A nominal and a continuous variable

Gender × social roles: Figure 14 of Mize (2019)

When one of the interacting variables is continuous, a plot of the predictions is almost always needed, and the tests have two sides: the effect of the continuous variable within each group, and the group difference at each value of the continuous variable. The article’s example is whether holding more social roles protects against high depressive symptoms (as a binary outcome) equally for men and women (Add Health Wave IV).

The model

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.woman i.parrole c.age i.race c.income i.college, vce(robust)
estimates store depmod

The predictions (Figure 14)

quietly margins woman, at(role=(0(1)10))
marginsplot, xdimension(role) recastci(rline) ciopts(lpattern(dash) color(*.4)) ///
    xlabel(0(1)10) ylabel(0(0.1)0.7) xtitle("Number of social roles") ///
    ytitle("Pr(High depressive symptoms)") ///
    title("Figure 14. Pr(high depressive symptoms) by gender and roles")
Variables that uniquely identify margins: role woman
graph export "fig/nli-roles-predictions.png", replace width(1400)
file fig/nli-roles-predictions.png saved as PNG format

Predicted probability of high depressive symptoms by number of social roles, for men and women, with confidence intervals.

Both curves fall as roles accumulate, and women sit above men. The two questions are whether the slope differs by gender and where along the range of roles the gender gap is significant.

The effect of social roles for men and women

The average effect of one additional role, for men and for women, and the second difference. uncentered makes the change run from each person’s observed count to one more. For most applications, we recommend using the default centered change.

mecompare role, models(depmod) by(woman) uncentered
Predicting: Pr(depB)

Marginal effects (N_depmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
role + 1 (uncentered)            |                                       
                             Man |     1     -0.032      0.005      0.000
                           Woman |     2     -0.030      0.006      0.000
metest 1 - 2
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
     role_woman_0 - role_woman_1 |    -0.002      0.008      0.758

Each additional role lowers the probability of high depressive symptoms by about three percentage points for both men and women; the second difference is not significant. The instantaneous rate of change uses amount(rate):

mecompare role, models(depmod) by(woman) amount(rate)
Predicting: Pr(depB)

Marginal effects (N_depmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
role(rate)                       |                                       
                             Man |     1     -0.035      0.006      0.000
                           Woman |     2     -0.031      0.007      0.000
metest 1 - 2
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
     role_woman_0 - role_woman_1 |    -0.004      0.008      0.664

The gender gap at each number of roles

The other side of the interaction is the marginal effect of gender at chosen numbers of roles. A good default for a continuous moderator is its 10th, 50th, and 90th percentiles, from summarize, detail: a low, a typical, and a high number of roles, all in the range of the data. The joint test is the test of interaction on this side; metest 3 - 1 is how much the gap changes from the 10th to the 90th percentile.

quietly summarize role, detail
mecompare i.woman, models(depmod) covariates(role=(`r(p10)' `r(p50)' `r(p90)'))
Predicting: Pr(depB)

Marginal effects (N_depmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
woman                            |                                       
                 Woman - Man     |                                       
                          role=4 |     1      0.076      0.023      0.001
                          role=6 |     2      0.088      0.014      0.000
                          role=8 |     3      0.089      0.019      0.000
metest 1 = 2 = 3
Tests of equality

                                 |      chi2         df     pvalue 
---------------------------------+--------------------------------
  woman_~4 = woman_~6 = woman_~8 |     7.889      2.000      0.019 
metest 3 - 1
                                 |  estimate         se     pvalue 
---------------------------------+--------------------------------
     woman_role_8 - woman_role_4 |     0.013      0.033      0.697

The full picture is the marginal effect of gender at each value of role, from covariates() with the full range. One numbered row per value, each with its own test.

mecompare i.woman, models(depmod) covariates(role=(0(1)10)) store(gap)
Predicting: Pr(depB)

Marginal effects (N_depmod=4307)

                                 |  ME #   Estimate  Robust SE      P>|z|
---------------------------------+---------------------------------------
woman                            |                                       
                 Woman - Man     |                                       
                          role=0 |     1      0.017      0.073      0.811
                          role=1 |     2      0.035      0.060      0.554
                          role=2 |     3      0.052      0.046      0.267
                          role=3 |     4      0.065      0.034      0.054
                          role=4 |     5      0.076      0.023      0.001
                          role=5 |     6      0.084      0.016      0.000
                          role=6 |     7      0.088      0.014      0.000
                          role=7 |     8      0.090      0.016      0.000
                          role=8 |     9      0.089      0.019      0.000
                          role=9 |    10      0.086      0.022      0.000
                         role=10 |    11      0.082      0.024      0.001

This is the information Figure 14 encodes in solid versus dashed lines: the gender gap is significant at three or more roles and not at zero to two. Plotted directly:

coefplot gap_depmod, vertical recast(line) ///
    ciopts(recast(rline) lpattern(dash) color(*.4)) yline(0) ///
    rename("^.*=(.*)$" = \1, regex) ///
    ylabel(-.2(.1).2) xtitle("Number of social roles") ///
    ytitle("Effect of gender: women - men") ///
    title("AME of gender by number of social roles") ///
    note("Effects above zero indicate women have a higher probability of high depressive symptoms"
)
graph export "fig/nli-roles-gender-gap.png", replace width(1400)
file fig/nli-roles-gender-gap.png saved as PNG format

The marginal effect of gender at each number of social roles, with 95% confidence intervals.

A joint test that the gap is the same at every number of roles is the overall test of interaction on this side:

metest 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 9 = 10 = 11
Tests of equality

                                 |      chi2         df     pvalue 
---------------------------------+--------------------------------
         1=2=3=4=5=6=7=8=9=10=11 |   104.705      5.000      0.000
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