The Distributional Properties of Rasch Item Fit Statistics

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Abstract
This study reports the results of an empirical investigation of the distributional properties of the item fit statistics that are commonly used in Rasch model calibration programs as indices of the fit of the responses to individual items to the measurement model. There are two aspects of this study: an investigation of the distributional properties of the item fit statistics when the data fit the model, and the power of the item fit statistics to detect measurement disturbances. This study is based on simulated data to control for the presence of confounding factors, such as multidimensionality, differences in the slopes of item characteristic curves, and guessing. The results indicate that, when that data fit the model, the distributional properties of the item fit statistics, corrected for use of estimated person parameters, are close to hypothesized mean and standard deviation and that it is possible to construct reasonable Type I error rates that can be used as a frame of reference when investigating the fit of actual data to the Rasch model. The item fit statistics also have the power to detect measurement disturbances of reasonable magnitude.

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