I have been running the "brant" package to check the proportional odds assumption for my model (Ordinary Logistic Regression created with the function "polr").
However, I do not understand why it says that the "Parallel Regression Assumption holds" in my case since I read it is rejected if "A p-value of less than 0.05 on this test—particularly on the Omnibus plus at least one of the variables".

The pvalue of the omnibus variable is 0 in my case as well as the pvalue of other coefficients.

Does anyone understand why it is not rejected in this case?

H_0 is the null hypothesis being tested against. If a parameter has a test statistic p-value less than some pre-selected threshold (conventionally 0.05, but that’s not magic) we “accept the null,” meaning in this case the hypothesis that the parallel regression assumption holds. If picky, we say “fail to reject.” For the results shown, the null holds in the case of four two parameters but in two four it does not, meaning that the alternative hypothesis, H_1 applies—the parallel regression assumption does not hold.

Why the assumption holds for some but not others depends on the data and their sources of random variability in the causal domain. If, for example, astrological sign had been thrown into the mix as a parameter it might not be surprising to see it join sexMale and expr.

Thank you for your reply.
I am a bit surprised because I read the opposite for this test (high p-value = not rejecting the Null hypothesis), that's why I would assume a different outcome in my case:

I added it to to the function output to remind persons what hypothesis they are testing because it is often not clear what the alternative (H_A and the null hypothesis (H_0) is. So it just tells you what the null hypothesis is and nothing about the acutal result. p < 0.05 means that H_0 can be rejected.

So in [S/O OP example] the parallel regression assumption does not hold. In generell[sic]: p-value of omnibus >= 0.05 => holds, p-value < 0.05 => does not hold (assumption: \alpha-value of 0.05).

Keeping the nulls straight is hard. (I got it backwards in my answer, now edited). Also confusing is the use of p-value and probability interchangably. In McNulty's example, everything is > 0.05, meaning reject the null and conclude that the parallel regression assumption does not hold if Schlegel's intepretation of the function he wrote is correct.

The original Brant paper is JStorWalled, so I can check it. {car} has an implementation, and checking against that might clarify things.