Learning Track: Regression and Causal Inference

A structured learning path through applied regression modelling and causal reasoning in R, from multiple regression to panel fixed effects — written for MA students with basic regression experience.

1 Who This Track Is For

This track is for MA students who have already encountered linear regression — you can fit a model, interpret a coefficient, and read a residuals plot — and want to take that foundation further in two directions: better regression (handling categorical outcomes, diagnosing problems, dealing with binary outcomes) and better causal reasoning (why coefficients are not automatically causal, how to think about what to control for, and how panel data helps).

By the end of this track you will be able to:

• Build and interpret regression models with categorical variables, interaction terms, and binary outcomes
• Diagnose model problems and understand what diagnostics can and cannot reveal
• Use DAGs to reason about what a regression coefficient actually estimates
• Estimate fixed effects models for panel data and interpret the within-R²
• Produce publication-ready figures for communicating quantitative results

The track broadly follows the arc: better regression → knowing its limits → causal thinking → panel methods → communication. Each resource is self-contained, so you can skip or revisit sections as needed.

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2 Core Sequence

2.1 1. Linear Regression in R (prerequisite)

Linear Regression in R

The foundation: lm(), coefficient interpretation, R², log and quadratic transformations, and omitted variable bias. This is the assumed starting point for everything that follows.

2.2 2. Categorical Variables and Interaction Terms

Categorical Variables and Interaction Terms in Regression

Extend your regression toolkit to handle binary and multi-category predictors, reference categories, and interaction terms. Worked through on a real earnings dataset where the age–earnings profile differs by gender.

2.3 3. Regression Diagnostics

Regression Residuals and Model Diagnostics

Learn what the four standard diagnostic plots are checking, when to worry, and what to do about it. The MA section adds the Gauss-Markov framing, functional form testing, robust standard errors, influential observation analysis, and — crucially — the silent nature of omitted variable bias.

2.4 4. Logistic Regression for Binary Outcomes

Logistic Regression for Binary Outcomes in R

When the outcome is binary, OLS breaks down. This page explains why and introduces logistic regression with glm(). Interpretation covers three levels: log-odds, odds ratios, and — most useful in practice — predicted probabilities and average marginal effects.

2.5 5. Causal Reasoning with DAGs

Causal Reasoning with DAGs

The methodological pivot: why a regression coefficient is not automatically a causal effect. Introduces DAGs as a framework for making causal assumptions explicit, identifies confounders, mediators, and colliders, and illustrates the bad control problem with a worked example on the gender wage gap. Uses dagitty and ggdag in R.

2.6 6. Panel Data and Fixed Effects

Panel Data and Fixed Effects in R

When you have repeated observations on the same units over time, fixed effects estimation controls for all stable unit-level characteristics — observed and unobserved. Covers the within-transformation, fixest::feols(), two-way FE, clustered standard errors, and the within-R².

2.7 7. Publication-Ready Figures

Publication-Ready Figures with ggplot2

Communicating results well is part of doing research well. This page covers the ugly/bad/wrong taxonomy, chart type selection, and five key ggplot2 extensions: patchwork, ggrepel, gghighlight, ggtext, and scales. Ends with the 7-item publication checklist and correct ggsave() usage.

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3 Practice Exercises

Each tutorial above has an associated exercise. Work through them in sequence:

Exercise	Skills practised
Predicting Firm Exit with Logistic Regression	glm(), odds ratios, predicted probabilities, inline R code
Causal Reasoning and the Gender Wage Gap	Three-model progression, DAG specification, analytical narrative writing

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4 Related Resources