The Distributional Properties of Rasch Standardized Residuals
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...
Richard M. Smith (1988). The Distributional Properties of Rasch Standardized Residuals. Educational and Psychological Measurement, 48(3), 657-667. https://doi.org/10.1177/0013164488483009