First of all, if this variable is not ordinal, it will be treated as actually having an order, and essentially you are fitting a linear model through the 4 levels, and I don't see any sense to that. I can't really guess how that would affect a predictive model, other than to say it's simple and easy to handle the variable properly (as nominal), and thus I would not recommend handling it as continuous. In fact, if I was a reviewer for a journal and someone turned a nominal (not ordinal) variable into continuous, I'd probably reject the paper.
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Paige Miller