The Polytomous Rasch Model III

Abstract

A category coefficientCategory coefficient$$ \kappa_{k} $$is the sum of the exceeded thresholdsThresholdfor response category k. The PRM can be rewritten in terms of principal componentsPrincipal components(Guttman) for the thresholdsThresholdinstead of the thresholdsThresholdthemselves. The principal component $$ \lambda $$characterizes the spread of the responses, the principal component $$ \eta $$characterizes the skewness, another principal component characterizes the kurtosis, etc. ThresholdsThresholdcan be recovered from principal componentsPrincipal componentsthrough the category coefficientsCategory coefficient. Only if a threshold does not discriminate between two adjacent response categories it is justified to combine adjacent response categories through rescoring the responses.