# Probit model: marginal effects cannot be estimated because one dummy variable was dropped for predicting failure perfectly

I have a basic question about the -margins- command in Stata: I was wondering if there was a workaround to run marginal effects for a model where one of the dummy variables was dropped for predicting failure perfectly. I fitted the following model:

$Cat01_i= Province_i + X_i$

Where $i$ indexes a household (the unit of analysis) and $Cat01_i$ is an indicator variable that takes the value of 1 if the household had catastrophic health expenditures during the period of observation and 0 otherwise; $Province_i$ is the province where the household is located (4 provinces in the country); and $X_i$ is a vector of household-level variables, such as household composition ($Composition_i$), household size ($HHsize_i$), and so on.

When I ran the model on the subsample of households in the "rich" wealth quintile, one of the 4 provinces dropped from the model, as none of the households experienced catastrophic health expenditures:

. svy, subpop(rich):probit cat01 i.composition i.hhsize i.femhead i.rural1 i.province i.hftime Utoilet Uwats ndhous
(running probit on estimation sample)

note: 4.province != 0 predicts failure perfectly
4.province dropped and 651 obs not used

Survey: Probit regression

Number of strata   =         1                  Number of obs      =     15660
Number of PSUs     =     15660                  Population size    =  20122241
Subpop. no. of obs =      4766
Subpop. size       = 6313622.5
Design df          =     15659
F(  14,  15646)    =      8.41
Prob > F           =    0.0000

------------------------------------------------------------------------------
|             Linearized
cat01 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
composition |
2  |   .1069954   .1119435     0.96   0.339    -.1124267    .3264175
3  |   -.032983   .1390949    -0.24   0.813     -.305625    .2396591
4  |   .2564817   .1241049     2.07   0.039     .0132219    .4997416
|
hhsize |
2  |   .0668393   .1467692     0.46   0.649    -.2208453    .3545239
3  |   .1200252    .159606     0.75   0.452    -.1928209    .4328713
4  |   .2342203   .1857467     1.26   0.207    -.1298648    .5983053
|
2.headgen |   .0094895   .1415363     0.07   0.947    -.2679381    .2869171
2.region |   .3577401   .1030666     3.47   0.001     .1557176    .5597626
|
province |
2  |  -.3977903   .1118677    -3.56   0.000    -.6170639   -.1785167
3  |  -.0668117    .093569    -0.71   0.475    -.2502177    .1165944
4  |          0  (empty)
|
2.hftime |   .3632561   .1001219     3.63   0.000     .1670056    .5595066
Utoilet |   .5646311   .1750698     3.23   0.001      .221474    .9077882
Uwats |   .0874042   .1067579     0.82   0.413    -.1218536    .2966621
ndhous |   .3183725   .0970297     3.28   0.001     .1281832    .5085618
_cons |  -2.656799   .2338666   -11.36   0.000    -3.115205   -2.198394
------------------------------------------------------------------------------


When I ran the -margins- command, I got the following error message:

. margins,dydx(*)
missing predicted values encountered within the estimation sample
r(322);


I think this is because Stata still considers those households in Province 4 to be part of the estimation sample, even though they were not used in the estimation. My two questions are then:

1. Is there a "workaround" to this (meaning force Stata to calculate the marginal effect on the estimation sample), or is my only course of action fit the model without Province 4 and run the margins after fitting the probit sans Province 4?

. svy, subpop(rich):probit cat01 i.composition i.hhsize i.femhead i.rural1 province2 province3 i.hftime Utoilet Uwats ndhous

2. If I do the latter (i.e. exclude Province 4), would my estimates for the "rich" subpopulation be comparable to my estimates for the other wealth quintiles where none of the variables were dropped for predicting success/failure completely?

• The usual solution to separation is to use penalized MLE, like firthlogit. Unfortunately, Firth's correction deals with the information matrix for iid data, which is explicitly not the case with survey data. – Dimitriy V. Masterov Apr 28 '15 at 20:32