Brant test, null hypothesis

[Maria Kaneva]

I am running oparallel test .
Tests of the parallel regression assumption

| Chi2 df P>Chi2
-----------------+----------------------
Wolfe Gould | 2646 57 0.000
Brant | 2739 57 0.000
score | 2799 57 0.000
likelihood ratio | 2632 57 0.000
Wald | 2748 57 0.000
What are the null hypotheses for these tests? Does p-value mean the parallel trend assumptions is violated?

[Carlo Lazzaro]

Maria:
you may want to take a look at ologit and brant test - Statalist

[Maarten Buis]

The null hypothesis for all 5 tests is that the parallel lines assumption holds, so a small p-value is an indication that that the parallel lines assumption does not hold.

That does not mean that you cannot use ologit. A model is by definition a simplification of reality, and "simplification" is just another word for "wrong in some useful way". So we did not need to test any assumption, because we already know that those assumptions are wrong (assumptions are what simplifies models, i.e. what makes them wrong). What we need to find out is if those assumptions are so wrong that they are no longer useful. Useful is by definition a subjective decision, so no computer program can make that decision for you. You just have to look at the estimates of the ordered logit model and a generalized ordered logit model and make a decision if you think they are different enough that that is meaningful, if you care about those estimates or they are "just" controls, if they are just controls, do they influence other statistics you do care about enough that you want to do something about it, etc. So you stare at the two tables and decide if the difference is worth the complication.

[Mike Lacy]

Two thoughts following on Maarten's perspective: First, a sample large enough to offer dependable -ologit- results will almost always be large enough that a significance test will support rejecting the null hypothesis of parallel lines. In fact, if one can't reject that null, then maybe the sample is too small to justify using a logit model at all. (That's a joke, but might be true.) For that reason, I'd suggest comparing model fit using a measure that doesn't depend on sample size. One possibility is my own ordinal R2 measure (see -ssc describe r2o- and the literature there). Using that measure, one might find that the R² for a model that relaxes the parallel lines assumption is "significantly" better by the Brant or similar test, but that the difference in ordinal R² is trivial, say 11% vs. 10.5%. I'd prefer the simpler model in that case.