A Conditional Item-Fit Index for Rasch Models

Abstract

A new item-fit index is proposed that is both a descriptive measure of deviance of single items and an index for statistical inference. This index is based on the assumptions of the dichotomous and polytomous Rasch models for items with ordered categories and, in particular, is a standardization of the conditional likelihood of the item pattern that does not depend on the item parameters. This approach is compared with other methods for determining item fit. In contrast to many other item-fit indexes, this index is not based on response-score residuals. Results of a simulation study illustrating the performance of the index are provided. An asymptotically normally distributed Z statistic is derived and an empirical example demonstrates the sensitivity of the index with respect to item and person heterogeneity. Index terms: appropriateness measurement, item discrimination, item fit, partial credit model, Rasch model.