Topic 17 Applied Mediation Analysis

Learning Goals

  • MEDI1: Formulate research questions that can be answered via mediation analysis
  • MEDI2: Conduct and interpret results from a mediation analysis





Assignment

A template RMarkdown document that you can start from is available here.

Pre-class reading

Write a short response to the article, How racial discrimination in law enforcement actually works. Use quotes from the article to discuss connections to mediation ideas and other concepts from our course. (Limit 500 words.)

Thoughtful responses will earn 2 M grades to apply to any objective of your choosing. (You can’t use this to skip parts of Homework 5 or 6 though.)



Applied mediation analysis

The New York Times recently featured research by a group who studied the effect of tenure-clock stopping policies on promotion and job security-related outcomes.

We’ll be looking at data from the study Equal but Inequitable: Who Benefits from Gender-Neutral Tenure Clock Stopping Policies? by Antecol, Bedard, and Stearns.

You’ll need to install the mediation package before getting started.

install.packages("mediation")

The data and data information are available on Moodle (aer_primarysample.csv and ReadMe.pdf).

library(dplyr)
library(ggplot2)
library(splines)
library(mediation)

tenure <- readr::read_csv("aer_primarysample.csv")


Context: Tenure clock-stopping policies broadly relate to delaying the timeline for tenure review due to life events. Often this is related to becoming a parent. The COVID pandemic has also generated discussions about clock-stopping policies for both its standalone impacts on faculty and its intersectional effects with other factors like parenthood. Clock-stopping policies are intended to affect scholarly output which in turn affects ultimate awarding of tenure.

Broad question: How do gender-neutral clock stopping policies affect the ultimate awarding of tenure, and how influential are publications in top journals in this process?

Information on variables starts at the bottom of Page 1 of ReadMe.pdf (“The independent variables of interest are…”). We will focus on the following variables:

  • gncs: a gender-neutral clock-stopping policy is in place (treatment)
  • top_pubs5: cumulative number of peer-reviewed publications in top-5 journals by year 5 since PhD completion (mediator)
  • tenure_policy_school: indicator for getting tenure at the university with the clock-stopping policy

Your task:

  • The authors assume that the variables female + phd_rank + post_doc + ug_students + grad_students + faculty + full_av_salary + assist_av_salary + revenue + female_ratio + full_ratio are enough to meet the exchangeability conditions discussed yesterday. Do you agree? Explain. State your final conditional exchangeability set.

  • Use visualizations to build appropriate models for the mediator and for the outcome. Focus on correctly capturing nonlinearity rather than interactions. Just make 3 plots for each model. Call the mediator model med_mod and the outcome model out_mod.

  • Use the mediate() function as demonstrated below to estimate the natural direct and indirect effects. (In the output, ACME stands for the indirect effect and ADE stands for the direct effect.)

set.seed(451)
mediate_out <- mediate(med_mod, out_mod, treat = "gncs", mediator = "top_pubs5", robustSE = TRUE, sims = 1000)

summary(mediate_out)

  • Decide whether NIE(0) or NIE(1) is more of interest to you and explain in a few sentences.

  • Interpret the chosen NIE, the corresponding NDE, the total effect, and the proportion mediated quantity contextually. (For a binary outcome, the effects in the output represent changes (differences) in the probability of \(Y = 1\).)