Bonus: Joint tests of interaction

Moderators with more than two categories

This example is not in Mize (2019), but it uses the same Add Health data as the other pages in this section.

When the moderator has more than two categories, there are more than two marginal effects to compare. A good first step is a joint test of whether they are all equal. If the joint test is significant, there is evidence of an interaction, and you can move on to testing which specific contrasts differ. If a specific difference is hypothesized, test it directly.

A continuous variable and a nominal moderator

Does the effect of social roles on high depressive symptoms differ across the five levels of education?

use "https://tdmize.github.io/data/data/nli_ah4", clear
(Add Health Wave IV | NLI - Nonlinear Interaction Effects | 2018-12-17)

. 
quietly logit depB c.role##i.educ i.woman i.parrole c.age i.race c.income, vce(robust)
estimates store depedmod

by(educ) reports the effect of one more role at each level of education, in rows 1 to 5. metest 1 = 2 = 3 = 4 = 5 is the joint test that the five effects are equal.

mecompare role, models(depedmod) by(educ)
Predicting: Pr(depB)

Marginal effects (N_depedmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
role + 1 (centered)              |                                       
           No High School Degree |     1     -0.069      0.016      0.000
              High School Degree |     2     -0.033      0.011      0.002
                    Some College |     3     -0.031      0.007      0.000
                  College Degree |     4     -0.021      0.010      0.027
                 Graduate Degree |     5     -0.018      0.014      0.184
metest 1 = 2 = 3 = 4 = 5
Tests of equality

                                 |      chi2         df     pvalue 
---------------------------------+--------------------------------
                       1=2=3=4=5 |     7.307      4.000      0.121

The joint test is not significant (p = 0.12), so there is no evidence that the effect of social roles differs by education, and we do not go on to test the pairs.

A nominal variable: one equality per contrast

With a nominal focal variable, each contrast with the base category has its own rows, so the joint test lists one equality per contrast. Here, the effect of education on drinking for men and for women – the other side of the gender × education interaction on the Two nominal variables page:

quietly logit alcB i.educ##i.woman c.age i.race c.income, vce(robust)
estimates store alcedmod
. 
mecompare i.educ, models(alcedmod) by(woman)
Predicting: Pr(alcB)

Marginal effects (N_alcedmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
educ                             |                                       
    High School - No High Sc     |                                       
                             Man |     1      0.025      0.047      0.590
                           Woman |     2      0.210      0.052      0.000
    Some Colleg - No High Sc     |                                       
                             Man |     3      0.080      0.045      0.075
                           Woman |     4      0.232      0.047      0.000
    College Deg - No High Sc     |                                       
                             Man |     5      0.099      0.047      0.036
                           Woman |     6      0.326      0.049      0.000
    Graduate De - No High Sc     |                                       
                             Man |     7      0.132      0.056      0.019
                           Woman |     8      0.294      0.054      0.000
metest (1 = 2) (3 = 4) (5 = 6) (7 = 8)
Tests of equality

                                 |      chi2         df     pvalue 
---------------------------------+--------------------------------
            (1=2)(3=4)(5=6)(7=8) |    12.497      4.000      0.014

The joint test is significant (p = 0.014): the effects of education differ for men and women. metest 1 - 2, metest 3 - 4, and so on test which contrasts differ.

With two nominal variables, the joint test is the same from either side of the interaction: it equals the joint test of the five gender gaps on the Two nominal variables page (metest 1 = 2 = 3 = 4 = 5; chi2 = 12.50 both ways). This is not true of interactions in general, e.g., when one of the variables is continuous.

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