Test if variance on random intercepts are 0 (svy: melogit)

[Selina Carter]

I am using survey weighted data with two (nested) random intercepts. I would like to test if the variances of the random intercepts are 0.
The lrtest command will not work, since I have used svy:melogit.

I looked at this post but my context is different enough such that I don't know the correct code.

* Set weights
svyset occ_group_cat, weight(weight_occ_cat) strata(state_abbr) || occ_cat, weight(weight_occ) strata(state_abbr)  || _n, weight(weight_respondent_rescale) strata(state_abbr)


*(Nested) random intercept model
svy: melogit t_tested_14d_dummy b1.gender b1.age_bucket b1.education b1.race_ethnicity b1.state_abbr ///
                                comorbid_Type1D comorbid_Type2D comorbid_Cancer comorbid_HeartDis comorbid_HighBP ///
                                comorbid_Asthma comorbid_ChronLungD comorbid_KidneyD comorbid_AutoImm comorbid_WeakImm ///
                                comorbid_Missing ///
                                b1.worry_catch_COVID_C9 ///
                                c.perc_Rep_2020_sc c.incid_prop_7dma_jhu_sc c.PVI_pop_conc_density_sc ///
                                || occ_group_cat: || occ_cat:, intpoints(2) startgrid(.11) intmethod(mcaghermite) iterate(5000)

Without showing full results, the variance estimates are as follows:



I want to perform two tests: whether the variances for the random intercepts (occ_group_cat and occ_cat) are equal to 0.

My (wrong) code is as follows:

test _b[var(occ_group_cat:_cons)] = 0
test _b[var(occ_cat:_cons)] = 0

Thank you very much.

[Andrew Musau]

See the -coeflegend- option on how to refer to the coefficients.

webuse towerlondon, clear
melogit dtlm difficulty i.group || family: || subject:, coeflegend
test (_b[/var(_cons[family])]= 0) (_b[/var(_cons[family>subject])]=0)

Res.:

. melogit dtlm difficulty i.group || family: || subject:, coeflegend

Fitting fixed-effects model:

Iteration 0:   log likelihood = -317.35042  
Iteration 1:   log likelihood = -313.90007  
Iteration 2:   log likelihood = -313.89079  
Iteration 3:   log likelihood = -313.89079  

Refining starting values:

Grid node 0:   log likelihood = -310.28429

Fitting full model:

Iteration 0:   log likelihood = -310.28429  
Iteration 1:   log likelihood = -307.36653  
Iteration 2:   log likelihood = -305.19357  
Iteration 3:   log likelihood = -305.12073  
Iteration 4:   log likelihood = -305.12041  
Iteration 5:   log likelihood = -305.12041  

Mixed-effects logistic regression               Number of obs     =        677

        Grouping information
        -------------------------------------------------------------
                        |     No. of       Observations per group
         Group variable |     groups    Minimum    Average    Maximum
        ----------------+--------------------------------------------
                 family |        118          2        5.7         27
                subject |        226          2        3.0          3
        -------------------------------------------------------------

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(3)      =      74.90
Log likelihood = -305.12041                     Prob > chi2       =     0.0000
--------------------------------------------------------------------------------
          dtlm | Coefficient  Legend
---------------+----------------------------------------------------------------
    difficulty |  -1.648505  _b[difficulty]
               |
         group |
            2  |  -.2486841  _b[2.group]
            3  |  -1.052306  _b[3.group]
               |
         _cons |  -1.485863  _b[_cons]
---------------+----------------------------------------------------------------
family         |
     var(_cons)|   .5692105  _b[/var(_cons[family])]
---------------+----------------------------------------------------------------
family>subject |
     var(_cons)|   1.137917  _b[/var(_cons[family>subject])]
--------------------------------------------------------------------------------
LR test vs. logistic model: chi2(2) = 17.54               Prob > chi2 = 0.0002

Note: LR test is conservative and provided only for reference.

. 
. test (_b[/var(_cons[family])]= 0) (_b[/var(_cons[family>subject])]=0)

 ( 1)  [/]var(_cons[family]) = 0
 ( 2)  [/]var(_cons[family>subject]) = 0

           chi2(  2) =    6.43
         Prob > chi2 =    0.0402

.

[Selina Carter]

Brilliant!! Thank you very much!