st: Regarding Hausman test

["Ali Karim" <mehryar@hotmail.com>]

Dear list readers,

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.

Thanks in advance.
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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