Abstract
This study was concerned with an investigation of the distributional properties of the standardized residual that is commonly used in Rasch model calibration programs to develop various indices of item and person fit. There were two aspects of this study: (a) an investigation of the distributional properties of the standardized residuals when the data fit the model and (b) the power of the standardized residual to detect measurement disturbances. This study was based on simulated data to control for the presence of confounding factors, such as multi-dimensionality, differences in the slopes of item characteristic curves, and guessing. The results indicated that when that data fit the model the distributional properties of the standardized residuals were 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 analysis of the simulated measurement disturbance data indicated that although the shape of the standardized residual distribution reacts to the presence of the disturbance, the magnitude of the response is small and the residuals lack the power of the item or person fit statistics to detect measurement disturbances.
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