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Date of Graduation
Doctor of Philosophy (PhD)
Department of Graduate Psychology
The Rasch model implies that the relation between examinee ability and the probability of correctly answering an item can be defined solely by a small set of parameters. In the case of Rasch modeling, there are only two parameters: the ability of an examinee and the difficulty of an item. When the data meet the requirements of the Rasch model, it possesses several appealing properties that distinguish it from Classical Test Theory and more complex Item Response Theory models.
However, the desirable properties of the Rasch model only exist when the data meet its strict requirements. Therefore, it is vital to check the fit of the data to the model, both the fit of the items and the examinees. The two primary fit statistics for Rasch models are Infit and Outfit. While useful statistics, they possess some inherent deficiencies. Therefore, it may be useful to supplement them with another fit statistic. One such fit statistic, which is computed and interpreted differently than Infit and Outfit, is the root integrated squared error (RISE). The purpose of this dissertation was to compare the performance of RISE, in terms of type 1 error rates and power, to Infit and Outfit. Additionally, RISE requires statistical smoothing in its computation. Therefore, an additional purpose of this dissertation was to examine the impact of smoothing amount and smoothing type on the performance of RISE.
A simulation study was conducted to examine, RISE, Infit, and Outfit. Responses to a 50 item test were generated, with 43 items that fit the Rasch model and 7 items that did not. Sample size was manipulated and had three levels: 200, 500, or 1,000 examinees. Two smoothing techniques were used: Hanning or Kernel smoothing with a Gaussian function. Within each smoothing technique, nine smoothing amounts were used.
The results showed that RISE performed similarly across smoothing techniques. Within each smoothing technique, smoothing amount often had a drastic impact on RISE, with the best results generally associated with a low to medium amount of smoothing. Across most of the misfitting items, Outfit and/or Infit outperformed RISE.
Waterbury, Glenn T., "Rise and shine: A comparison of item fit statistics for the Rasch model" (2020). Dissertations, 2020-current. 20.