Multinomial probit (mprobit): Syntax for specifying constraints

[John Mullahy]

Colleagues: The model being estimated is

mprobit y i.(x1 x2 x3 x4 x5)

LHS variable y has 5 distinct categories and is coded {0,1,2,3,4}. Each x-variable is binary.

I would like to estimate a constrained version of the model where the all coefficients corresponding to outcome categories 1, 2, and 3 are constrained to be equal. The first such constraint might be specified as

constraint 1 [1]_cons=[2]_cons

etc. etc.

Is it the case that each constraint for each pair of parameters must be defined in separate constraint commands, or are there any wildcard (or other shortcuts) that would permit all parameters (_cons, x1, ..., x5) for one outcome to be constrained equal to those for another outcome?

Thanks very much in advance for any suggestions.

[Andrew Musau]

Maybe the following helps.

webuse sysdsn1
constraint 1  [Prepaid=Uninsure] :age :male :nonwhite :2.site :3.site :_cons
mprobit insure age male nonwhite i.site, constraints(1)

Result:

. constraint 1  [Prepaid=Uninsure] :age :male :nonwhite :2.site :3.site :_cons

. mprobit insure age male nonwhite i.site, constraints(1)

Iteration 0:   log likelihood = -652.53577  
Iteration 1:   log likelihood = -635.40528  
Iteration 2:   log likelihood = -635.39863  
Iteration 3:   log likelihood = -635.39863  

Multinomial probit regression                   Number of obs     =        615
                                                Wald chi2(5)      =      25.98
Log likelihood = -635.39863                     Prob > chi2       =     0.0001

 ( 1)  [Prepaid]age - [Uninsure]age = 0
 ( 2)  [Prepaid]male - [Uninsure]male = 0
 ( 3)  [Prepaid]nonwhite - [Uninsure]nonwhite = 0
 ( 4)  [Prepaid]2.site - [Uninsure]2.site = 0
 ( 5)  [Prepaid]3.site - [Uninsure]3.site = 0
 ( 6)  [Prepaid]_cons - [Uninsure]_cons = 0
------------------------------------------------------------------------------
      insure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Indemnity    |  (base outcome)
-------------+----------------------------------------------------------------
Prepaid      |
         age |  -.0090318   .0047737    -1.89   0.058     -.018388    .0003245
        male |   .4383369   .1558006     2.81   0.005     .1329734    .7437004
    nonwhite |    .680846    .179048     3.80   0.000     .3299184    1.031774
             |
        site |
          2  |  -.0278458   .1630128    -0.17   0.864     -.347345    .2916534
          3  |  -.4080612   .1710502    -2.39   0.017    -.7433134    -.072809
             |
       _cons |  -.1806967   .2525669    -0.72   0.474    -.6757187    .3143252
-------------+----------------------------------------------------------------
Uninsure     |
         age |  -.0090318   .0047737    -1.89   0.058     -.018388    .0003245
        male |   .4383369   .1558006     2.81   0.005     .1329734    .7437004
    nonwhite |    .680846    .179048     3.80   0.000     .3299184    1.031774
             |
        site |
          2  |  -.0278458   .1630128    -0.17   0.864     -.347345    .2916534
          3  |  -.4080612   .1710502    -2.39   0.017    -.7433134    -.072809
             |
       _cons |  -.1806967   .2525669    -0.72   0.474    -.6757187    .3143252
------------------------------------------------------------------------------

[John Mullahy]

Thanks very much, Andrew. I was not aware of that syntax, but it is exactly what I need.

I suppose it was too much to hope that there would be some sort of wildcard. A middle ground I'll consider is to use a local that can be invoked repeatedly, e.g.

webuse sysdsn1
local rhs "age male nonwhite 2.site 3.site"
constraint 2 [Prepaid=Uninsure] :`rhs' :_cons
mprobit insure age male nonwhite i.site, constraints(2)

Results

Multinomial probit regression                   Number of obs     =        615
                                                Wald chi2(5)      =      25.98
Log likelihood = -635.39863                     Prob > chi2       =     0.0001

 ( 1)  [Prepaid]age - [Uninsure]age = 0
 ( 2)  [Prepaid]male - [Uninsure]male = 0
 ( 3)  [Prepaid]nonwhite - [Uninsure]nonwhite = 0
 ( 4)  [Prepaid]2.site - [Uninsure]2.site = 0
 ( 5)  [Prepaid]3.site - [Uninsure]3.site = 0
 ( 6)  [Prepaid]_cons - [Uninsure]_cons = 0
------------------------------------------------------------------------------
      insure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Indemnity    |  (base outcome)
-------------+----------------------------------------------------------------
Prepaid      |
         age |    -0.0090     0.0048    -1.89   0.058      -0.0184      0.0003
        male |     0.4383     0.1558     2.81   0.005       0.1330      0.7437
    nonwhite |     0.6808     0.1790     3.80   0.000       0.3299      1.0318
             |
        site |
          2  |    -0.0278     0.1630    -0.17   0.864      -0.3473      0.2917
          3  |    -0.4081     0.1711    -2.39   0.017      -0.7433     -0.0728
             |
       _cons |    -0.1807     0.2526    -0.72   0.474      -0.6757      0.3143
-------------+----------------------------------------------------------------
Uninsure     |
         age |    -0.0090     0.0048    -1.89   0.058      -0.0184      0.0003
        male |     0.4383     0.1558     2.81   0.005       0.1330      0.7437
    nonwhite |     0.6808     0.1790     3.80   0.000       0.3299      1.0318
             |
        site |
          2  |    -0.0278     0.1630    -0.17   0.864      -0.3473      0.2917
          3  |    -0.4081     0.1711    -2.39   0.017      -0.7433     -0.0728
             |
       _cons |    -0.1807     0.2526    -0.72   0.474      -0.6757      0.3143
------------------------------------------------------------------------------

Thanks again for your help and for the tutorial.