In this case study Aki Vehtari demonstrates how it is possible to compare a standard gaussian regression to a binomial regression when the outcome variable is a count. Because of the properties of the count variables (positive integers) you can compare the two different models using loo-cv.
I was wondering if the same thing is true of comparing a standard gaussian regression to and ordinal regression. The cumulative
family in brms
allows you to analyse the outcome if it is a positive integer, so can you compare a regression model with family = gaussian
to a model with family = cumulative
?