# Why do we require ordinality of the response with respect to the predictors in the proportional odds model

I've recently been reading about ordinal regression with a focus on the proportional odds model in the book regression modelling strategies. The author states "A basic assumption of all commonly used ordinal regression models is that the response variable behaves in an ordinal fashion with respect to each predictor. Assuming that a predictor X is linearly related to the log odds of some appropriate event, a simple way to check for ordinality is to plot the mean of X stratified by levels of Y . These means should be in a consistent order."

I've had difficulty understanding why we need the response to be ordinal with respect to the predictors, the response should still be able to be a valid ordinal response without this assumption. As an example, suppose that I wanted to model the severity of symptoms of a disease with respect to age, using a proportional odds model. The severity of symptoms have the following categories.

• mild symptoms
• intermediate symptoms
• severe symptoms

Suppose the population is relatively old and that mostly young people get intermediate symptoms and mostly old people get severe symptoms. Then plotting the average age stratified on the symptoms level would reveal a V-shape and the severity of symptoms would not be consider ordinal with respect to age. However the severity of symptoms have a clear order.

1. Does this mean that we cannot use age as a predictor and why? Is it because age in some sense poorly explain the ordinality of response?
2. Where in the model do we get this assumption?

None of this means you cannot use age in the model, but if age turns about to not act in PO you many need a Peterson-Harrell (1990) partial proportional odds model as implemented in the R VGAM or rmsb packages.
However a better way to go about all this is to assess the impact of making the PO assummption, for which a newer function in the R rms package called impactPO is helpful. This approach is written up in a blog article here.