# Interpreting fixed effects coefficients with categorical independent variables

I am trying to find out if change in marital status have effect on person's health. I am using 2 data points panel data.

My question is, how to interpret fixed coefficients if independent variable is categorical? Does coefficient in fixed effect mean that if person change marital status from married (reference category) to divorced, his health get better by .25?

Reason why I ask (other than this within change disproves my theory), if I make for example "widowed" category reference, I still get fixed effects. It's really unlikely for person to get from "widowed" to "divorced" in 4 years (50+ population).

So, am I interpreting the fixed effects with categorical independent variables wrong?

Thanks!

Coefficients in fixed effects models are interpreted in the same way as in ordinary least squares regressions. For the categorical variables, i.mar_stat generates dummies for the observed marital status and Stata omits one of these dummies which will be your base/reference category. In this case this reference group are people who are never married. So a coefficient of 0.2599 means that divorced individuals have 0.2599 "more health" (the exact interpretation depends on how this health status is measured) compared to those who were never married. However, when you look at the p-value of this coefficient you will notice that it is not significant. For this reason you can't say that divorced individuals have a better health status than those who were never married because your test rejects the hypothesis that 0.2599 is significantly different from the reference group.

Another side-note on your methodology: when you interpret your coefficients it's also important to remember that you are only estimating a correlation between marital status and health, not a causal one. Consider someone who is in such bad health that no girl wanted to marry him in the first place, then his health status is lower than those of divorced individuals but this has nothing to do with his marital status but because he was in poor health to begin with. So you might have an endogeneity problem here.

As this question has so many views and ranks highly in google search, I would like to add to the excellent answer before (+1) that one has to be careful about actually interpreting the effects as within effects. Probably the most common empirical mistake in applied work. There is a very nice paper on this (not mine):

Mummolo, J., & Peterson, E. (2018). Improving the interpretation of fixed effects regression results. Political Science Research and Methods, 6(4), 829-835.

• This still seems to be the most popular post on this topic. I agree about the within interpretation. However, I am still having trouble interpreting what demeaning truly means for dummy coded factors. For example if a person was divorced in one wave out of four in a survey, what does a score of -0.25 mean in three of the waves? At the individual level interpretation of what a within effect represents for a continuous variable is clear (e.g. change a persons income change relative to mean income), so a negative score makes sense. Jul 26, 2023 at 13:29