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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?

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    $\begingroup$ You didn't explain how information-losing cutoffs would help. And note that if a cutoff for a variable exists it must be a function of the values of the other variables. $\endgroup$ – Frank Harrell Nov 13 '13 at 23:37
  • $\begingroup$ @FrankHarrell the information-losing due to using single predictor is not of my concern.I mentioned that in case if some one said that it's better to use all five variables.What do mean that cutoff for one variable should be a function of other four variables as well? in addition to categorical DV? $\endgroup$ – Amin Nov 13 '13 at 23:45
  • $\begingroup$ Why are you doing all this? What are you trying to find out? This seems a very complex procedure full of assumptions. $\endgroup$ – Peter Flom Nov 13 '13 at 23:49
  • $\begingroup$ @PeterFlom I assumed that we have a latent categorical variable that divides the sample into different groups.Then we need to find cutoff values for each category in order to categorize future data without doing the same procedure. $\endgroup$ – Amin Nov 14 '13 at 0:48
  • $\begingroup$ What I was referring to is that if there is any place for making cutoffs, the cutoff must be made on the predicted $Y$, e.g., predicted $Prob[Y=1]$. Then solve for which values of $X$ put you in the high group of predictions. You will find that this induces a cutoff for $X_{1}$ that is dependent on the continuous value of $X_{2}$. By the way why the need to categorize future data? $\endgroup$ – Frank Harrell Nov 14 '13 at 13:21

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