Session 3: Regression coefficients and model matrices

Lecture

Learning Objectives

1. Interpret main coefficients in logistic regression
2. Interpret interaction terms in logistic regression
3. Define and interpret model matrices for (generalized) linear models

Outline

1. Review of GLM
2. Interpretation of logistic regression coefficients
3. Introduction to model matrices

Lab

Learning objectives

1. perform and interpret logistic regression
   • interpret logistic regression coefficients
   • make predictions based on a logistic regression model
2. perform and interpret likelihood ratio test

Exercises

1. What is the mean fraction of women using birth control for each age group? Each education level? For women who do or don't want more children?
   • Hint: look at the "data wrangling" cheat sheet functions mutate, group_by, and summarize
2. Based on fit1, write on paper the model for expected probability of using birth control. Don't forget the logit function.
3. Based on fit1, what is the expected probability of an individual 25-29 years old, with high education, who wants more children, using birth control? Calculate it manually, and using predict(fit1)
4. Based on fit1: Relative to women under 25 who want to have children, what is the predicted increase in odds that a woman 40-49 years old who does not want to have children will be taking birth control?
5. Using a likelihood ratio test, is there evidence that a model with interactions improves on fit1 (no interactions)?
6. Which, if any, variables have the strongest interactions?
7. Looking at the effect of age only, consider contrasts between every pair of age groups. Between which age groups is the contrast significant?