Distinguishing among parametric item response models for polychotomous ordered data

Several item response models have been proposedfor fitting Likert-type data. Thissen & Steinberg (1986)classified most of these models into difference modelsand divide-by-total models. Although they have differentmathematical forms, divide-by-total and differencemodels with the same number of parameters seem toprovide very similar fit to the data. The ideal observermethod was used to compare two models with the samenumber of parameters-Samejima’s (1969) graded responsemodel (a difference model) and Thissen &Steinberg’s (1986) extension of Masters’ (1982) partialcredit model (a divide-by-total model-to investigatewhether difference models or divide-by-total modelsshould be preferred for fitting Likert-type data. Themodels were found to be very similar under the conditionsinvestigated, which included scale lengths from 5to 25 items (five-option items were used) and calibrationsamples of 250 to 3,000. The results suggest thatboth models fit approximately equally well in mostpractical applications. Index terms: graded responsemodel, IRT, Likert scales, partial credit model, polychotomousmodels, psychometrics.