xtoprobit vs xtreg, fe

[Mary Anderson]

I want to run a fixed effects regression model in stata using panel data to examine the change in individuals' responses over time. My dependent variable is ordinal so I was planning on using xtoprobit, however, I realize this would be using random effects.

Should I use xtoprobit even though it uses random effects? Or would it be best to run a linear regression with fixed effects (xtreg, fe)? Thank you

[Clyde Schechter]

If it is reasonable to believe that in some sense the numerical codes used in the ordinal response variable correspond to equally spaced points on some dimension, then, yes this would be reasonable. That is, let's say the response options are 1,2, 3, 4, and 5. If on some dimension that this variable purports to measure, the difference between 1 and 2 is the same as the difference between 2 and 3, which is the same as the difference between 3 and 4 and the difference between 4 and 5, then you can certainly treat this as an interval-level variable and use -xtreg-.

I must add, however, that I find the desire to avoid using random effects less than compelling. The aversion to random effects estimation in some fields is not universally shared. With appropriate inclusion of covariates, the degree of inconsistency of estimation in random effects models may be minimal. Moreover, the distortion of the outcome variable by treating it as interval level if the equally-spaced property does not hold is most likely a more serious mis-specificaton problem than the issues raised by using random-effects.

[Mary Anderson]

Thank you for your response! To make sure I am understanding correctly, it would be reasonable to use -xtreg- rather than xtoprobit? One of my dependent variables, for example, is "do you think redistricting in your state helped or hurt Democrats?" 0=hurt dems, 1=neither helped nor hurt, 2=helped dems, so I believe it follows the dimensions you describe. I had initially planned on using -xtoprobit- for ease of interpretation also.
I have tried running both models, and the -xtreg- outputs are more conservative when it comes to statistical significance. I want to ensure I am objectively using the right model for analysis though. Thanks again

[Clyde Schechter]

For the response set you describe, the notion of equal spacing seems plausible. So I think the use of -xtreg- here is probably defensible.

Without getting into a very long philosophical discussion, I think that a great deal of very bad statistical practice comes from the desire to (appear to) be "objectively" correct. Perhaps one of the truest statements ever uttered by a statistician is Box's quip that all models are wrong, but some are useful. Usefulness is inherently subjective. I can assure you that whatever model or analysis you use, it is objectively wrong, and you will never find an objectively right model. Content yourself with one that, in reasonable subjective judgment, is useful.