I aim to build for the first time an ordinal logistic regression between a dependent ordinal categorical variable (temperature sensation vote TSV, Y) coded on a bipolar ordered 6-point scale (from very cold to very hot) and a continuous independent variable, which represents the intensity of human body stress to heat (X).
I checked following the book of Harrel F., 2015 ("Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis", chapter 13 )the ordinality assumption by computing the mean of the heat stress indices X by levels of temperature sensation Y. " a basic assumption of all commonly used ordinal regression model is that the response variable behaves in an ordinal fashion with respect to each predictor. Assuming that the predictor X is linearly related to the log of the 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. if for many of the Xs, two adjacent categories of Y do not distinguish the means, that it is the evidence that those levels of Y should be pooled."
It appears that the means of X do not always behave in an ordinal fashion.
Here, is an example of the means of X stratified by levels of Y for a given location:
In my case, I cannot pool the Y as I need to build the best accurate predictive model for different locations and compare them. The question is what happens if this assumption is not fully respected by the data? Can I still apply an ordinal logistic regression? This is not stated in the book.
Answer from Frank Harrel posted on the comments of a deleted answer: "You're interpreted the material in RMS correctly. But you neglected to put sample sizes in the table. When all cell sample sizes are not huge you can't worry too much about a lack of ordinality. Note for others not used to thinking this way: The mean of X | Y is highly related to score residuals from the ordinal logistic model that are used to check the proportional odds assumption when X has a linear effect on log odds. For resources on ordinal models see: fharrell.com/post/rpo and fharrell.com/post/impactpo, the latter showing the harm of not assuming prop. odds. – Frank Harrell, Jan 4 at 10:25 "