What can cause violation of the proportional odds assumption? What can the reasons be that the assumption of proportional odds / assumption of parallel regression lines is not met?
By using MASS::polr in R, I tried to run different models and change variables, but the brant test shows non-proportionality persistently.
How can I study and find out what may cause this? I looked at the correlationsplot and vif, the variables are not correlated and there is no multicollinearity using the vif/tolerance method.
Using boxplot(df$var1, plot = TRUE)$out and length(boxplot(df$var1)$out) I can see that there are outliers.. however there are too many for what I will say that they are outliers.
Even though I decide to remove the outliers there are many outliers in the dependent variable which is ordinal discrete and the same for the independent variables. Meaning that if category 1 in the dependent variable is outlier and the count of it is 100, I don't see it as a good idea to remove them or replace with NA. Some variables have 10 outliers, others have more than 200.
What are other methods you can suggest? I'm not asking what to do when the parallel regression assumption is not met but how I can find out what cause this violation.
 A: One obvious starting place to investigate a possible violation is to fit the separate logistic regression models, and inspect which odds ratio(s) are heterogeneous.
glm(I(y>1) ~ x, family=binomial)
glm(I(y>2) ~ x, family=binomial, subset = y>1)
glm(I(y>3) ~ x, family=binomial, subset = y>2)
...

When the proportional odds assumption holds, we expect the coefficient of x to be the same in each model. A lot of times, "intermediate" quantities tend to be pretty sparse, especially for questionnaire data. In those cases, you may find odds ratios that are wildly variable, and it's enough to miscalibrate any sort of global test like Brant. The solution at times may just be to dichotomize data, since such an analysis while potentially inefficient, would be well understood and generalizable - or alternately, you might simply fit a simple linear regression model! Treating ordinal outcomes as continuous is widely discussed, widely accepted, and highly generalizable, even in spite of the issue of "overprediction".
