Dummy variable in random effects panel regression

[Leon Schuetze]

Dear Statalist members,
I found answers to many of my Stata- or statistics-related questions before on this forum, but this specific question does not seem to have come up yet. So I hope someone can help me today, even though the question is more on regression analysis that on a problem with Stata!
From a reviewer on a paper of mine, I recieved a comment that I just do not understand.

The comment revolves around a random effects panel regression using -xtlogit.
I have a continuous dependent variable and several time-invariant independent variables for health centers like staff, service volume etc. The health centers I study are located in 19 different regions (which has an influence on my outcome), so I also control for regional variation by including each region as an independent dummy variable. I use similar word in the manuscript to describe this.

xtlogit depvar staff service_volume distance insurance_rate i.region, re vce(cluster id)

Comment by the reviewer:
"Why is region treated as a fixed factor? It has 19 categories and should therefore be treated as a random factor."

This is what I don't understand. By including region as a dummy variable, I don't make it a "fixed factor" (whatever that is), do I? Or is there anything I am missing?
Would be thankful for any insights on this since I am struggeling with replying to the comment, as is my mor eexperienced colleague.

Best regards,
Leon

[Clyde Schechter]

By including region as a dummy variable, I don't make it a "fixed factor" (whatever that is), do I?

Yes, you do. In fact, that is the definition of a "fixed factor."

And what is the random factor here? That is, what is the panel variable you used in your -xtset- command. If it is also region, then you have region entered as both fixed and random and that is just an invalid model whose results are uninterpretable. If it is something other than region, then you might consider going to a three level model and making region a true random effect.

However, I don't fully agree with the reviewer when he/she says "It has 19 categories and should therefore be treated as a random factor." While I would endorse the converse of this, if a variable has only a small number of categories it should not (usually) be used as a random factor, just because a variable has a large number of categories does not automatically make it a candidate for treatment as a random effect. The "classical" criterion for a random effect is: do you conceptualize the values of region in your data as a (random) sample drawn from a population of regions, and do you intend your results to be generalizable to the entire population of regions? This, of course, is a little vague and invites attempted mind-reading on the part of readers and reviewers. But a much more solid criterion is: do you want the results for the other model variables to reflect within-region or between-regions effects. If you want to interpret your results as showing what happens within a given region when there are differences in the values of the other independent variables, then you should be using region as a -fixed- effect. If you want to interpret them as showing how different regions differ from each other when they have different values of the other independent variables, then you should be using region as a -random- effect (or better still, do a Mundlak model using -xthybrid- to get both the within- and between-region effect estimates).

That said, the reviewer missed the biggest problem of all. You shouldn't be using any kind of logistic model with a continuous dependent variable. In Stata, what happens when you do that is that your dependent variable is interpreted as if it were a dichotomous variable, with non-zero values being interpreted as "true" and zero values as "false." That is almost certain to produce nonsense results.