Testing for difference in marginal effects at two values of same continuous independent variable

[Kelsey Wright]

Hi all, and thanks in advance for any responses.

I'm estimating the following model: mlogit enroll_method ses_index2 i.race2 physical2 emotion2 i.enroll_site enroll_age i.period, vce(robust), where enroll_method is one of six contraceptive methods selected at enrollment in a study and ses_index2 is a composite index with continuous values.

For each enroll_method, I have run the margins command to get the predicted probability at the 10th and 90th percentile values of the ses_index2:
margins, at(ses_index2=(1 6)) predict(outcome(2))

For this example I get the following results:

Predictive margins Number of obs = 12,316
Model VCE : Robust

Expression : Pr(enroll_method==2), predict(outcome(2))

1._at : ses_index2 = 1

2._at : ses_index2 = 6

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | .1607696 .004946 32.50 0.000 .1510756 .1704636
2 | .114489 .0061308 18.67 0.000 .102473 .1265051
------------------------------------------------------------------------------


I now want to test whether .1607696 is significantly different than .114489, but am having trouble finding sufficient documentation to do this on (1) a continuous independent variable and (2) for different values of the same independent variable.

Any and all advice would be deeply appreciated!
Best,
Kelsey

[Marcos Almeida]

I recommend to use - margins - plus - contrast - for that matter. Use the categorical variable such as "r.var" for that matter.

[Dimitriy V. Masterov]

You can accomplish this in at least two ways:

cls
webuse sysdsn1
mlogit insure age male nonwhite i.site

/* one-step contrasts of margins method, but has confusing syntax */
margins, at(age = (20 40)) predict(outcome(2)) contrast(atcontrast(r._at) wald)
// or use contrast(atcontrast(a._at) wald) to flip the sign

/* two-step method: post margins results to make them behave like estimation results and then test */
margins, at(age = (20 40)) predict(outcome(2)) post
test _b[1._at] == _b[2._at]

[Bruce Weaver]

Hi Dimitriy. If I follow, your code in #3 is generates a test contrasting two predicted probabilities. Is there a way to include xb somewhere to get a contrast of the log-odds?

Thanks,
Bruce

[Dimitriy V. Masterov]

Bruce Weaver, I think changing the predict() option should do it:

margins, at(age = (20 40)) predict(xb outcome(2)) contrast(atcontrast(r._at) wald)

-pr- is the default, so I omitted it above.

[Bruce Weaver]

Hi Dimitriy. That's more or less what I was trying without success. Tacking that line on to the end of your code in #3 is generating an error:

. margins, at(age = (20 40)) predict(outcome(2) xb) contrast(atcontrast(r._at) wald)
option at() not allowed
r(198);

search for r(198)                                                        (manual:  [R] search)
----------------------------------------------------------------------------------------------

Search of official help files, FAQs, Examples, SJs, and STBs

[P]     error . . . . . . . . . . . . . . . . . . . . . . . .  Return code 198
        invalid syntax
        option __________ incorrectly specified
        option __________ not allowed
        __________ invalid
        range invalid
        __________ invalid obs no
        invalid filename
        __________ invalid varname
        __________ invalid name
        multiple by's not allowed
        __________ found where number expected
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[Dimitriy V. Masterov]

That's happening because I posted the margins, which overwrites the original mlogit estimation results, which breaks the at() option. The error is not very helpful here.

If you just re-run the mlogit it should work fine:

. webuse sysdsn1
(Health insurance data)

. mlogit insure age male nonwhite i.site

Iteration 0:   log likelihood = -555.85446  
Iteration 1:   log likelihood = -534.67443  
Iteration 2:   log likelihood = -534.36284  
Iteration 3:   log likelihood = -534.36165  
Iteration 4:   log likelihood = -534.36165  

Multinomial logistic regression                 Number of obs     =        615
                                                LR chi2(10)       =      42.99
                                                Prob > chi2       =     0.0000
Log likelihood = -534.36165                     Pseudo R2         =     0.0387

------------------------------------------------------------------------------
      insure |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Indemnity    |  (base outcome)
-------------+----------------------------------------------------------------
Prepaid      |
         age |   -.011745   .0061946    -1.90   0.058    -.0238862    .0003962
        male |   .5616934   .2027465     2.77   0.006     .1643175    .9590693
    nonwhite |   .9747768   .2363213     4.12   0.000     .5115955    1.437958
             |
        site |
          2  |   .1130359   .2101903     0.54   0.591    -.2989296    .5250013
          3  |  -.5879879   .2279351    -2.58   0.010    -1.034733   -.1412433
             |
       _cons |   .2697127   .3284422     0.82   0.412    -.3740222    .9134476
-------------+----------------------------------------------------------------
Uninsure     |
         age |  -.0077961   .0114418    -0.68   0.496    -.0302217    .0146294
        male |   .4518496   .3674867     1.23   0.219     -.268411     1.17211
    nonwhite |   .2170589   .4256361     0.51   0.610    -.6171725     1.05129
             |
        site |
          2  |  -1.211563   .4705127    -2.57   0.010    -2.133751   -.2893747
          3  |  -.2078123   .3662926    -0.57   0.570    -.9257327     .510108
             |
       _cons |  -1.286943   .5923219    -2.17   0.030    -2.447872   -.1260134
------------------------------------------------------------------------------

. margins, at(age = (20 40)) predict(xb outcome(2)) contrast(atcontrast(r._at) wald)

Contrasts of predictive margins
Model VCE    : OIM

Expression   : Linear prediction, insure==Prepaid, predict(xb outcome(2))

1._at        : age             =          20

2._at        : age             =          40

------------------------------------------------
             |         df        chi2     P>chi2
-------------+----------------------------------
         _at |          1        3.59     0.0580
------------------------------------------------

--------------------------------------------------------------
             |            Delta-method
             |   Contrast   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
         _at |
   (2 vs 1)  |  -.2348998   .1238921     -.4777238    .0079243
--------------------------------------------------------------

[Bruce Weaver]

Ah, yes. Of course. (I'd insert a palm-to-forehead emoticon if there was one.) Thanks for that, Dimitriy.

And if Kelsey wants the log-odds for each value of her variable, she could add another -margins- command without the contrast option.

clear *
webuse sysdsn1
mlogit insure age male nonwhite i.site
margins, at(age = (20 40)) predict(xb outcome(2))
margins, at(age = (20 40)) predict(xb outcome(2)) contrast(atcontrast(r._at) wald)
margins, at(age = (20 40)) predict(xb outcome(2)) contrast(atcontrast(a._at) wald)