Negative -hausman- in the logit/xtlogit decision

[Tim Meier]

I have unbalanced panel data and want to decide whether to compute (pooled) -logit-, -xtlogit,fe- or -xtlogit,re- (with Stata 14.2). The rho value of -xtlogit,re- is <0.05, so xtlogit,re is preferable compared to logit. Then, I have tested something similar for xtlogit,fe. After calculating -logit- and -xtlogit,fe-, I used -hausman-.
A value <0.05 would mean that I should prefer -xtlogit,fe- over the -logit- approach.

logit C_0 c.cube_root_A1 c.Sy2 Di3 c.Ex4
estimates store logit_C_0_1
xtlogit C_0 c.cube_root_A1 c.Sy2 Di3 c.Ex4, fe
estimates store xtlogit_fe_C_0_2
hausman  logit_C_0_1 xtlogit_fe_C_0_2

Here we come to the question: -hausman- gives a negative value. I cannot use the functions "sigmamore" and "sigmaless", because Stata then gives me the following message: "Estimators do not save e(sigma) or e(rmse), sigma option not allowed". Using the command -suest-, as Stata suggests, makes no sense, because the command is not suitable for panel data. I cannot use the command -xtoverid- either, because the command does not work with (xt)logit. What other options do I have in such a situation?
In the Stata manual of the hausman test (page 9) it says: "[...]the χ2 statistic is actually negative. We might interpret this result as strong evidence that we cannot reject the null hypothesis." Can I apply this to my scenario? In that case (pooled) logit would be preferable to xtlogit,fe. In this case I would finally decide for the xtlogit,re approach. Is this procedure correct?

[Joro Kolev]

Why are you not comparing -xtlogit, re- to -xtlogit, re- with your Hausman test?

[Tim Meier]

I assume you meant the Hausman test between -xtlogit,fe- and -xtlogit,re-, right? As I understand it, I don't do the test until I have previously been able to rule out that (pooled) -logit- is not the more sensible procedure. Therefore, I looked at whether (pooled) -logit- is preferable to -xtlogit,re- and/or -xtlogit,fe-.

[Carlo Lazzaro]

Tim:
Stata performs this test for you, as the likelihood-ratio test at the foot of -xtlogit,re- outcome table actually compares the pooled estimator (logit) with the panel estimator.

[Tim Meier]

However, the test only referred to a comparison between -xtlogit,re- and pooled -logit-. The test says nothing about whether -xtlogit,fe- is more or less suitable than pooled -logit-. Or do I understand something wrong?

[Carlo Lazzaro]

Tim:
yes, you're correct.
You can suspect (but not test) that a panel-wise effect exists for the -fe- specification as well if the likelihood-ratio test for -xtlogit,re- specification reaches statistical significance.

[Joro Kolev]

Yes, there was a typo in what I wrote. I meant what you said: "Hausman test between -xtlogit,fe- and -xtlogit,re-."

These are two different and separate issues. Carlo told us how you can easily test the pooled vs random effects. My idiosyncratic view on the matter is that this test is not too interesting, because both the pooled and the random effects model are consistent under more or less the same set of assumptions. If I have panel data structure I go directly for the random effects model, because this is the natural model for this structure. What can go wrong if you have a pooled true model, but you estimate random effects? (But also it does not hurt to perform the test of pooled vs random effects.)

Now you need to do what is the important test, Hausman test between -xtlogit,fe- and -xtlogit,re-. And this test is important because if your so called "fixed effects" are correlated with the regressors, your estimates will be inconsistent.

I assume you meant the Hausman test between -xtlogit,fe- and -xtlogit,re-, right? As I understand it, I don't do the test until I have previously been able to rule out that (pooled) -logit- is not the more sensible procedure. Therefore, I looked at whether (pooled) -logit- is preferable to -xtlogit,re- and/or -xtlogit,fe-.

[Tim Meier]

Thank you very much for your answers. Do I understand it correctly? So basically I can test if -xtlogit,re- is preferable to pooled -logit-. If this is the case, I can also assume this for -xtlogit,fe-. A separate test is not possible. If the test shows that pooled -logit- is preferable, it is still recommended to use -xtlogit,re- or -xtlogit,fe- due to the panel structure and to check this with the Hausman test. Have I summarized your statements correctly?

[Carlo Lazzaro]

Tim:
correct.

[Tim Meier]

Thank you very much for your support!