In the social sciences I have encountered that it is common to treat ordinal variables as continuous, for example variables originating from rating or Likert scales (strongly disagree, disagree, agree, strongly agree).
This topic has been discussed for example in this post from 2010: Under what conditions should Likert scales be used as ordinal or interval data?
I am looking for a more formal comparison/evaluation especially in the context of regression modeling. Rhemtulla et al. (2012) examine the performance of treating ordinal variables as continuous and make recommendations for structural equation models (SEM). I am not very familiar with SEMs, so I'm not sure if their results would also apply to regression problems.
Does anyone know about similar studies/literature in the context of regression?
Edit: Just to answer the question below: I'm mainly interested in the case where the outcome variable is ordinal (with possibly an ordinal covariate).