Interpreting confidence intervals of predictive margins after logit

[Wes King]

Hello all,

I have a logistic regression model including an interaction term between two categorical variables (sex and race). I am using population representative data. The output (slightly edited for readability) is pasted below. My question is: How do I interpret the 95% CIs that cross 0? My understanding is that marginal predictions after logistic regression are interpreted as predicted probabilities, so I was expecting to see CIs constrained to be between 0 and 1.

. margins sex#race4, vce(unconditional)

Predictive margins

Number of strata =  76                            Number of obs   =    2,389
Number of PSUs   = 843                            Population size =    2,352.5017
Design df       =    767

Expression: Pr(outcome), predict()

        
Linearized
Margin   std. err.      t    P>t    [95% conf.    interval]
        

      0. Male   #1. White  |   .0477874   .0066719     7.16   0.000     .0346899    .0608848
      0. Male   #2. Black  |   .0869118   .0247047     3.52   0.000      .038415    .1354086
   0. Male   #3. Hispanic  |   .0127917   .0088384     1.45   0.148    -.0045588    .0301421
0. Male   #4. Other/Multi  |   .0740847   .0329425     2.25   0.025     .0094165     .138753
       1. Female#1. White  |   .0840895   .0160033     5.25   0.000      .052674     .115505
       1. Female#2. Black  |   .0266466   .0174556     1.53   0.127    -.0076199     .060913
    1. Female#3. Hispanic  |   .1230033   .0744384     1.65   0.099    -.0231239    .2691304
 1. Female#4. Other/Multi  |   .0486798   .0288685     1.69   0.092    -.0079909    .1053504

Thank you

[George Hoffman]

you can use the (undocumented) margins option citype(logit) . i use this not infrequently. unfortunately, the dislpayed CI are not stored in the results matrix for marginsplot, so graphical display of the bounded CI's is a problem. i've asked Statacorp to consider a possble modification to margins or marginsplot to enhance this frequent workflow.
maybe there's a better offical response.

[Wes King]

Thank you George! You predicted my next move too- marginsplot to display the results. For now, no one has called me on my current "solution" of setting the axis to 0-1 and letting the CI extend past it an unseen amount, but I would of course like a more statistically sound approach.

[Andrew Musau]

coefplot from SSC allows -citype(logit)-. You could use it to create the marginsplot graph.

webuse lbw, clear
logit low age ht ui i.smoke##i.ftv, robust
est store low
margins 0.smoke#ftv, vce(unconditional)
margins 0.smoke#ftv, vce(unconditional) citype(logit)
marginsplot, xdimension(ftv) title(Marginsplot) saving(gr1, replace)


margins 0.smoke#ftv, vce(unconditional) post
coefplot,  vertical recast(connected) ///
xlab(1 "0" 2 "1" 3 "2" 4 "3" 5 "4") plotregion(margin(zero)) ///
xtitle(`:var lab ftv') ytitle(Pr(low)) title(Coefplot) ///
saving(gr2, replace)

coefplot,  citype(logit) vertical recast(connected) ///
xlab(1 "0" 2 "1" 3 "2" 4 "3" 5 "4")  ///
xtitle(`:var lab ftv')  ytitle(Pr(low)) ///
title(Coefplot with citype(logit)) saving(gr3, replace)

gr combine gr1.gph gr2.gph gr3.gph, col(1)

Res.:

. margins 0.smoke#ftv, vce(unconditional)

Predictive margins                                         Number of obs = 187

Expression: Pr(low), predict()

------------------------------------------------------------------------------
             |            Unconditional
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   smoke#ftv |
Nonsmoker#0  |   .2867769   .0592071     4.84   0.000      .170733    .4028207
Nonsmoker#1  |   .1842438   .0662768     2.78   0.005     .0543436     .314144
Nonsmoker#2  |   .2775391   .0986583     2.81   0.005     .0841724    .4709058
Nonsmoker#3  |   .3470778   .2954094     1.17   0.240    -.2319139    .9260696
Nonsmoker#4  |   .3877901   .2741585     1.41   0.157    -.1495507    .9251309
------------------------------------------------------------------------------

. 
. margins 0.smoke#ftv, vce(unconditional) citype(logit)

Predictive margins                                         Number of obs = 187

Expression: Pr(low), predict()

------------------------------------------------------------------------------
             |            Unconditional
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   smoke#ftv |
Nonsmoker#0  |   .2867769   .0592071     4.84   0.000     .1856629    .4149018
Nonsmoker#1  |   .1842438   .0662768     2.78   0.005     .0868958    .3489696
Nonsmoker#2  |   .2775391   .0986583     2.81   0.005     .1277423    .5019168
Nonsmoker#3  |   .3470778   .2954094     1.17   0.240     .0396629    .8724783
Nonsmoker#4  |   .3877901   .2741585     1.41   0.157     .0618054    .8589679
------------------------------------------------------------------------------

[Jeff Pitblado (StataCorp)]

In Stata 19 update on 03jun2026, we fixed support for citype() in marginsplot.

14. marginsplot, when used after proportion, did not respect the method
specified in proportion's option citype(), which is used to compute
the reported confidence limits for the estimated proportions. This
has been fixed.

While this is not a documented feature of margins, marginsplot will
now also respect the method specified in margins's option citype()
when plotting the reported confidence limits.