Generalized Linear Mixed Models without mixed effects. A meaningless question?

[eric1708]

Hi there,

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.

 

[hlsmith]

Yes, I know what you are talking about. If they don't have mixed effects then it is not a mixed effects model.

Perhaps the confusions comes, at times, from what procedure they are using in their software. I can use a mixed effects procedure (e.g., SAS: proc glimmix), try to design the model and end up with out any significant fixed or perhaps random effects. However, I still take the results from the procedure, since you can run a only fixed or perhaps random effects model and the procedure is still controlling for the levels or design (multiple measurements). Then when these results get presented, it appears that the person may have ran a mixed model. I am trying to get better at this, but when presenting your final model you should state if you had random intercepts and effects and be very specific how everythiing was in the model. This way readers know exactly what you did.

Another issue is the lack of consistency in the use of modeling (multilevel, hierarchical, random..., mixed, etc.).

 

[eric1708]

Ok, thanks for the reply. Really useful. But this looks still weird to me.

Ok, let phrase this in another way around. Mixed models are presented as a method to handle non-independent, correlated data. But - in my view - they are rather for models having both random and fixed effects (that's what the word "mixed" means actually).

What I understand from the discussion above, is that mixed models can actually be sometimes not mixed (..) when there are only fixed or only random effects.

But you can also have sometimes a model that has both random and fixed effects but on data that are totally independent (i.e., non-correlated). So what is the point of presenting mixed models as models designed to handle correlated data if their real feature is rather to have both random and mixed components only. This is totally misleading in my view.

I thus still think there is something important I am missing.

Thanks again for any help on this.

Eric.

 

[hlsmith]

I started just calling some multilevel or cluster when addressing correlated observations.