Logistic regression VS ordinal regression using cumulative logits?

Question

What's the difference between a logistic regression and an ordinal regression using cumulative logits?

Answer 1

Logistic regression is usually taken to mean binary logistic regression for a two-valued dependent variable $Y$. Ordinal regression is a general term for any model dedicated to ordinal $Y$ whether $Y$ is discrete or continuous. The cumulative logit model is a poorly formed term for the proportional odds model, also called the ordinal logistic model. The terminology cumulative logit is poor for two reasons: there are no logits being accumulated (the model is stated in terms of cumulative probabilities), and the inventor of the term, McCullagh (1980), did not reference the inventors of the proportional odds model, Walker and Duncan (1967). Sometimes you will see the full terminology proportional odds ordinal logistic model.

My RMS course notes go into more detail - see links at http://www.fharrell.com/p/blog-page.html