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st: RE: RE: RE: Reference group for categorical interactions


From   "Hussein, Mustafa (Mustafa Hussien)" <[email protected]>
To   "[email protected]" <[email protected]>
Subject   st: RE: RE: RE: Reference group for categorical interactions
Date   Wed, 25 Sep 2013 23:53:52 +0000

Why would you need to reconcile that? The purpose of having interaction terms along with main effects is to get a grasp of the whole picture. Have you tried to see the marginal effects on your separate terms (in your model with interactions)? They may too differ from what you would expect from their ORs. Though widely used, ORs mask the heterogeneity in the marginal effects across subjects, and their interpretation in the presence of interaction terms is not straightforward. I would suggest sticking to the marginal effects at the means, if that's meaningful, or estimate them at some relevant representative values for other covariates. 

A very user friendly reference (including instructions on some useful commands for interaction effects) is by Karaca-Mandic, Norton & Dowd (2012): http://onlinelibrary.wiley.com/doi/10.1111/j.1475-6773.2011.01314.x/abstract 

very best,
-Mustafa    
________________________________________
From: [email protected] [[email protected]] on behalf of Valle, Giuseppina [[email protected]]
Sent: Wednesday, September 25, 2013 6:30 PM
To: [email protected]
Subject: st: RE: RE: Reference group for categorical interactions

Thank you. That was a thought that crossed my mind. Do you know any way of reconciling this?

Thanks,
Pina
________________________________________
From: [email protected] <[email protected]> on behalf of Hussein, Mustafa (Mustafa Hussien) <[email protected]>
Sent: Wednesday, September 25, 2013 4:13 PM
To: [email protected]
Subject: st: RE: Reference group for categorical interactions

Hi Pina,

I wonder if that's because of the odds ratios/marginal effects associated with your un-interacted terms "maleoral" and "agesex". Margins takes into account all the ways a given term is expressed on the rhs of your model.

Hope that helps.
Mustafa
________________________________________
From: [email protected] [[email protected]] on behalf of Valle, Giuseppina [[email protected]]
Sent: Wednesday, September 25, 2013 3:20 PM
To: [email protected]
Subject: st: Reference group for categorical interactions

Hello. I am trying to examine an interaction between two categorical predictors, each with 4 categories. For both of the variables:

1 = early
2 = normative
3 = late
4 = none

I want 2 or "normative" to be the referent for both variables, so I use the code:

fvset base 2 maleoral
fvset base 2 agesex

Then for the regression, I run:

svy, subpop(if gender==1): logistic conflict i.race ///
        agew4 i.famstw1 fameduc paedmis faminc incmiss adrel ///
        i.respeduc i.respinc sexforce std nonmar ///
        i.maleoral i.agesex i.maleoral#i.agesex

I get the following for the interaction term:

maleoral#agesex |
           1 1  |   2.626719   1.802462     1.41   0.162     .6756814     10.2114
           1 3  |          1  (empty)
           1 4  |   .6300918   1.185243    -0.25   0.806      .015239    26.05259
           3 1  |   2.467789   2.386861     0.93   0.352     .3640513    16.72836
           3 3  |    2.14585   .7743234     2.12   0.036     1.050786    4.382122
           3 4  |   2.751272   1.981607     1.41   0.162     .6616117      11.441
           4 1  |   1.601467   1.969695     0.38   0.702     .1404772    18.25703
           4 3  |   .5788523   .4207023    -0.75   0.453     .1374108    2.438454
           4 4  |   .3059179   .2770581    -1.31   0.193     .0509737     1.83596

I thought my reference group was respondents who were normative on "maleoral" AND normative on "agesex." But when I graph these, the results do not line up.

When I run the code:

margins maleoral#agesex, subpop(if gender==1) atmeans

Here is what I get:

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
maleoral#agesex |
           1 1  |   .2800785   .0805011     3.48   0.001     .1222993    .4378577
           1 2  |   .2389972   .1031905     2.32   0.021     .0367476    .4412468
           1 3  |          .  (not estimable)
           1 4  |   .0800896   .1295187     0.62   0.536    -.1737624    .3339417
           2 1  |   .1584989   .0410836     3.86   0.000     .0779765    .2390213
           2 2  |   .2854029   .0164211    17.38   0.000     .2532181    .3175876
           2 3  |   .1714103   .0296434     5.78   0.000     .1133102    .2295103
           2 4  |   .1494563   .0549283     2.72   0.007     .0417989    .2571137
           3 1  |   .1995144   .1381576     1.44   0.149    -.0712694    .4702983
           3 2  |   .1763853   .0405574     4.35   0.000     .0968943    .2558763
           3 3  |   .1922673   .0243652     7.89   0.000     .1445124    .2400222
           3 4  |   .2058666   .0774489     2.66   0.008     .0540695    .3576636
           4 1  |   .3372326   .2668201     1.26   0.206    -.1857253    .8601904
           4 2  |   .4025265    .108945     3.69   0.000     .1889982    .6160547
           4 3  |   .1680508   .0923209     1.82   0.069    -.0128949    .3489965
           4 4  |    .083139   .0436156     1.91   0.057     -.002346    .1686239

According to the odds ratios above, 3 and 3 (late and late) should results in a greater probability of my outcome compared to 2 and 2 (normative and normative), but according to the margins, 3 and 3 = 0.19 and 2 and 2 = 0.28. Am I confused about my reference group?

Any help would be greatly appreciated.

Thanks,
Pina Valle




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