# st: Testing IIA of multinomial logistic survey?

 From "Jens Clausen" To Subject st: Testing IIA of multinomial logistic survey? Date Mon, 01 Aug 2005 14:32:48 +0200

```Dear all,

I have a 'how-to' question which I would really appreciate some help
with: How to test IIA of a multinomial logistic model for survey data?
Below is some explanation of the setup (I appreciate corrections and
suggestions)

The survey contains several responses (Y can take the values 0 1 2 3)
for some subjects (one row/line/record for each response for each
subject). The subjects are identified by IDNR and should be weighted by
VGT1. The explanatory variables in `xlist' are constant for each
subject. I estimating the model and test simple hypotheses by

. svyset [pweight=VGT1], psu(IDNR);
. svydes;
. svymlogit Y `xlist', basecategory(0);
. testparm AGEGRP*;

However, I am not sure how to test the IIA assumption. I seem to be
unable to (figure out how to?) use lrtest or the estimates from
svymlogit for testing, so instead I re-estimate the model using
iweight-ed mlogit (with one resonse left out at a time) and then use
suest,svy to get the robust covariance matrix for testing between the
models:

. quietly mlogit Y `xlist' [iweight=VGT1], basecategory(0)
score(iia0_*);
. est store iia0;
. foreach i in 1 2 3 {;
.   quietly mlogit Y `xlist' [iweight=VGT1] if Y~=`i', basecategory(0)
score(iia`i'_*);
.   est store iia`i';
. };
. suest iia*, svy;

Now I can think of two ways of testing, either test equality of
differences from the base model iia0:

. foreach i in `xlist' {;
.   quietly test ([iia0_1]`i'-[iia0_2]`i'=[iia3_1]`i'-[iia3_2]`i')
.     ([iia0_1]`i'-[iia0_3]`i'=[iia2_1]`i'-[iia2_3]`i')
.     ([iia0_2]`i'-[iia0_3]`i'=[iia1_2]`i'-[iia1_3]`i'), notest
accumulate;
. };
. test, accumulate;

or test equality with the base model:

. test ([iia0_1=iia2_1=iia3_1]) ([iia0_2=iia1_2=iia3_2])
([iia0_3=iia1_3=iia2_3]), common;

but which is correct, if any of the two? Or is there a better way to
test the IIA of such a survey?
(The two tests give the same F-value but the second has twice as many
degrees of freedom)

Thank you,
Jens Clausen
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