**Guest lecture by Sunny Tseng**

- Finish up Survival Analysis (Vincenzo)
- Ordinal regression discussion: notes (Sunny)
- Ordinal regression live coding: worksheet.R (Sunny)

By the end of the lecture, students are expected to be able to:

(**To be updated based on what was actually discussed**)

- Identify whether a variance is ordinal.
- Identify the model assumptions in a proportional odds model.
- Interpret the regression coefficients in a proportional odds model.
- Fit a proportional odds model in R, extract relevant quantities, and make predictions.

- Chapter 8 of Applied Logistic Regression by David W. Hosmer, Jr., Stanley Lemeshow.

- A variable is ordinal if its values have a natural ordering.
- For example, months have an inherent order.

- A proportional odds model is a commonly used model that allows us to interpret how predictors influence an ordinal response. Let’s consider lower levels as being “worse”.
- It models an individual’s odds of having an outcome “worse than” (less than or equal to) level
`k`

for all`k`

as being some baseline odds, multiplied by`exp(eta)`

, where`eta`

is a linear combination of the predictors. Sometimes (like in R’s`MASS::polr()`

)`eta`

is a*negative*linear combination of predictors, so that the multiplicative factor is`exp(-eta)`

. - The coefficient
`beta`

on a predictor`X`

(contained in`eta`

) has the following interpretation (if`eta`

is defined as a linear combination of predictors without a negative sign in front): an increase in`X`

by one unit is associated with`exp(beta)`

times the odds of being worse off. If`eta`

is defined with a negative sign, the same interpretation follows with`exp(-beta)`

instead of`exp(beta)`

.

- It models an individual’s odds of having an outcome “worse than” (less than or equal to) level