Violations of the Assumption of Independence II—The Polytomous Rasch Model

Abstract

Items hypothesized to be dependent can be combined into higher orderOrderpolytomousPolytomousitems and the data reanalysed using the PRM. If the reliabilityReliabilityestimate from an analysis where items hypothesized to be dependent are combined into higher orderOrderpolytomousPolytomousitems is lower than the reliabilityReliabilityestimate from the original analysis, dependence is present. The spread or dispersion parameter provides another way of detecting dependence in a data set. There are ways of estimating the magnitude of response dependenceMagnitude of response dependenceor multidimensionalityMultidimensionality. One method of testing for multidimensionalityMultidimensionalityis to take two subsets of items, estimate the person parametersT-test for equivalence of person estimates from two subsetsbased on each of these subsets, and then testing if the estimate for each person from the two subtests is statistically equivalent using a t-testTest.