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Abstract
According to Rasch (1960/1980), good model-data fit is necessary for invariant measurement, and data must have certain properties to meet the requirements of invariant measurement. If data does not reflect these required properties, Rasch suggests the data does not follow the Rasch model. The concept of data not fitting a measurement model is different from the usual approach to model-data fit within statistics. Rasch emphasized that the requirements of specific objectivity must exist within the data for the Rasch model to yield invariant item calibration and person measurement (Rasch, 1977). In Rasch measurement theory, the most widely used indicators for evaluating goodness-of-fit are residual based with the common approaches being the Infit and Outfit statistics (Mead 1975; Wright 1977; Wright 1980). This dissertation explores a framework for assessing item and person fit using the nonparametric smoothing Tukey-Hann procedure and the root integrated squared error (RISE) statistic. The RISE statistic is used to examine the differences between the nonparametric and estimated parametric Rasch curves. This framework is applied to analyze a classroom test in college statistics to demonstrate its performance for measuring fit for items and persons. Simulations are also used to explore Type I error rates and the power of this framework to evaluate its utility to detect misfit compared to traditional Rasch fit statistic.