Exam

You will take one in-class exam, which serves as an important mid-quarter check of your understanding. The exam will be held during one of our lab sessions. It will be closed-book open-book and without access to the internet.

The exam covers the assigned materials, our classes, and your assignments. Here is a rough overview of things you should be familiar with. The exam will not cover “sample size calculations and clustered data”.

The causal revolution

You should understand…

  • …the difference between identifying correlation (math) and identifying causation (philosophy and theory)
  • …what it means for a relationship to be causal
  • …what it means for an author to engage in a “motte-and-bailey” strategy
  • …how a causal model encodes our understanding of a causal relationship
  • …how to identify backdoor paths between treatment/exposure and outcome
  • …why we close backdoor paths
  • …why adjusting for mediators can distort causal effects
  • …why adjusting for colliders can distort causal effects
  • …why adjusting for potential confounders can distort causal effects, if the confounder was measured post treatment
  • …the difference between individual-level causal effects, average treatment effects (ATE), conditional average treatment effect (CATE), average treatment on the treated effects (ATT), and average treatment on the untreated (ATU)
  • …what the “fundamental problem of causal inference” is and how we can attempt to address it
  • …what a counterfactual is, and how it relates to the potential outcomes framework

You should be able to…

  • …draw a possible directed acyclic graph (DAG)
  • …identify all pathways between treatment/exposure and outcome
  • …identify which nodes in the DAG need to be adjusted for (or closed)
  • …identify colliders and mediators (which should not be adjusted for)

Review of regression analysis

You should understand…

  • …the difference between outcome/response/dependent and explanatory/predictor/independent variables
  • …what each of the components in a regression equation stand for, in both “flavors” of notation:
    • \(y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \epsilon\) for the statistical flavor
    • \(y = \alpha + \beta x_1 + \gamma x_2 + \epsilon\) for the econometrics flavor
  • …how sliders and switches work as metaphors for regression coefficients
  • …what it means to hold variables constant (or to control for variables)
  • …how “big data” (or even data on the full population) helps little with causal inference
  • …how standard errors can be thought of in terms of repeated draws from a population

You should be able to…

  • …interpret regression coefficients
  • …interpret standard errors, p-values, and confidence intervals
  • …interpret other regression diagnostics like \(R^2\)
  • …write out the regression equation for a study that uses random assignment and for a study that uses regression analysis without random assignment

Interactions and transformations

You should understand…

  • …the main motivation for (and against) using log-transformed and standardized variables
  • …the general idea behind and common applications of interactions
  • …what “moderation” means (and how it differs from confounding)
  • …how additional subgroup analyses reflect multiple hypothesis testing and the implications for statistical significance
  • how “slopes”, “marginal effects”, and “partial derivatives” are closely related

You should be able to…

  • …transform variables
  • …interpret the results of regressions that use log-transformed and standardized variables
  • …interpret the results of regressions that use interaction terms
  • …write out the regression equation for an analysis that uses an interaction
  • …use regression results to calculate the expected means and probabilities for subgroups

Discrete outcomes and regression adjustment

You should understand…

  • …the benefits and limitations of linear probability models
  • …what link and index functions are in the context of generalized linear models
  • …the difference between marginal effects at the mean and average marginal effects
  • …how Oster’s method uses coefficient stability and the R-squared to bound causal effects

You should be able to…

  • …interpret the results of a linear probability model
  • …interpret marginal effects at the mean and average marginal effects in the context of logistic regression
  • …use a rule of thumb to interpret the results of a logit model
  • …make predictions about coefficient movements as you close backdoors in a causal model
  • …use and interpret the results of Oster’s bounding method

Fixed effects, value added, and randomized experiments

You should understand…

  • …how fixed effects work and how they relate to demeaning
  • …how fixed effects can “close backdoors” even if you do not have data on these backdoors
  • …how value-added estimation relates to fixed effects
  • …the “menu” of options you may choose from as you design a randomized trial, including their respective benefits and limitations
  • …the benefits of using regression to analyze the results of a randomized trial
  • …the motivation behind controlling for covariates even in the context of a randomized trial

You should be able to…

  • …write the regression equation for a model that includes fixed effects
  • …(decide whether to) use fixed effects in your final project
  • …interpret the results from value-added models, and describe their benefits and limitations
  • …read and interpret the results of academic articles that use a randomized controlled trial
  • …decide on and execute analyses for a randomized controlled trial