Item Fit Statistics

Abstract

Often it is argued that the parsimonious Rasch model is too simple to have a chance to fit real-life data. Therefore, it is important to provide strong empirical evidence supporting the claim that the Rasch model is adequate for data. This chapter describes two types of item fit statistics that can be used for this purpose. The first type takes all the fundamental assumptions of the Rasch model as given and tries to assess the degree to which the separate items appear to have conditional response probabilities that do not depart from the Rasch model probabilities. The second type addresses the assumption of no differential item functioning (DIF), but does it one item at a time, assuming all the other items do not violate the Rasch model assumptions. The theory of Rasch models uses two types of residuals: individual response residuals and group residuals.

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