Distinguishing among parametric item response models for polychotomous ordered data

Several item response models have been proposed for fitting Likert-type data. Thissen & Steinberg (1986) classified most of these models into difference models and divide-by-total models. Although they have different mathematical forms, divide-by-total and difference models with the same number of parameters seem to provide very similar fit to the data. The ideal observer method was used to compare two models with the same number of parameters-Samejima’s (1969) graded response model (a difference model) and Thissen & Steinberg’s (1986) extension of Masters’ (1982) partial credit model (a divide-by-total model-to investigate whether difference models or divide-by-total models should be preferred for fitting Likert-type data. The models were found to be very similar under the conditions investigated, which included scale lengths from 5 to 25 items (five-option items were used) and calibration samples of 250 to 3,000. The results suggest that both models fit approximately equally well in most practical applications. Index terms: graded response model, IRT, Likert scales, partial credit model, polychotomous models, psychometrics