I have data set that all variables are categorical, and the dependent variable is consisting of three categories. I am planning to run MLR, but I noticed that majority of examples of such model has incorporated continuous variable which is not my case.

Moreover, When I used MLR for my data, the issue of unexpected singularities has come up and still there despite compressing of categories or excluding some variables.

Meanwhile, I am just asking if Goodman and Kruskal's λ is a good option to reveal association and decreasing the error of prediction that can substitute MLR in my case?

I would appreciate also if anyone can share practical guide for MLR in which all dependent and independent variables are categorical!