xtgee with multinomial outcome

[MJ Smith]

HI all, is it possible to run GEE with a multinomial outcome? I'm using Stata 15.

I found this from several years ago, but wondered if there is an update.

https://www.stata.com/statalist/arch.../msg00884.html

thank you!

[Leonardo Guizzetti]

From what I can tell, -help xtgee- does not have list a generalized logit link nor does it handle nominal multinomial data. SAS does support this (now) if that's something you have access to.

[MJ Smith]

Thank you! I believe this can be run in R as well.

[Joseph Coveney]

SAS does support this (now) if that's something you have access to.

I believe this can be run in R as well.

. . . and, as mentioned in that 17-year-old Statalist post, the model can be fitted in Stata, as well.

Results for the multinomial GEE example given in the online SAS documentation are replicated in Stata below.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ/*ÿDatasetÿfromÿ
>ÿÿÿÿM.ÿS.ÿHurlbut,ÿP.ÿA.ÿWood,ÿandÿR.ÿL.ÿHough,
>ÿÿÿÿÿÿProvidingÿIndependentÿHousingÿforÿtheÿHomelessÿMentallyÿIll:ÿAÿNovelÿ
>ÿÿÿÿÿÿÿÿApproachÿtoÿEvaluatingÿLong-TermÿLongitudinalÿHousingÿPatternsÿ
>ÿÿÿÿÿÿÿÿ_JournalÿofÿCommunityÿPsychology_ÿ24:291–310,ÿ1996
>ÿÿÿÿvia
>ÿÿÿÿhttps://documentation.sas.com/doc/en/statcdc/14.2/statug/statug_code_geeex6.htmÿ*/
.ÿ
.ÿquietlyÿinputÿintÿIDÿbyte(HousingÿTimeÿSec)

.ÿ
.ÿmlogitÿHousingÿib1.Sec,ÿvce(clusterÿID)ÿbaseoutcome(2)ÿnolog

MultinomialÿlogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿÿ1,289
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(2)ÿÿ=ÿÿ60.93
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿ=ÿ0.0000
Logÿpseudolikelihoodÿ=ÿ-1331.734ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿPseudoÿR2ÿÿÿÿÿ=ÿ0.0360

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(Std.ÿerr.ÿadjustedÿforÿ361ÿclustersÿinÿID)
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿRobust
ÿÿÿÿÿHousingÿ|ÿCoefficientÿÿstd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
0ÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ0.Secÿ|ÿÿÿ.9226118ÿÿÿ.1852991ÿÿÿÿÿ4.98ÿÿÿ0.000ÿÿÿÿÿ.5594322ÿÿÿÿ1.285791
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.9531952ÿÿÿ.1267465ÿÿÿÿ-7.52ÿÿÿ0.000ÿÿÿÿ-1.201614ÿÿÿ-.7047767
-------------+----------------------------------------------------------------
1ÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿ0.Secÿ|ÿÿÿ1.264483ÿÿÿ.1644369ÿÿÿÿÿ7.69ÿÿÿ0.000ÿÿÿÿÿ.9421922ÿÿÿÿ1.586773
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.6561586ÿÿÿ.1065288ÿÿÿÿ-6.16ÿÿÿ0.000ÿÿÿÿ-.8649512ÿÿÿÿ-.447366
-------------+----------------------------------------------------------------
2ÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿ(baseÿoutcome)
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Leonardo Guizzetti]

Thanks for demonstrating the equivalence, Joseph Coveney.

[Jeff Wooldridge]

Just to be clear, almost any Stata command can be used for pooled estimation with panel data. I can use logit, probit, tobit, poisson, and so on and cluster my standard errors to account for serial correlation and misspecified density. When I see people wanting to use xtgee I assume they want a more efficient estimator than just using a pooled method (and then clustering standard errors). To me, pooled MLE is GEE in a very limited sense. If you want to exploit, say, an exchangeable correlation structure with the hope of improving efficiency then I don't think Stata supports that with a multinomial response. It does for binary, fractional, and count (generally, nonnegative) responses. Stata could support a multinomial response -- at least using two-step GEE.

In my experience, the pooled method is often sufficient, and once one compares cluster robust standard errors across the methods, GEE doesn't seem to deliver much by way of smaller standard errors with discrete responses. But this is just my experience -- there must be cases where GEE delivers efficiency gains. I'd actually like to see one if anyone has an example.

[MJ Smith]

Thanks all - this discussion is extremely helpful.