How to validate "equal slopes" (proportional odds) in ordinal regression I would like to fit an ordinal regression model using proportional odds. I learned to test for "equal slopes" in order to say something about the model's validity.
Therefore, I fit a model with equal slopes and I fit a model without equal slopes (e.g. with R using the VGAM package).
After that, I do a Chi-square test to compare both results.
If this test is not significant, we have equal slopes. If this test is significant, we do not.
A colleague states that those tests lack power. With such low power, it could happen that the test is not significant (e.g. $p=.2$) while there are different slopes.
My questions are:


*

*Is there a more powerful way to test for equal slopes?

*Are there other ways to test the validity of the model?


Thx in advance!
 A: The problem is that not-significant does not mean equal slopes but that there is not enough evidence to reject the hypothesis that the slopes are equal. This makes a difference as an absence of evidence is not the same as evidence of absence. So it is definately possible that the slopes are different but that you do not find such a difference with your test, as your collegue mentioned.
I don't think you should be looking for different tests, but instead use it as statistical tests were intended to be used. In your case you would "hope" for a significant result and than inspect the coefficients and "hopefully" find that they are similar enough to justify a model that sets them as equal. We don't believe that models are true, we just inspect the data and find that the model is a reasonable simplification of reality (simplification is just another word for "wrong in some useful way"). When your test is significant, you know that there is something to inspect. When it is not significant, you will have to find some justification outside your data (e.g. another study using different data)
