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In testing the parallel regression assumption in ordinal logistic regression I find there are several approaches. I've used both the graphical approach (as detailed in Harrell´s book) and the approach detailed using the ordinal package in R.

However I would also like to run the Brant test (from Stata) for both the individual variables and also for the total model. I've looked around but cannot find it implemented in R.

Is there an implementation of the Brant test in R?

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  • $\begingroup$ Don't know of any implementation, but this section from J. Scott Long's book provides a detailed description of how to compute the test that I believe you refer to. $\endgroup$
    – NRH
    May 30, 2013 at 21:14
  • $\begingroup$ Thx--I´ve looked at the original paper and also the .ado file from stata. However, the required programming is beyond my level. $\endgroup$
    – Misha
    May 31, 2013 at 6:59
  • $\begingroup$ This Class notes touch on the topic More on the Proportional Odds/Parallel Regressions Assumption $\endgroup$ Sep 16, 2015 at 22:05

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I implemented the brant test in R. The package and function is called brant and it's now available on CRAN.

The brant test was defined by Rollin Brant to test the parallel regression assumption (Brant, R. (1990) Assessing proportionality in the proportional odds model for ordinal logistic regression. Biometrics, 46, 1171–1178).

Here is a code example:

data = MASS::survey
data$Smoke = ordered(MASS::survey$Smoke, levels=c("Never","Occas","Regul","Heavy"))
model1 = MASS::polr(Smoke ~ Sex + Height, data=data, Hess=TRUE)
brant(model1)

In the example, the parallel regression assumption holds, because all p-values are above 0.05. The Omnibus is for the whole model, the rest for the indvidual coefficents.

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  • $\begingroup$ It seems like your package is designed for polr. Is there also the possibility to use it with mixor? $\endgroup$
    – Nerd
    Apr 16, 2021 at 9:58
  • $\begingroup$ So fare not, I would have to look into mixor (I hear the first time now about this package). $\endgroup$ Apr 17, 2021 at 14:00
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Yes -- in fact the ordinal package that you linked can do it (although they don't call it the Brant test). Take a look at pages 6 and 7 of your link, which demonstrate "a likelihood ratio test of the equal slopes or proportional odds assumption," which is exactly what you are looking for.

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  • $\begingroup$ I´ve compared the output between the two approaches but they are not similar. I believe the Brant test is more of a score test. $\endgroup$
    – Misha
    Jul 29, 2013 at 19:26
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    $\begingroup$ No, in finite samples all these approaches are different though asymptotically they should be the same. The Brant test estimates an approximation of the unconstrained model using seperate logistic regression and than performs a Wald test. A comparison of the various methods can be found here $\endgroup$ Feb 24, 2014 at 8:00
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Some notes on the topic

The R package VGAM in the cumulative command (Ordinal Regression with Cumulative Probabilities) allows to change the proportional odds assumptions, with the option parallel=FALSE.

It is known to be a common problem (from the book: Regression Models for Categorical Dependent Variables Using Stata, Second Edition, By J. Scott Long, Jeremy Freese)

"A Caveat regarding the parallel regression assumption: We find that the parallel regression assumption (PRA) is frequently violated. When this is rejected alternatives models that do not impose the constraint of parallel regressions should be considered. Violation of the PRA is not rationale for usig OLS regression since the assumptions implied by the application of the LRM to ordinal data are even stronger. Alternative models that can be considered include models for nominal outcomes [...] Stereotype Logistic model or Stereotype ordered model; the Generalized Ordered Logit model; the continuation Ratio model, are alternatives" (page 221)

This paper goes in depth in this topic, being clear and well written, but it does not consider the VGAM package or the "cumulative" command: Ordinal logistic regression in epidemiological studies

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This tutorial about ordinal logistic regression in R covers testing the proportional odds assumption.

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    $\begingroup$ Would someone please remind me of the difference between the Brant test of PO and the Peterson & Harrell 1990 score test for PO? We showed that the score test is anti-conservative and should usually be avoided. Many tests find trivial differences for large N. I would favor an assess based on predicted vs observed category proportions, where predicted = assuming PO. When there is only one variable in the model this is easy to do. Not sure how to do it for the multivariable situation. I guess you could use the multinomial logistic model. $\endgroup$ Feb 26, 2022 at 21:04

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