HAUSMAN test for neg bin Random and Fixed effect models

[Roberta Pilgrim]

Hi!

I'm using negative binomials models and I'm turning them into Random Effects Models and Fixed Effects Models (using for random effect the command "menbreg" and for the fixed effect the command "nbreg" with a specification.

I attached my hausman test, the results are unclear to me: the prob>chi2 is a high negative number.

Could someone help me to interpret it?
Is it normal that results completely change if I use "hausman random fixed" instead of "hausman fixed random"?

Thank you so much in advance,
Roberta

[Clyde Schechter]

Yes, this is perfectly normal. The terms random and fixed that you have assigned to the estimates of the different models are not interpreted by the Hausman command. The hausman command expects the consistent model to be named first and the efficient model to be named second. It assumes that whatever you call them, that they fit that rubric. It then calculates the test, which is based on the differences in coefficients between the two models squared times the inverse of the difference in their covariance matrices, taken in the order specified. If you reverse the order, then you get negative results instead of positive.

[Roberta Pilgrim]

Thank you Clyde!

But in this case, I should assume that the model to use in my case is the random one? Am I wrong?

[Clyde Schechter]

Well, no. There are a couple of problems here. The first is that you correctly specified the order of the models in the second -hausman- command, which is the one that gives negative results followed by a message indicating that its assumptions are violated. So your -hausman- test is really just inapplicable here and provides no useful guidance.

Next, using -nbreg- with indicators for group variables is not a fixed-effects negative binomial regression, and it does not provide consistent estimation of the effects. It's a model that probably isn't useful for any purpose. That trick only works for linear models. You should be using -xtnbreg, fe- if you want a fixed-effects analysis here. However, that is not directly comparable to the random effects model estimated by -meglm- (which, by the way, is the same as the model estimated by -menbreg- and by -xtnbreg-) because -xtnbreg, fe- does not adjust for and estimate the fixed effects. Instead it estimates the coefficients of the predictors conditional on the fixed effects. So you can't even really do a Hausman or Hausman-like test to compare them. Non-linear models are a lot more difficult than linear ones in these respects.

If there is a formal test to contrast the suitability of -xtnbreg, fe- and -xtnbreg, re- (or -menbreg-) I'm not aware of it. But there could easily be something I don't know about out there, and if so, I hope somebody else will chime in. In my line of work we generally do not rely on formal tests to choose between fixed and random effects analyses. We generally prefer the flexibility of random effects analyses and are willing to tolerate a modest amount of inconsistency in return for the increased efficiency and the ability to model the effects of constant-within-group covariates Generally we would avoid random effects only when there would be a pretty obvious missing variable bias associated with using it. Other disciplines take a different view, and I won't attempt to adjudicate the difference of opinion.

[Roberta Pilgrim]

I hope this reference can be useful: it is from Paul Allison, who teaches at my University.

http://statisticalhorizons.com/fe-nbreg

He strongly recommended not to use xtnbreg, but I'll try to see if it works better.

About choosing if it's better to use Fixed or Random effect: the reason why I would prefer to use the Fixed Effect, is that in my sample there are more or less 200 institutions and they are really different between eachother, I was thinking that using fixed effect was a good way to overcome that problem and take into account the unobserved heterogeneity.

Just to be sure that I got this point: the hausman test won't be useful for me for these cases.

Thank you!

[Clyde Schechter]

Thank you for posting that. In part he reiterates what I said (in that -xtnbreg, fe- is not a fixed effects analog of -xtnbreg, re-), but he approves of using -nbreg- with indicator variables. That's interesting and it goes against what I was taught. But tomorrow I'll try to pull the full article and read it.

[Roberta Pilgrim]

No, Thank you, for helping me so much!