Logistic Regression

Week 8: February 24, 2025

Reading

  • Diez et al. Chapter 9: Logistic Regression, from pp 371; sec. 9.5
  • See resources

Introduction to the Topic

This week, we focus on logistic regression, a statistical method used to model binary outcomes and predict probabilities. Logistic regression is a cornerstone technique in statistical modeling, particularly for research questions involving categorical dependent variables.

Key Concepts:

  • Logistic Regression Models: Analyze the relationship between independent variables and a binary dependent variable (e.g., success vs. failure).
  • Odds Ratios: Interpret the effect of predictors on the likelihood of the outcome.
  • Model Fit and Diagnostics: Evaluate the accuracy and robustness of logistic regression models.

Relevance:

  • Students will learn how to build logistic regression models and interpret their results, including coefficients, odds ratios, and predicted probabilities.
  • Students will explore model evaluation techniques, such as goodness-of-fit measures and ROC curves.

Why This Is Important:

  • Logistic regression is widely used in various fields, including social sciences, medicine, and marketing, to answer questions about classification and prediction.
  • Understanding logistic regression provides the foundation for advanced modeling techniques like multinomial and ordinal regression.

How This Ties Into the Overall Course:

  • Builds upon previous weeks’ focus on linear regression and effect sizes, extending these concepts to binary outcomes.
  • Prepares students for upcoming topics like machine learning classification models and survival analysis, where logistic regression plays a foundational role.

By the end of this week, students will be able to confidently apply logistic regression to real-world problems, interpret model outputs, and evaluate model performance for binary classification tasks.

Class Files

Lecture Notes

R Code

Data Sets

  • GPA-College Enrollment Example: In class example showing the mechanics of logistic regression?
  • Predicting Probabilities with Logistic Regression Here is an excel file illustrating the math behind predicting probabilities
  • An annotated jasp file of logistic regression output including how to do the log-likelihood test

Resources

  • There are a million ways to recode variables in R
  • Now that you are familiar with using R, check out this amazing book called R for Data Science which is written by the Hadley who co-authored the tidyverse suite.

Additional Notes

  • Keep calm and don’t be a dummy.