Interpretation hausman for xtlogit

[Meike Wenzl]

Hello everyone,

I am performing a hausman test on a xtlogit and I am not quite sure if I interpret the outcome correctly.

this is the result:

. hausman fe re

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
zchangeinROA | .0438614 .0750483 -.0311869 .
Narcissimi~x | -.0930629 -.095981 .0029181 .053062
interaction | .0484003 .0523081 -.0039078 .
zlnrevenue | -.2653698 -.241142 -.0242277 .2565521
zlntotal_a~s | -.4117256 .1293709 -.5410965 .3242538
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtlogit
B = inconsistent under Ha, efficient under Ho; obtained from xtlogit

Test: Ho: difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 2.53
Prob>chi2 = 0.7719
(V_b-V_B is not positive definite)


I would say, I reject the null and choose a random effect model instead. I now wanted to check whether the random effects is appropiate or if I have to do a OLS regression. However, the command "xttest0" which tests for Breusch and Pagan Lagrangian multiplier test for random effects does not work; Stata tells me that the lasts estimates are not found, although I ran the test immediately after the xtlogit, re command. Or is it not possible to do this in a logistic regression? Also, maybe someone can explain to me the difference between xtprobit and xtlogit? Is there any difference? If I run both within my model, the results differ not too greatly. Any help is appreciated! Thanks

[Carlo Lazzaro]

Meike:
- your hausman -outcome- is limping, in that -vc-e matrix is not positive definite; you may want to see if scaling some of your coefficients brings about some change. Unfortunately, -suest- is critical when applied to -xtlogit-;
- You're right that -xttest0- cannot be applied after -xtlogit-. However, you can look at the p-value ofthe -rho- parameter reported as a footnote of the -xtlogit, re- outcome table; if it's significant, there's evidence of -re-; otherwise, you should go pooled -logit-.

[Meike Wenzl]

Random-effects logistic regression Number of obs = 2249
Group variable: firm_ID Number of groups = 199

Random effects u_i ~ Gaussian Obs per group: min = 2
avg = 11.3
max = 13

Wald chi2(5) = 7.73
Log likelihood = -974.92068 Prob > chi2 = 0.1718

---------------------------------------------------------------------------------
downsizing | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
zchangeinROA | .0750483 .0563666 1.33 0.183 -.0354282 .1855248
Narcissimindex | -.095981 .0720316 -1.33 0.183 -.2371603 .0451983
interaction | .0523081 .0529923 0.99 0.324 -.0515549 .1561711
zlnrevenue | -.241142 .1298099 -1.86 0.063 -.4955647 .0132806
zlntotal_assets | .1293709 .1119655 1.16 0.248 -.0900774 .3488192
_cons | -1.859112 .0986989 -18.84 0.000 -2.052559 -1.665666
----------------+----------------------------------------------------------------
/lnsig2u | -.1787602 .2165675 -.6032247 .2457043
----------------+----------------------------------------------------------------
sigma_u | .9144979 .0990253 .7396247 1.130717
rho | .2026832 .0349979 .1425742 .2798626
---------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 74.10 Prob >= chibar2 = 0.000


The likelihood ratio test of rho tells me that the panel estimator is not different from the pooled estimator.. So does this mean I could technically choose a OLS logistic regression?

[Carlo Lazzaro]

Meike:
No, the opposite holds.
-chibar2-=74.10; p-value

[Meike Wenzl]

Carlo:

thanks.