Is -sigmamore- suitable to hausman test after xtlogit?

[Alex Mai]

Dear statalists,

I am comparing RE xtlogit and FE xtlogit for a balanced panel database of 1500 observations. The following is the command:

xtset id t (where id refers to individuals and t refers to time)
quietly xtlogit depvar indepvar i.t, fe nolog
estimates store fe
quietly xtlogit depvar indepvar i.t, re nolog- (I want to control for time in both fe and re xtlogit)
estimates store re
hausman fe re

Then Stata showed result (insignificant, in favour of re) with a note of (V_b-V_B is not positive definite).

In order to solve this problem of being not positive definite, following some advices I used -hausman fe re, sigmamore-
but Stata then generated a warn of "Estimators do not save e(sigma) or e(rmse),sigma option not allowed".

I do not why stata shows this, because my commands are the same as what in Cameron and Trivedi (2009), except for xtlogit but not xtreg in my case.

Stata manual mentions that "These (sigmamore and sigmaless) options can be specified only when both estimators store e(sigma) or e(rmse), or with the xtreg command. e(sigma e) is stored after the xtreg command with the fe or mle option. e(rmse) is stored after the xtreg command with the re option. But I do not understand how to do e(sigma) and e(rmse)

So here are my questions:
Is there anything wrong in my hausman syntax that makes the option of sigmamore fail to be done?
Is sigmamore suitable to xtlogit or only suitable to xtreg? (this seems to be possible, seen through the manual).
If sigmamore is not suitable, how shall I solve the "not positive definite" problem for hausman test after xtlogit?

I really appreciate if someone could give answers to my problems.

Thank you very much!

[Alex Mai]

Just a supplement to my question. I know from a previous post that if the rho in the footnote of random-effect model is significant, then random-effects model should be used (suggested by Carlo in that post).

The post: http://www.statalist.org/forums/foru...an-for-xtlogit

In the footnote of my RE xtlogit, the coefficient of rho is 0.558055, and its standard error is 0.079342.

rho is significant (Coefficient/S.E.=0.558055/0.079342=7.03>1.96), so I should use random-effect model.

Is my interpretation correct?

Thank you!

[Carlo Lazzaro]

Alex:
no it is not.
You should look at the -LR test of rho=0-, that

formally compares the pooled estimator (logit) with the panel estimator...

(please see Example 1, -xtlogit- entry, Stata .pdf manual).

[Sinem Ates]

Dear All,

I have a similar problem in the post #1. I run xtpoisson with re and fe. Then I run Hausman test, due to the error below, I run Hausman test with sigmamore option, however the command does not provide any result. Could you please advise me about the solution of this problem?

. xtpoisson GRI HDI EF FII FMI WGI TRADE i.YEAR, re

Fitting Poisson model:

Iteration 0:   log likelihood = -1451.9488  
Iteration 1:   log likelihood =  -1449.335  
Iteration 2:   log likelihood = -1449.3319  
Iteration 3:   log likelihood = -1449.3319  

Fitting full model:

Iteration 0:   log likelihood = -775.52875  
Iteration 1:   log likelihood = -735.45721  
Iteration 2:   log likelihood = -727.31961  
Iteration 3:   log likelihood = -726.81391  
Iteration 4:   log likelihood = -726.80864  
Iteration 5:   log likelihood = -726.80864  

Random-effects Poisson regression               Number of obs     =        168
Group variable: ID                              Number of groups  =         24

Random effects u_i ~ Gamma                      Obs per group:
                                                              min =          7
                                                              avg =        7.0
                                                              max =          7

                                                Wald chi2(12)     =     386.37
Log likelihood  = -726.80864                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         GRI |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         HDI |  -2.129105   1.810007    -1.18   0.239    -5.676654    1.418444
          EF |   .0816759   .0522113     1.56   0.118    -.0206564    .1840083
         FII |   2.705611   .4744586     5.70   0.000     1.775689    3.635533
         FMI |  -.4729769   .3773934    -1.25   0.210    -1.212654    .2667007
         WGI |   -.000713   .0054791    -0.13   0.896    -.0114519     .010026
       TRADE |   .0001113   .0025765     0.04   0.966    -.0049386    .0051612
             |
        YEAR |
       2011  |   .2862886   .0524807     5.46   0.000     .1834283     .389149
       2012  |   .4348557   .0538862     8.07   0.000     .3292407    .5404707
       2013  |   .5966997   .0597691     9.98   0.000     .4795544    .7138449
       2014  |   .5981661   .0653963     9.15   0.000     .4699917    .7263406
       2015  |   .6523947   .0737901     8.84   0.000     .5077687    .7970207
       2016  |   .6066961   .0798463     7.60   0.000     .4502002     .763192
             |
       _cons |   3.560237   1.281759     2.78   0.005     1.048035    6.072439
-------------+----------------------------------------------------------------
    /lnalpha |  -.3780745   .3327322                     -1.030218    .2740687
-------------+----------------------------------------------------------------
       alpha |   .6851795   .2279813                      .3569293    1.315305
------------------------------------------------------------------------------
LR test of alpha=0: chibar2(01) = 1445.05              Prob >= chibar2 = 0.000

. estimates store RE

. xtpoisson GRI HDI EF FII FMI WGI TRADE i.YEAR, fe

Iteration 0:   log likelihood = -777.14038  
Iteration 1:   log likelihood = -562.10773  
Iteration 2:   log likelihood = -559.96973  
Iteration 3:   log likelihood = -559.96948  
Iteration 4:   log likelihood = -559.96948  

Conditional fixed-effects Poisson regression    Number of obs     =        168
Group variable: ID                              Number of groups  =         24

                                                Obs per group:
                                                              min =          7
                                                              avg =        7.0
                                                              max =          7

                                                Wald chi2(12)     =     393.98
Log likelihood  = -559.96948                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         GRI |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         HDI |  -.4062424   2.476247    -0.16   0.870    -5.259596    4.447112
          EF |   .1910001   .0522478     3.66   0.000     .0885964    .2934038
         FII |   2.509861   .4907356     5.11   0.000     1.548037    3.471685
         FMI |  -.7382897   .3941709    -1.87   0.061     -1.51085    .0342711
         WGI |   .0055388   .0057093     0.97   0.332    -.0056512    .0167288
       TRADE |   .0053887   .0025473     2.12   0.034     .0003961    .0103812
             |
        YEAR |
       2011  |   .2482556   .0535355     4.64   0.000      .143328    .3531831
       2012  |   .3987725   .0568557     7.01   0.000     .2873374    .5102076
       2013  |   .5593102   .0678905     8.24   0.000     .4262472    .6923731
       2014  |   .5515506   .0770526     7.16   0.000     .4005302     .702571
       2015  |   .6309981   .0872209     7.23   0.000     .4600483     .801948
       2016  |   .5913739   .0954913     6.19   0.000     .4042144    .7785334
------------------------------------------------------------------------------

. estimates store FE

. hausman FE RE

Note: the rank of the differenced variance matrix (10) does not equal the number of coefficients being tested (12); be sure this is what you
        expect, or there may be problems computing the test.  Examine the output of your estimators for anything unexpected and possibly
        consider scaling your variables so that the coefficients are on a similar scale.

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       FE           RE         Difference          S.E.
-------------+----------------------------------------------------------------
         HDI |   -.4062424    -2.129105        1.722863        1.689873
          EF |    .1910001     .0816759        .1093242        .0019501
         FII |    2.509861     2.705611       -.1957505        .1253415
         FMI |   -.7382897    -.4729769       -.2653128        .1137756
         WGI |    .0055388     -.000713        .0062518        .0016047
       TRADE |    .0053887     .0001113        .0052773               .
        YEAR |
       2011  |    .2482556     .2862886       -.0380331        .0105744
       2012  |    .3987725     .4348557       -.0360832        .0181341
       2013  |    .5593102     .5966997       -.0373895        .0321991
       2014  |    .5515506     .5981661       -.0466155        .0407484
       2015  |    .6309981     .6523947       -.0213966        .0465027
       2016  |    .5913739     .6066961       -.0153222        .0523752
------------------------------------------------------------------------------
                       b = consistent under Ho and Ha; obtained from xtpoisson
        B = inconsistent under Ha, efficient under Ho; obtained from xtpoisson

    Test:  Ho:  difference in coefficients not systematic

                 chi2(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =    -4.08    chi2<0 ==> model fitted on these
                                        data fails to meet the asymptotic
                                        assumptions of the Hausman test;
                                        see suest for a generalized test

. hausman FE RE,sigmamore
Estimators do not save e(sigma) or e(rmse),
sigma option not allowed
r(198);