While thinking about methods on how to predict a dependent variable that is ordinal and constrained (0, 1, 2, 3, 5 are the only possible values), I found that an ordered logistic regression is an common approach used in the community and as a strategy, that make sense to me.
However, I was trying to understand why another method that came into my mind is a bad idea.
The method in question would be to use a simple linear regression and then map the predicted outcome to the closest integer in the range [0, 5].
Would that be bad? Why?
Explanations with references to theory would be greatly appreciated to fill the all the gaps I have in this matter.