Confidence intervals in mixed-effects logistic model

[Abdullah Algarni]

Dear Statalisters,

I have a dataset collected from 8 countries and ≥20 hospitals. I want to fit a nested, mixed-effect logistic regression (hence has a 3-level) as this reference suggests (Reference). So, I used hospitals nested within countries as random effects and fit the model. However, I get an unexpected 95% CI for the countries (please see below).
What does that mean? Does it mean no need to include countries as random-effect?

melogit died30in age_sd cci_sd i.(sex cci_htn) ib(frequent).race ib(frequent).infx_source || country: || hospital:, nolog or


note: 3.infx_source != 0 predicts failure perfectly;
      3.infx_source omitted and 23 obs not used.

note: 10.infx_source != 0 predicts failure perfectly;
      10.infx_source omitted and 44 obs not used.


Mixed-effects logistic regression               Number of obs     =      3,207

        Grouping information
        -------------------------------------------------------------
                        |     No. of       Observations per group
         Group variable |     groups    Minimum    Average    Maximum
        ----------------+--------------------------------------------
                country |          7          6      458.1      1,865
               hospital |         21          6      152.7        474
        -------------------------------------------------------------

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(14)     =     187.86
Log likelihood = -776.97614                     Prob > chi2       =     0.0000
------------------------------------------------------------------------------------------------
                      died30in | Odds ratio   Std. err.      z    P>|z|     [95% conf. interval]
-------------------------------+----------------------------------------------------------------
                        age_sd |   1.218493    .136446     1.76   0.0776     .9783766     1.51754
                        cci_sd |   2.401467   .2392206     8.79   0.0000     1.975535    2.919231
                               |
                           sex |
                          Man  |          1  (base)
                        Woman  |   1.299266    .180295     1.89   0.0592     .9898734    1.705362
                               |
                       cci_htn |
                           No  |          1  (base)
                          Yes  |    .861246   .1566368    -0.82   0.4115     .6029999    1.230091
                               |
                          race |
                        Asian  |   1.034492   .6099411     0.06   0.9541     .3257281    3.285484
                        Black  |   2.072429   .7169011     2.11   0.0352     1.052033    4.082535
                  South Asian  |   2.446634   .8445341     2.59   0.0095     1.243797    4.812696
                        White  |          1  (base)
                               |
                   infx_source |
                    Abdominal  |   .5330493   .1407734    -2.38   0.0172     .3176676    .8944619
                  Bloodstream  |   1.154067    .336441     0.49   0.6231     .6517534    2.043519
                Bone & joints  |          1  (empty)
                     COVID-19  |   1.270447   .2622513     1.16   0.2462     .8477109    1.903993
                 Neurological  |   3.828529   2.292373     2.24   0.0250     1.184038    12.37936
Respiratory (except COVID-19)  |          1  (base)
       Soft/cutaneous tissues  |   .5645505   .1520924    -2.12   0.0338     .3329549    .9572386
                   Urogenital  |    .535857   .1095438    -3.05   0.0023     .3589551    .7999406
               Unknown source  |    2.90591   1.196004     2.59   0.0095     1.297023    6.510534
                        Other  |          1  (empty)
                               |
                         _cons |   .0542853   .0176503    -8.96   0.0000     .0287027    .1026696
-------------------------------+----------------------------------------------------------------
country                        |
                     var(_cons)|   6.01e-34   3.61e-18                             .           .
-------------------------------+----------------------------------------------------------------
country>hospital               |
                     var(_cons)|   1.287618   .4979894                      .6033688    2.747839
------------------------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation to odds ratios.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 150.55      Prob >= chibar2 = 0.0000

---

Reference: Multilevel and Longitudinal Modeling Using Stata, Fourth Edition

[Clyde Schechter]

Take a look at the value of the variance at the country level: 6.01e-34. That means that, at least after adjustment for everything else in the model, there is, for practical purposes, 0 variance at the country level. Country just doesn't matter here. When a variance component in a model is very close to zero, Stata has a lot of difficulty even estimating it, and even more difficulty in calculating a confidence interval. But really, in this situation, all that matters is that the variance at that level is negligible. In fact, I would recommend rerunning the model and omitting the country level altogether.

[Abdullah Algarni]

Thank you so much Clyde Schechter ,, that was very helpful; I have omitted the country level altogether