Group comparisons
Section 4.2 of Mize and Han (forthcoming).
Separate models for each group let every effect differ across the groups. These examples fit a model to each group and compare the effects across the models.
library(suest)
library(marginaleffects)
library(haven)
gss <- zap_labels(read_dta("https://tdmize.github.io/data/data/gss_cme.dta"))
wvs <- zap_labels(read_dta("https://tdmize.github.io/data/data/lvm_wvs6.dta"))
factorize <- function(data, variables) {
data[variables] <- lapply(data[variables], factor)
data
}Separate models for men and women (Table 6)
The probability of being very happy among employed GSS respondents from 2000 on, modeled separately for men and for women.
vars6 <- c("vhappy", "college", "wages", "occprest", "age", "married",
"parent", "woman", "conserv", "race")
dat6 <- subset(gss, year >= 2000 & employed == 1)
dat6 <- dat6[complete.cases(dat6[vars6]), ]
dat6 <- factorize(dat6, c("college", "married", "parent", "conserv", "race"))
men6 <- glm(vhappy ~ college + married + parent + conserv + race + age + I(age^2),
family = binomial("logit"), data = dat6, subset = woman == 0)
women6 <- glm(vhappy ~ college + married + parent + conserv + race + age + I(age^2),
family = binomial("logit"), data = dat6, subset = woman == 1)
fit6 <- suest(men6, women6, model_names = c("Men", "Women"))The effect of every predictor, each averaged over its own group’s sample, with all of the race contrasts and a one-standard-deviation increase in age:
effects6 <- avg_comparisons(fit6,
variables = list(college = "reference", married = "reference",
parent = "reference", conserv = "reference",
race = "pairwise", age = sd(dat6$age)),
newdata = suest_newdata(fit6))
effects6 Term Group Contrast Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
age Men +13.0646159309931 0.00671 0.00806 0.832 0.40533 1.3 -0.00909 0.02251
age Women +13.0646159309931 0.00905 0.00844 1.072 0.28381 1.8 -0.00750 0.02560
college Men 1 - 0 0.04088 0.01406 2.907 0.00365 8.1 0.01332 0.06845
college Women 1 - 0 0.06428 0.01437 4.474 < 0.001 17.0 0.03612 0.09243
conserv Men 1 - 0 0.04570 0.01361 3.358 < 0.001 10.3 0.01903 0.07237
conserv Women 1 - 0 0.04599 0.01431 3.214 0.00131 9.6 0.01795 0.07403
married Men 1 - 0 0.19668 0.01443 13.631 < 0.001 138.1 0.16840 0.22496
married Women 1 - 0 0.20439 0.01420 14.393 < 0.001 153.6 0.17656 0.23222
parent Men 1 - 0 0.02299 0.01608 1.429 0.15296 2.7 -0.00854 0.05451
parent Women 1 - 0 -0.04546 0.01663 -2.733 0.00627 7.3 -0.07806 -0.01286
race Men 2 - 1 -0.00238 0.02130 -0.112 0.91114 0.1 -0.04413 0.03938
race Men 3 - 1 -0.03481 0.02094 -1.662 0.09644 3.4 -0.07586 0.00623
race Men 3 - 2 -0.03243 0.02783 -1.165 0.24389 2.0 -0.08699 0.02212
race Women 2 - 1 -0.01969 0.01863 -1.057 0.29053 1.8 -0.05619 0.01682
race Women 3 - 1 -0.01473 0.02342 -0.629 0.52946 0.9 -0.06064 0.03118
race Women 3 - 2 0.00496 0.02774 0.179 0.85819 0.2 -0.04942 0.05934
Type: responseThe difference between men and women in each effect:
hypotheses(effects6, hypothesis = difference ~ revpairwise | term + contrast) Term Contrast Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
age +13.0646159309931 (Men) - (Women) -0.002341 0.0117 -0.2005 0.84107 0.2 -0.0252 0.0205
college 1 - 0 (Men) - (Women) -0.023394 0.0201 -1.1636 0.24457 2.0 -0.0628 0.0160
conserv 1 - 0 (Men) - (Women) -0.000289 0.0197 -0.0146 0.98832 0.0 -0.0390 0.0384
married 1 - 0 (Men) - (Women) -0.007709 0.0202 -0.3808 0.70337 0.5 -0.0474 0.0320
parent 1 - 0 (Men) - (Women) 0.068448 0.0231 2.9584 0.00309 8.3 0.0231 0.1138
race 2 - 1 (Men) - (Women) 0.017310 0.0283 0.6117 0.54075 0.9 -0.0382 0.0728
race 3 - 1 (Men) - (Women) -0.020082 0.0314 -0.6391 0.52273 0.9 -0.0817 0.0415
race 3 - 2 (Men) - (Women) -0.037392 0.0393 -0.9515 0.34137 1.6 -0.1144 0.0396Example interpretation: Married men and married women both report being happier than their unmarried counterparts, and college degrees and conservatism have similar positive effects for both. The one significant gender difference is the effect of being a parent: it does not affect the probability of being very happy for men, but women who are parents are less likely to be very happy than women who are not.
Separate models for Germany and Nigeria
Acceptance of same-sex relationships in the World Values Survey, regressed on age (with a squared term) separately in Germany and Nigeria. Each country has its own coefficients and its own observations, so the cross-model difference reflects both.
wvs <- subset(wvs, age >= 18 & country %in% c(276, 566))
germany <- lm(Jgaylesbian ~ age + I(age^2), data = wvs, subset = country == 276)
nigeria <- lm(Jgaylesbian ~ age + I(age^2), data = wvs, subset = country == 566)
fit_countries <- suest(germany, nigeria, model_names = c("Germany", "Nigeria"))
age_effects <- avg_comparisons(fit_countries, variables = list(age = 10),
newdata = suest_newdata(fit_countries))
age_effects Group Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
Germany -0.4282 0.0417 -10.27 <0.001 79.8 -0.51 -0.3465
Nigeria -0.0902 0.0358 -2.52 0.0117 6.4 -0.16 -0.0201
Term: age
Type: response
Comparison: +10hypotheses(age_effects, hypothesis = difference ~ revpairwise) Hypothesis Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
(Germany) - (Nigeria) -0.338 0.0549 -6.15 <0.001 30.3 -0.446 -0.23Example interpretation: A ten-year increase in age reduces acceptance of same-sex relationships in both countries, but much more in Germany than in Nigeria.
Reference
Mize, Trenton D. and Bing Han. Forthcoming. “Marginal effects: a flexible method for substantively meaningful interpretations across linear and nonlinear models.” In Understanding Data Modeling and Data Analysis. Edward Elgar Publishing.