A2.4 Interaction effect with factor syntax
use "https://tdmize.github.io/data/data/cda_gss", clear(cda_gss.dta | GSS 1972-2021 CDA - Categorical Data Analysis | date created 202
> 3)regress occprest c.age##i.woman i.college Source | SS df MS Number of obs = 58,304
-------------+---------------------------------- F(4, 58299) = 4703.09
Model | 2777942.63 4 694485.657 Prob > F = 0.0000
Residual | 8608766.27 58,299 147.665762 R-squared = 0.2440
-------------+---------------------------------- Adj R-squared = 0.2439
Total | 11386708.9 58,303 195.302281 Root MSE = 12.152
-------------------------------------------------------------------------------
occprest | Coefficient Std. err. t P>|t| [95% conf. interval]
--------------+----------------------------------------------------------------
age | 0.072 0.004 16.316 0.000 0.063 0.081
|
woman |
Women | 2.365 0.290 8.146 0.000 1.796 2.934
|
woman#c.age |
Women | -0.055 0.006 -9.343 0.000 -0.067 -0.044
|
college |
College De.. | 16.392 0.121 135.948 0.000 16.156 16.628
_cons | 35.226 0.216 162.811 0.000 34.802 35.650
-------------------------------------------------------------------------------*Stata makes it easy to include product terms for interaction effects. Make sure you have specified c. or i. on the variables of interest and then add ## between them. Stata will include each constituent variable’s main effect and the product term
Plotting interaction effects
We can easily plot the effects from an interactive model with margins and marginsplot. No special code is needed; the code is the same with or without interaction effects—however, you must have used the i. and c. prefixes on the regress command
qui margins, at(age=(20(5)80) woman=(0 1))
marginsplot, ///
recastci(rline) ciopts(lpat(dash) col(gs14)) ylab(38(2)46) ///
title("Predicted Occupational Prestige Based on Person's Age and Gender") ///
subtitle("Interaction Term: Gender X Age") ///
ytitle("Occupational Prestige")Interpreting interaction effects using marginal effects
One thing the coefficients cannot tell us is whether the effect of age is significant for both men and women. That is, the significance test on the product term coefficient indicates that the effects differ—but are either significant? In addition, while we can add multiple coefficients together to get what the effects are for each group (i.e. effect of age for men; effect of age for women)—this is only the case when the effects are linear. Marginal effects can tell us whether each effect is significant and what the effect is regardless as to whether the effect is linear or nonlinear
*Calculate AMEs of age for men and women
mchange age, at(woman=0)regress: Changes in xb | Number of obs = 58304
Expression: Linear prediction, predict()
| Change p-value
-------------+---------------------
age |
+1 | 0.072 0.000
+SD | 1.235 0.000
Marginal | 0.072 0.000
Average prediction
42.247
Base values of regressors
| woman
-------------+----------
at | 0 mchange age, at(woman=1)regress: Changes in xb | Number of obs = 58304
Expression: Linear prediction, predict()
| Change p-value
-------------+---------------------
age |
+1 | 0.017 0.000
+SD | 0.287 0.000
Marginal | 0.017 0.000
Average prediction
42.063
Base values of regressors
| woman
-------------+----------
at | 1 On average, for men an additional year of age is associated with a 0.072 point increase in occupational prestige
On average, for women an additional year of age is associated with a 0.017 point increase in occupational prestige