Interpreting marginal effect in melogit with odds ratio

[Taka Sakamoto]

Dear Statalisters:

I am trying to correctly interpret the results of marginal effects that are produced with melogit with odds ratio option. Attached below are the commands and results. I tell Stata to calculate marginal effects with the command "margins, dydx(i.singlemom3) at(nordic=(0(1)1)) expression(exp(predict(xb)))". Both singlemom3 and nordic are dummy variables.

In this case, is it correct to interpret the marginal effect of singlemom3 with nordic==1 that when nordic==1, the odds ratio is .0073617, and it suggests that the odds of pov50 happening when nordic==1 are 99.3% lower? I'd like to make sure 2 things: that I'm calculating the odds ratio correctly and that I'm interpreting the meaning of .0073617 correctly.

Thank you for your help in advance.

Best,

Taka

. use pov50 age age2 educ nhhmem17 child5 nordic limatppp_L3 itotedupergdp_L3 lalmptotppp_L3 age singlemom3 cid emp_ilo using $mydata/tsakam/lis15pov.dta

. melogit pov50 age age2 educ nhhmem17 child5 nordic##singlemom3 limatppp_L3 itotedupergdp_L3 lalmptotppp_L3 if age>24&age<55 & age~=.&emp_ilo==1 || cid: , or vce(cl cid)

Fitting fixed-effects model:

Iteration 0:   log likelihood = -359581.21  
Iteration 1:   log likelihood = -298766.56  
Iteration 2:   log likelihood = -297421.02  
Iteration 3:   log likelihood = -297396.28  
Iteration 4:   log likelihood = -297396.27  

Refining starting values:

Grid node 0:   log likelihood = -296811.38

Fitting full model:

Iteration 0:   log pseudolikelihood = -296811.38  (not concave)
Iteration 1:   log pseudolikelihood = -296805.38  (not concave)
Iteration 2:   log pseudolikelihood = -296799.35  (not concave)
Iteration 3:   log pseudolikelihood = -296794.37  (not concave)
Iteration 4:   log pseudolikelihood = -296790.26  (not concave)
Iteration 5:   log pseudolikelihood = -296786.89  (not concave)
Iteration 6:   log pseudolikelihood =  -296781.2  (not concave)
Iteration 7:   log pseudolikelihood = -296778.86  (not concave)
Iteration 8:   log pseudolikelihood = -296776.93  (not concave)
Iteration 9:   log pseudolikelihood = -296776.13  
Iteration 10:  log pseudolikelihood = -296735.71  
Iteration 11:  log pseudolikelihood =  -296638.1  
Iteration 12:  log pseudolikelihood = -296603.27  
Iteration 13:  log pseudolikelihood =  -296603.2  
Iteration 14:  log pseudolikelihood =  -296603.2  

Mixed-effects logistic regression               Number of obs     =    2017275
Group variable:             cid                 Number of groups  =         14

                                                Obs per group:
                                                              min =      2,091
                                                              avg =  144,091.1
                                                              max =    748,229

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(11)     =  987786.79
Log pseudolikelihood =  -296603.2               Prob > chi2       =     0.0000
                                        (Std. Err. adjusted for 14 clusters in cid)
-----------------------------------------------------------------------------------
                  |               Robust
            pov50 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
              age |   .8267114   .0442137    -3.56   0.000     .7444413    .9180733
             age2 |   1.002135   .0005695     3.75   0.000     1.001019    1.003251
             educ |   .5662244   .0347937    -9.26   0.000     .5019766    .6386952
         nhhmem17 |   1.159116   .0329424     5.20   0.000     1.096316    1.225514
           child5 |   1.028166    .106204     0.27   0.788     .8397282     1.25889
         1.nordic |   .3562969   .0983028    -3.74   0.000     .2074743    .6118709
     1.singlemom3 |   4.729612   .7387682     9.95   0.000     3.482309    6.423677
                  |
nordic#singlemom3 |
             1 1  |    .315331   .0472083    -7.71   0.000     .2351436    .4228635
                  |
      limatppp_L3 |   1.065768   .0688701     0.99   0.324     .9389829    1.209671
 itotedupergdp_L3 |   1.114404   .0699055     1.73   0.084       .98548    1.260195
   lalmptotppp_L3 |   1.032103    .054843     0.59   0.552     .9300204     1.14539
            _cons |   1.626621   1.818156     0.44   0.663     .1819097    14.54511
------------------+----------------------------------------------------------------
cid               |
        var(_cons)|   .0814162   .0573185                      .0204857    .3235727
-----------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).

. margins, dydx(i.singlemom3) at(nordic=(0(1)1)) expression(exp(predict(xb)))

Average marginal effects                        Number of obs     =  2,017,275
Model VCE    : Robust

Expression   : exp(predict(xb))
dy/dx w.r.t. : 1.singlemom3

1._at        : nordic          =           0

2._at        : nordic          =           1

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
0.singlemom3  |  (base outcome)
--------------+----------------------------------------------------------------
1.singlemom3  |
          _at |
           1  |   .1568204   .0401026     3.91   0.000     .0782208    .2354199
           2  |   .0073617    .001456     5.06   0.000      .004508    .0102154
-------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

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end of do-file