Applicability of the Rasch Model with Varying Item Discriminations

Among the varieties of logistic models, those at tributed 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 Birn baum 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 distribu tions of different form (uniform, normal, and posi tively skewed), the poorest overall fit appeared within the uniform distribution. For each distribu tion there was only a slight increase in the lack of fit as the variances increased.