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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?

Thanks in advance!

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I’m author of RMS. The ordinality assessment is a quick and semi-clean way to look at model assumptions. Mean age stratified by levels of Y is related to score residuals, and score residuals are diagnostic tools for assess the proportional odds (PO) assumption if you are using the PO ordinal logistic model. A V-shaped relationship in predicting X from Y indicates trouble about to happen when predicting Y from X in a model that assumes parallelism (constant slope; PO).

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.

Another place to discuss RMS questions is at datamethods.org/rms . If you go to the ordinal regression chapter link near the top of that page you’ll see other discussions about ordinal regression.

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    $\begingroup$ Thank you for an insightful answer and for the resources. I will have to look into score residuals. The link does not work and the reason seems to be that it's missing an m in com. $\endgroup$ Nov 4, 2023 at 10:45
  • $\begingroup$ Thanks. I fixed the link. I suggest not looking into score residuals as much as following the workflow in the link. $\endgroup$ Nov 4, 2023 at 11:59
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    $\begingroup$ I read the post and will definitely try this approach. I also did not know about the PO models relation to the Wilcoxon test which was a nice surprise for me. The PO model appears to be more interesting than I first thought. Thanks for the help. $\endgroup$ Nov 5, 2023 at 23:20

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