The influence of test and sample dimensionality on latent trait person ability and item difficulty calibrations

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Abstract
The present study was designed to test the effects of violation of the unidimen sionality assumption on Rasch Model estimates of item difficulty and person ability. Also considered was the sensitivity of the Bejar Method, Rasch Model fit statistics, classical internal consistency estimation and principal components analysis in detecting the nature and extent of violations of unidimensionality. For the study of test item dimensionality, use was made of a simulated testing situation involving a two-dimensional 60-item test administered to an illustra tive 120-person sample. For investigation of person sample dimensionality, the simulation involved use of a 120-item test with an illustrative 60-person sample. Results clearly suggested that violations of item unidimensionality produced distorted estimates of person ability, and violations of person unidimen sionality produced distorted estimates of item difficulty. The Bejar Method was found to be sensitive to such distortions, and results of applying the Bejar Method along with internal consistency estimation and principal components analysis were mutually confirmatory.