Using loo-cv to compare a Gaussian model treating a 0-10 integer variable as numeric to another model treating the same variable as ordinal

Modeling
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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?

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Yes, if the outcome for the family = gaussian are the same positive integers and the scale of Gaussian is not so small that the piecewise constant approximation is not good (as discussed in that case study)

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