# st: Regarding Hausman test

 From "Ali Karim" To statalist@hsphsun2.harvard.edu Subject st: Regarding Hausman test Date Wed, 25 Jun 2003 17:58:00 +0000

I am comparing two independent samples over two points in time. Since the surveys were two-stage cluster design, I used random effects model. I am interested in the effect of the survey period variable (time). When I do the Hausman test, the variable indicating the survey period is dropped from the fixed effects model (since survey period does not vary within clusters). However, I still get the results for the Hausman test. My question is whether my conclusion regarding the Hausman test result is still valid.

Below are my outputs:

. xi:xtlogit d6_1 time sex age i.edu marital if a1==1,i(cluster) fe
i.edu _Iedu_1-5 (naturally coded; _Iedu_1 omitted)

note: multiple positive outcomes within groups encountered.
note: 4 groups (38 obs) dropped due to all positive or
all negative outcomes.
note: time omitted due to no within-group variance.
Iteration 0: log likelihood = -420.47136
Iteration 1: log likelihood = -418.83676
Iteration 2: log likelihood = -418.83658

Conditional fixed-effects logit Number of obs = 888
Group variable (i) : cluster Number of groups = 42

Obs per group: min = 2
avg = 21.1
max = 65

LR chi2(5) = 4.84
Log likelihood = -418.83658 Prob > chi2 = 0.4357

------------------------------------------------------------------------------
d6_1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | -.1968472 .1751073 -1.12 0.261 -.5400512 .1463567
age | .0011349 .006369 0.18 0.859 -.0113481 .0136179
_Iedu_2 | -.1049612 .2071721 -0.51 0.612 -.5110111 .3010886
_Iedu_5 | -.1907531 .2411841 -0.79 0.429 -.6634652 .2819591
marital | .2770258 .2294834 1.21 0.227 -.1727534 .726805
------------------------------------------------------------------------------

. hausman,save

. xi:xtlogit d6_1 time sex age i.edu marital if a1==1,i(cluster) re
i.edu _Iedu_1-5 (naturally coded; _Iedu_1 omitted)

Fitting comparison model:

Iteration 0: log likelihood = -640.90148
Iteration 1: log likelihood = -606.46413
Iteration 2: log likelihood = -606.42604
Iteration 3: log likelihood = -606.42604

Fitting full model:

rho = 0.0 log likelihood = -606.42604
rho = 0.1 log likelihood = -574.10894
rho = 0.2 log likelihood = -560.0787
rho = 0.3 log likelihood = -552.24879
rho = 0.4 log likelihood = -547.62653
rho = 0.5 log likelihood = -544.94849
rho = 0.6 log likelihood = -544.66845
rho = 0.7 log likelihood = -548.99673
Iteration 0: log likelihood = -544.66845
Iteration 1: log likelihood = -543.85549
Iteration 2: log likelihood = -543.7076
Iteration 3: log likelihood = -543.70749

Random-effects logit Number of obs = 926
Group variable (i) : cluster Number of groups = 46

Random effects u_i ~ Gaussian Obs per group: min = 2
avg = 20.1
max = 65

Wald chi2(6) = 19.46
Log likelihood = -543.70749 Prob > chi2 = 0.0035

------------------------------------------------------------------------------
d6_1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time | 1.14196 .2959349 3.86 0.000 .5619387 1.721982
sex | -.2173222 .1730642 -1.26 0.209 -.5565218 .1218775
age | .0004927 .0062969 0.08 0.938 -.0118489 .0128344
_Iedu_2 | -.1427462 .2049882 -0.70 0.486 -.5445157 .2590234
_Iedu_5 | -.2360893 .2398125 -0.98 0.325 -.7061132 .2339346
marital | .2561022 .2257651 1.13 0.257 -.1863892 .6985937
_cons | -.5236707 .3810858 -1.37 0.169 -1.270585 .2232437
-------------+----------------------------------------------------------------
/lnsig2u | .3019552 .225919 -.140838 .7447484
-------------+----------------------------------------------------------------
sigma_u | 1.162971 .1313686 .9320032 1.451176
rho | .2913385 .0141779 .2088807 .3902886
------------------------------------------------------------------------------
Likelihood ratio test of rho=0: chibar2(01) = 125.44 Prob >= chibar2 = 0.000

. hausman,eq(1:1)

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| Prior Current Difference S.E.
-------------+-------------------------------------------------------------
sex | -.1968472 -.2173222 .0204749 .0266707
age | .0011349 .0004927 .0006421 .0009558
_Iedu_2 | -.1049612 -.1427462 .0377849 .0300019
_Iedu_5 | -.1907531 -.2360893 .0453362 .0256852
marital | .2770258 .2561022 .0209235 .0411432
---------------------------------------------------------------------------
b = less efficient estimates obtained previously from clogit
B = fully efficient estimates obtained from xtlogit

Test: Ho: difference in coefficients not systematic

chi2( 5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 6.94
Prob>chi2 = 0.2252

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