st: Wald test in Random Coefficient Model

[Shikha Sinha <shikha.sinha414@gmail.com>]

Hello Statalist members,

I have an individual level data from 50 countries. I want to examine
the association between material deprivation and health. In the pooled
analysis, I find a negative association between materail deprivation
and health. To test whether the individual relationship between
material deprivation and health varied systematically across
countries, I estimate a random coefficient model. Since, my dependent
variable is a binary variable, I used -xtmelogit syntax in stata.
Below is the output:

bysort wb_income_group: xtmelogit dprsnl_hlth drel age dfemale
dmarried dyear* highschool college religiosity if age < 76 || wp5:
drel, cov (unstructured) variance or

---------------------------------------------------------------------------------------------------------------------------------------------
-> wb_income_group = High income: OECD
note: dyear5 omitted because of collinearity

Refining starting values:

Iteration 0:   log likelihood = -26443.813  (not concave)
Iteration 1:   log likelihood = -26428.072  (not concave)
Iteration 2:   log likelihood = -26396.888

Performing gradient-based optimization:

Iteration 0:   log likelihood = -26396.888
Iteration 1:   log likelihood = -26309.086  (not concave)
Iteration 2:   log likelihood = -26301.598  (not concave)
Iteration 3:   log likelihood = -26295.836
Iteration 4:   log likelihood = -26293.757
Iteration 5:   log likelihood = -26292.994
Iteration 6:   log likelihood = -26292.803
Iteration 7:   log likelihood = -26292.799
Iteration 8:   log likelihood = -26292.799

Mixed-effects logistic regression               Number of obs      =     60604
Group variable: wp5                             Number of groups   =        41

                                                Obs per group: min =       443
                                                               avg =    1478.1
                                                               max =      4601

Integration points =   7                        Wald chi2(11)      =   2324.18
Log likelihood = -26292.799                     Prob > chi2        =    0.0000

------------------------------------------------------------------------------
 dprsnl_hlth | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drel |   2.118035   .0996632    15.95   0.000     1.931435    2.322662
         age |   .9719757   .0007352   -37.58   0.000     .9705357    .9734178
     dfemale |   .7882532   .0179943   -10.42   0.000     .7537624    .8243223
    dmarried |   1.228628   .0289709     8.73   0.000     1.173139    1.286743
      dyear1 |   .9609855   .1030671    -0.37   0.711     .7787969    1.185795
      dyear2 |   .8201067   .0430446    -3.78   0.000     .7399352    .9089647
      dyear3 |   .9043089   .0476424    -1.91   0.056     .8155908    1.002678
      dyear4 |     .94283   .0395463    -1.40   0.160     .8684212    1.023614
      dyear5 |  (omitted)
  highschool |   1.304839   .0406918     8.53   0.000     1.227473    1.387082
     college |    1.58343   .0587545    12.39   0.000     1.472361    1.702877
 religiosity |   .9546723   .0238213    -1.86   0.063     .9091068    1.002522
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
wp5: Unstructured            |
                   var(drel) |    .037479   .0209765      .0125136    .1122521
                  var(_cons) |   .1952712   .0515963      .1163391    .3277558
             cov(drel,_cons) |  -.0052752   .0251633     -.0545943    .0440439
------------------------------------------------------------------------------
LR test vs. logistic regression:     chi2(3) =  2132.55   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference.
-----------------------------------------------------------------------------------------------------------------------
My question is How do test the significance of randome coefficient
variance at country level? I saw a few papers using wald statistics.
Could you suggest how to get the walt statistic from the above output?
  Is it this - Wald chi2(11)      =   2324.18?

Thanks
Shikha
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