mlogit/mprobit: Standard error for marginal effect on combination of outcomes

[Klaus Nowotny]

Dear statalist users,

when estimating a multinomial logit or probit model for a dependent variable with multiple outcomes, one can calculate the marginal effect on a combination of outcomes, e.g., the marginal effect on "either outcome 1 or outcome 2", as the sum of the marginal effect on outcome 1 and the marginal effect on outcome 2, since the outcomes are mutually exclusive.

But how would one calculate the standard error for the marginal effect on "either outcome 1 or outcome 2"? Or is there another way to calculate the marginal effect on the joint probability of more than one outcome?

Any help is greatly appreciated!

[Richard Williams]

Is this what you want? If so, do

findit spost13_ado

and install it to get mlincom and other great commands.

webuse nhanes2f, clear
mlogit health weight
margins, post
mlincom 1+2, stat(e se z p ll ul) dec(5)

Here is the output:

. webuse nhanes2f, clear

. mlogit health weight, nolog

Multinomial logistic regression                 Number of obs     =     10,335
                                                LR chi2(4)        =      18.98
                                                Prob > chi2       =     0.0008
Log likelihood = -15754.909                     Pseudo R2         =     0.0006

------------------------------------------------------------------------------
      health |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
poor         |
      weight |   .0049858   .0026369     1.89   0.059    -.0001825    .0101541
       _cons |  -1.755365   .1965752    -8.93   0.000    -2.140645   -1.370085
-------------+----------------------------------------------------------------
fair         |
      weight |   .0040704   .0019692     2.07   0.039     .0002108    .0079299
       _cons |  -.8596221   .1460849    -5.88   0.000    -1.145943    -.573301
-------------+----------------------------------------------------------------
average      |  (base outcome)
-------------+----------------------------------------------------------------
good         |
      weight |  -.0011393   .0017626    -0.65   0.518    -.0045939    .0023153
       _cons |  -.0439027   .1293509    -0.34   0.734    -.2974257    .2096203
-------------+----------------------------------------------------------------
excellent    |
      weight |    -.00358   .0018124    -1.98   0.048    -.0071322   -.0000277
       _cons |   .0566302   .1323952     0.43   0.669    -.2028596    .3161199
------------------------------------------------------------------------------

. margins, post

Predictive margins                              Number of obs     =     10,335
Model VCE    : OIM

1._predict   : Pr(health==poor), predict(pr outcome(1))
2._predict   : Pr(health==fair), predict(pr outcome(2))
3._predict   : Pr(health==average), predict(pr outcome(3))
4._predict   : Pr(health==good), predict(pr outcome(4))
5._predict   : Pr(health==excellent), predict(pr outcome(5))

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _predict |
          1  |    .070537   .0025181    28.01   0.000     .0656017    .0754723
          2  |   .1615868   .0036191    44.65   0.000     .1544935    .1686801
          3  |   .2842767    .004437    64.07   0.000     .2755804    .2929731
          4  |   .2507015   .0042632    58.81   0.000     .2423459    .2590571
          5  |   .2328979   .0041559    56.04   0.000     .2247524    .2410434
------------------------------------------------------------------------------

. mlincom 1+2, stat(e se z p ll ul) dec(5)

             |   lincom        se    zvalue    pvalue        ll        ul 
-------------+------------------------------------------------------------
           1 |  0.23212   0.00415  55.93531   0.00000   0.22399   0.24026 

.

You can probably do this without spost13 but spost13 makes it easier.

[Klaus Nowotny]

Dear Richard, this is exactly what I was looking for, thank you so much!