ENH: Add Hausman specification test

[eirki]

This adds the Hausman specification test, commonly used to choose between a fixed effects model and a random effects model. The function includes the options include_constant, sigmamore, and sigmaless - which mirrors Stata.

I haven't updated the documentation, but will be happy to do so if you want.

The function calculating an alternative covariance can perhaps be removed and replaced with adding a parameter to the covariance estimation.

I realize there is already a wu_hausman method for testing exogeneity in IV models, but I could not find a way to re-use it. Maybe the mathematics could be extracted into a shared function. Also I guess I should make the naming consistent.

Finally, I have written tests, but they do not look at the actual numerical results. Do you generally generate these using Stata and then test against them?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.38%. Comparing base (556bde7) to head (3bf7264).
Report is 430 commits behind head on main.

Additional details and impacted files

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[bashtage]

Should this be a method attached to a RandomEffectsResults class? This would likely simplify the calculations and logic. It also makes sure that we aren't trying to compare invalid models (e.g. a 2-way FE model with a RE model).

[eirki]

That's a good idea, I've moved it to a method.

I'm trying to generate test data using Stata, but the generated .do-file uses a stats command that I cannot find. Could you point me in the right direction?

[FeiYao-Edinburgh]

I will keep a big eye on this issue. Hausman tests for FE and RE deserves a add! Currently I need to calculate by myself based on the estimates of FE and RE.

[eirki]

I have now added tests against pre-calculated values from Stata. Let me know if anything needs to be changed/added!