I think that John Emmet <[email protected]> asked whether he could do a
Hausman to test a fixed versus random effects specification in a panel logit
model.
The answer is yes.
Here is an example using the union dataset used in the -xtlogit- manual
entry.
. webuse union
(NLS Women 14-24 in 1968)
. xtlogit union age grade not_smsa south southXt , i(id) re nolog
Random-effects logistic regression Number of obs = 26200
Group variable (i): idcode Number of groups = 4434
Random effects u_i ~ Gaussian Obs per group: min = 1
avg = 5.9
max = 12
Wald chi2(5) = 221.95
Log likelihood = -10556.294 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
union | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0092401 .0044368 2.08 0.037 .0005441 .0179361
grade | .0840066 .0181622 4.63 0.000 .0484094 .1196038
not_smsa | -.2574574 .0844771 -3.05 0.002 -.4230294 -.0918854
south | -1.152854 .1108294 -10.40 0.000 -1.370075 -.9356323
southXt | .0237933 .0078548 3.03 0.002 .0083982 .0391884
_cons | -3.25016 .2622898 -12.39 0.000 -3.764238 -2.736081
-------------+----------------------------------------------------------------
/lnsig2u | 1.669888 .0430016 1.585607 1.75417
-------------+----------------------------------------------------------------
sigma_u | 2.304685 .0495526 2.209582 2.403882
rho | .6175213 .0101565 .5974278 .6372209
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 5978.89 Prob >= chibar2 = 0.000
. estimates store re
. xtlogit union age grade not_smsa south southXt , i(id) fe nolog
note: multiple positive outcomes within groups encountered.
note: 2744 groups (14165 obs) dropped due to all positive or
all negative outcomes.
Conditional fixed-effects logistic regression Number of obs = 12035
Group variable (i): idcode Number of groups = 1690
Obs per group: min = 2
avg = 7.1
max = 12
LR chi2(5) = 78.16
Log likelihood = -4511.1042 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
union | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0079706 .0050283 1.59 0.113 -.0018848 .0178259
grade | .0811808 .0419137 1.94 0.053 -.0009686 .1633302
not_smsa | .0210368 .113154 0.19 0.853 -.2007411 .2428146
south | -1.007318 .1500491 -6.71 0.000 -1.301409 -.7132271
southXt | .0263495 .0083244 3.17 0.002 .010034 .0426649
------------------------------------------------------------------------------
. estimates store fe
. hausman fe re, eq(1:1)
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
age | .0079706 .0092401 -.0012695 .0023661
grade | .0811808 .0840066 -.0028258 .0377743
not_smsa | .0210368 -.2574574 .2784942 .0752826
south | -1.007318 -1.152854 .145536 .1011512
southXt | .0263495 .0237933 .0025562 .0027563
------------------------------------------------------------------------------
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)
= 17.30
Prob>chi2 = 0.0040
In this example, we reject the null hypothesis that the unobserved
individual level effects are uncorrelated with the other covariates. This
implies that we should use the fixed-effects estimator instead of the
random-effects estimator.
--David
[email protected]
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