Nested logit models and mediation/attenuation

Example 6.2 of Mize, Doan, and Long (2019). The same example in Stata uses mecompare.

This example uses binary logit models to see how the effect of college changes when more variables are added to the model.

library(suest)
library(marginaleffects)
library(haven)

gss <- zap_labels(read_dta("https://tdmize.github.io/data/data/gss_cme.dta"))

factorize <- function(data, variables) {
  data[variables] <- lapply(data[variables], factor)
  data
}
vars62 <- c("vhappy", "college", "wages", "occprest", "age", "married",
            "parent", "woman", "conserv", "reltrad", "year", "employed")
dat62 <- subset(gss, year >= 2000 & employed == 1)
dat62 <- dat62[complete.cases(dat62[vars62]), ]
stopifnot(nrow(dat62) == 9216)
nrow(dat62)
[1] 9216
dat62 <- factorize(dat62, c("college", "married", "parent", "woman", "conserv",
                            "reltrad", "year"))

model62a <- glm(vhappy ~ college, family = binomial("logit"), data = dat62)
model62b <- glm(vhappy ~ college + married + parent + woman + conserv + reltrad +
                  year + age + I(age^2), family = binomial("logit"), data = dat62)
fit62 <- suest(model62a, model62b, model_names = c("Model 1", "Model 2"))

effects62 <- avg_comparisons(fit62, variables = "college", newdata = dat62)
effects62
   Group Estimate Std. Error    z Pr(>|z|)    S  2.5 % 97.5 %
 Model 1   0.0718     0.0103 6.95   <0.001 38.0 0.0516 0.0921
 Model 2   0.0599     0.0105 5.69   <0.001 26.2 0.0393 0.0806

Term: college
Type: response
Comparison: 1 - 0
hypotheses(effects62, hypothesis = difference ~ revpairwise)
            Hypothesis Estimate Std. Error    z Pr(>|z|)   S 2.5 % 97.5 %
 (Model 1) - (Model 2)   0.0119    0.00402 2.95  0.00313 8.3 0.004 0.0198

Example interpretation for the effect of college: On average, the probability of being very happy is 0.072 higher for people with a college degree than for those without one (\(p < .001\)). Model 2 adds demographic controls, reducing the average marginal effect of college to 0.060, which remains statistically significant. A direct test shows that adding the controls decreases the effect of college by 0.012 (\(p < .01\)).

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