Applicability of the Rasch model with varying item discriminations

Abstract

Among the varieties of logistic models, those attributed to Birnbaum (involving the parameters of item discrimination, item difficulty, and person ability) and Rasch (involving only item difficulty and person ability) have received attention. The present research simulated the responses of 75 subjects responding to 30 items under the Birnbaum model and then attempted a fit to the data using the Rasch model. When item discriminations varied from a variance of .05 to .25 within distributions of different form (uniform, normal, and positively skewed), the poorest overall fit appeared within the uniform distribution. For each distribution there was only a slight increase in the lack of fit as the variances increased.