A comparison of three polychotomous Rasch models for super-item analysis

Local dependency is a prevalent phenomenon in educational tests where several dichotomous items are based on a single prompt. This is a violation of one of the major assumptions of Rasch and other IRT models and poses restriction on the analysis of such tests with these models. To solve the problem, it has been suggested that the items which belong to a single prompt be bundled together and analysed as independent polychotomous super-items. However, in the last few decades there has been an array of polychotomous models with different properties and assumptions which makes the choice of the right model rather difficult. The purpose of the present study is two-fold: 1) tocompare the performance of three psychotomous Rasch models for super-item analysis and 2) to check the consequences of using ‘inappropriate’ models when the assumption of equal distances between steps within and across items is violated. To this end, a reading comprehension test comprising six independent passages each containing six dichotomous items was analysed with three Rasch models, namely, Andrich’s (1978) rating scale model (RSM), Andrich’s (1982) equidistant model and Masters’ (1982) partial credit model (PCM). Results show that there is not much difference in the three models as far as model data fit, standard error of parameter estimates and discrimination are concerned. Nevertheless, noticeable differences were observed in the estimates of the difficulty parameters across the three models.