proportional odds (PO) ordinal logistic regression model as nonparametric ANOVA that controls for covariates

Question

I have continuous response variables that are parameters returned by a reinforcement learning+working memory model. My group variable includes three levels: healthy controls, unipolar depression, and bipolar depression.

I would like to compare the parameters between groups (for example, do people with unipolar depression have a lower reward learning rate than healthy controls), while controlling for age and gender. The parameters are not normally distributed and previous studies used non-parametric tests such as the Kruskal-Wallis H or Mann-Whitney U-test. I would like to control for age and gender, so I researched that the Wilcoxon-Mann-Whitney two-sample rank-sum test is a special case of the proportional odds (PO) ordinal logistic regression model.

Right now, I used the 'orm' function from the 'rms'package in R:

orm(RL_alpha ~ GROUP_any_lifetime_MD + demographics_gender + 
    demographics_age, data = mydata_RLWM)

Does it seem like a valid approach? Are there any alternatives or additional checks?

I am new to the forum and I really appreciate any advice!

Answer 1

The outcome variables don't need to be normally distributed for linear regression to work; what's important is that the residuals around the model predictions be well behaved. See this thread among others on this site.

That said, ordinal regression can be a useful tool for flexible modeling of outcomes. See Frank Harrell's course notes and book for details on types of ordinal regression models (e.g., proportional-odds versus continuation-ratio), the choice of distribution family (proportional odds uses a logistic family, but other choices are possible; see the help page for orm.fit), and ways to check, validate and calibrate models. Chapter 14 of the book has an extended presentation of how to apply ordinal regression, in a case study.