# Ordinal Regression - Online Course

Distinguished Speaker Series: A Seminar Taught by

Frank Harrell
Schedule: All sessions are held live via Zoom. All times are ET (New York time).

1:00pm-4:00pm (convert to your local time)

ABSTRACT

Ordinal regression is a kind of semiparametric regression model that is being used with increasing frequency. The most popular ordinal regression models are the proportional odds model (Walker and Duncan, 1967) and the proportional hazards model (Cox, 1972). Ordinal regression is very much preferred for a discrete ordered response variable (Y) or when there are floor or ceiling effects in a response scale.

Less well-known is that ordinal regression has excellent performance for continuous Y, which makes it a direct competitor to ordinary linear regression. In that setting, a major advantage is that the regression coefficients from fitting an ordinal model do not change if Y is monotonically transformed (logged, etc.). As a result, a major burden in determining how to transform Y is lifted from the analyst.

Other advantages include robustness to Y-outliers and automatically handling detection limits for Y. Ordinal regression allows the analyst to estimate effect ratios, probabilities of chosen Y levels, the mean of Y (when Y is interval-scaled), and quantiles of Y (when Y is continuous).

Just as the log-rank test is a special case of the Cox model, the Wilcoxon and Kruskal-Wallis nonparametric rank tests are special cases of the proportional odds (PO) model. Hence the two rank tests make the PO assumption just as the log-rank test makes the proportional hazards assumption. This will be explained in detail, along with how to convert between an odds ratio and a Wilcoxon statistic.

We will also discuss how to assess the impact of making the PO assumption, and we’ll show that the PO assumption is not needed to successfully use the PO model to infer which treatment group fares better. However, PO is needed to get accurate predicted probabilities of specific outcome categories. We will also show that even when PO is violated, analyzing Y as an unordered categorical variable can be worse.

This seminar will explore detailed ordinal regression case studies using R, and will introduce the Bayesian Wilcoxon test through a Bayesian PO model. It covers the necessary theory behind ordinal models but is more concerned with practical application.

Who should attend: Researchers experienced with using regression analysis in their work who are interested in analyzing ordered categorical response variables, variables with floor or ceiling effects, using less-assumption-laden ordinal regression models for analyzing more continuous responses, or learning how to generalize nonparametric statistical tests (such as the Wilcoxon test) to allow for covariate adjustment will benefit from this seminar.

This Distinguished Speaker Series seminar will consist of three hours of lecture and Q&A, held live* via the free video-conferencing software Zoom.

*The video recording of the seminar will be made available to registrants within 24 hours and will be accessible for four weeks thereafter. That means that you can watch all of the class content and discussion even if you cannot participate synchronously.

Closed captioning is available for all live and recorded sessions. Live captions can be translated to a variety of languages including Spanish, Korean, and Italian. For more information, click here.

If you’d like to learn more about nonparametric statistics, be sure to check out Nonparametric and Semiparametric Statistics. You can also further your knowledge of other types of nonlinear regression in Categorical Data Analysis.