I am analyzing survey data that has dependent variable in the form of an ordinal variable (Likert scale 1-7). The predictors (~50) are a combination of ordinal variables and categorical variable. I have performed one-hot encoding to convert categorical predictors into dummies.Also, I performed a factor analysis for variable reduction of ordinal predictors. Now, for certain reasons I can’t use the factors as such for further analysis. Hence picked one to two variables from each factor based on high factor loading and business sense.
Now, the objective is to find relative importance of these predictors in driving the ordinal variable.
Question is which technique(s) could help me achieve the objective? Assume, I have a constraint i.e.
I can’t make any transformations to the ordinal dependent variable (i.e. combining categories to reduce the # classes)
P.S. - I can fall back on OLS (not the best method given nature of data) and ordinal logistic regression but want to hear if you have tried anything else for this kind of problem- RF, Lasso etc.??