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I have a situation where I have a set of j distinct categories, let's call them C. I have measured C in i different ways for a number of observations. I want to find the category Cj that best represents each observation based on the i measures of C. So, I basically want to go from a set of (# of items in C) * i variables on each observation, to only the category Cj which is the best representation of that particular observation.

Because for each measurement i in my list, there is a benefit of having a larger value of i in the category, I have though about the option of ranking the categories for each observation based on i, and do this for all i, and then combine the rankings. So in this case I get i lists with values ranging from 1 to (# of items in C) for each observation. If I rank them, so that rank 1 is the largest value in terms of the measure i, I can combine the elements of the i lists with for instance an average, and the smallest value of the combination, with position j, will then be used as the best category Cj, representing the observation.

I want a good way to find the category Cj that best represents each observation. Is there a general method to approach this problem?

Thanks.

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You might want a finite mixture model, which is essentially a latent variable model (like factor analysis) with categorical latent variables. Your items are the indicators of class membership. Given that you know how many classes there are, you can fix the number of classes in the model (which is usually itself estimated by the procedure). The output is, for each individual, the probability that they come from each given class, and the class for which they have the highest probability is often considered the best estimate of their true class membership. I know Mplus has capabilities for mixture models.

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