A few issues -

Don't let the overall unimportance of a predictor make you worry about
non-ordinality (e.g., when scale of plot.xmean.ordinaly has a low range on
the y-axis).

We frequently have to face the issue of using an imperfect model by fitting
a few variables that don't exactly meet our assumptions, if the majority of
variables do.  One reason for this is that competing methods may fare worse.

Another option is to fit a more flexible model such as the partial
proportional odds model.  I haven't implemented this in my packages. 
Another R package may do the job (but without model validation mechanisms
provided by rms).

Frank

apeer wrote:
> 
> I'm not implying they should be discarded; however, at the same time I'm
> not certain I fully understand why we should check the ordinality
> assumption if in the end we're going to include predictors with which the
> response variable behaves in a non-ordinal fashion.
> 


-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
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