Muddy Points

Lesson 6: Interpretations and Visualizations of Odds Ratios

Muddy Points from Spring 2025

1. For “Transformations of continuous variable to make more interpretable,” what does the “c” actually represent?

\(c\) represents any scalar value. Scalar just means it can be a single numerical quantity, so it can be 10, 5, -3, 0.01, etc. If we want to estimate the odds ratio for a 8-year difference in age, then we’ll look at \(c=8\) so that we compare two ages that are 8 years apart.

2. Also, what makes the scale if Logit(pi(x)) linear? Is it because we are changing the values of x itself or is it because we change the scale of our y-axis?

Head back to Lesson 5 on Simple Logistic Regression. We are transforming our outcome (y-axis as you put it) so that we can map \(X\) to \(Y\) only using the parameters (\(\beta\) coefficients). The “linear” part refers to the parameters taking on this intercept and slope that make a line.

Muddy Points from Spring 2024

None?? Wowza!