I have a data set with five continuous variables measuring an index in a population. For finding underlying classifications in the population based on the five observed variables, I did a latent profiles analysis (LPA) for two and three categories model using all five variables.The task is to find cutoff values for each variable in order to classify new observations without doing the whole procedure.
Then I used produced categorization from LPA to find relative weights of each of the five variables using logistic (for two-category solution) and multinomial (for three-category solution) regression.That was for finding the relative contribution of each variable to the classification.Next step was to find cutoff values for each variable for future use.
For finding cutoff values for each variable, I could find cutoff for each variable in two-category solution by using logistic regression and setting the regression equation equal to 0.5 and then finding corresponding value of the variable.In other words,I used predicted categorization by LPA as a criterion (DV) for each variable in logistic regression.I didn't use ROC because it didn't give me reasonable results.
My question is, how to do the same thing for three-category solution? I tried multinomial regression but I didn't came up with a solution. with three categories I need to have two cutoff values in order to define category boundaries for each variable.
Or simply, how to determine cutoff values for a variable based on a predefined categorizes to match with the categories?