03 – Binary Regression Models

Categorical Data Analysis (Soc 681) · Purdue University · Fall 2026

The lecture notes for this section of the course, with the Stata and R code and output for every example. This site contains all the material and code for the course. If you prefer the slides in PDF format and/or the Stata replication do-file, these can be downloaded at: lecture slides · replication code.

Binary outcome models

  • For all categorical DV models:
    • Functional form is inherently nonlinear, even without polynomials
    • All effects are interactive—meaning the effect of one variable can differ across various levels of other variables in the model, even without product terms
    • The size of the coefficient often does not clearly represent the size of the effect
      • Coefficients are not in the natural metric of the dependent variable
    • Predictions must be transformed into the natural metric of the dependent variable for more useful interpretations
      • Marginal effects can be calculated from predictions in the natural metric

Two S-shaped probability curves, for d = 0 and d = 1: the gap between the curves and the change in the probability for a one-unit change in x both depend on where on the curves they are measured.

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