), the fitted models are not "Mixed" at all, so I actually do not see why these models are actually called "Generalized Linear Mixed Models".

I guess I am missing an important point here. And, if someone could explain this, this would be of great help.

Thanks in advance for this.

Cheers, Eric.