Comparing ME inequalities across models

Example 4.3.b of Mize and Han (2025), in R: tests of mediation/attenuation

How much of the racial-ethnic inequality in an outcome is accounted for by education and wealth? Fit the model with and without those variables and combine them with suest, which gives the joint covariance needed to test whether the ME inequality differs across the models. The example uses a count of functional limitations from the Health and Retirement Study. The same example in Stata is on the meinequality page.

Load and prepare the data

library(haven)           # Read Stata data
library(marginaleffects) # Marginal effects and hypotheses
library(MASS)            # Negative binomial regression
library(suest)           # Combine models

source("https://raw.githubusercontent.com/tdmize/Rfunctions/main/ME_helper_functions.R")

hrs <- read_dta("https://tdmize.github.io/data/data/cda_hrs.dta")

vars <- c("iadl", "race4cat", "collegeB", "wealth_w", "income_w")
hrs <- hrs[complete.cases(hrs[vars]), vars]
hrs[c("race4cat", "collegeB")] <- lapply(hrs[c("race4cat", "collegeB")], as_factor)
nrow(hrs)
[1] 15609

Fit and combine the models

basemod <- glm.nb(iadl ~ race4cat, data = hrs)
medmod <- glm.nb(iadl ~ race4cat + collegeB + wealth_w + income_w, data = hrs)

fit <- suest(basemod, medmod, model_names = c("Base", "Mediators"))

ME inequality in each model

meineq() returns the ME inequality in each model:

ineq <- avg_comparisons(fit,
  variables = list(race4cat = "pairwise"),
  newdata = hrs,
  hypothesis = meineq(fit))
ineq
     Group Estimate Std. Error    z Pr(>|z|)    S  2.5 % 97.5 %
 Base        0.0464     0.0118 3.92   <0.001 13.5 0.0232 0.0696
 Mediators   0.0377     0.0113 3.35   <0.001 10.3 0.0157 0.0598

Term: race4cat
Type: response

Test the difference

hypotheses(ineq, hypothesis = difference ~ revpairwise)
           Hypothesis Estimate Std. Error     z Pr(>|z|)   S   2.5 % 97.5 %
 (Base) - (Mediators)  0.00869     0.0224 0.389    0.698 0.5 -0.0351 0.0525

The difference is the reduction in racial-ethnic inequality once education, wealth, and income are in the model, with its standard error and p-value: the part of the inequality those variables account for. Here the reduction is small and not statistically significant.

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