Hello fellow statisticians!

I have got a quick question that (hopefully) a more experienced statistician is able to answer.

I have a balanced panel data set where I am looking at several dependent variables. Some of them are continuous (%) and some of them are ordinal (categories 1-4, ordered from highest to lowest).

The continuous variables, I want to analyse with a standard Fixed Effects (within) estimator. However, as far is I know, I cannot just do this for the ordinal variables right, because they are not linear? Is there any way to justify that the ordinal variables can be treated as continuous? I do know this works if the ordinal variable is an independent variable, I normally follow this methodology when encountering this problem: https://www3.nd.edu/~rwilliam/xsoc73...ndependent.pdf


So to sum up my question: Is it possible to 'argue' that my ordinal dependent variables can be treated as continuous and I can therefore use FE for them as well? If yes - could you point me towards the appropriate literature/methodology? Or is this not possible and I need to use logit/probit for the ordinal dependent variables?

Many thanks in advance folks!!
Andreas