Fit indices for the Rasch model.

摘要

This dissertation introduces a new family of non-parametric fit tests for the Rasch model combining the elements of Monte Carlo method, traditional hypothesis testing, and Item Response Theory model fit. The new tests do not make assumptions regarding the distributions of their test statistics. Rather, distributions used for testing model fit are generated “on the fly” using a Monte Carlo method. The developmental phases and algorithms for performing the tests are discussed in detail. Differences between the new method and the usually accepted residual-based fit tests are presented from theoretical and practical perspectives, as well as the correspondence between the new indices and the general case of fit analysis. Comprehensive validity and stability studies are conducted using real and computer simulated test data to demonstrate the performance of the proposed indices under various conditions and to make comparisons with previously used Rasch fit indices. The results of the new global fit analysis, also introduced in this thesis, show that when fit analysis is performed with the aid of the new tests the Rasch model performs very well. It is demonstrated using several test scenarios that the traditional mean-square fit index reports false misfit quite frequently. Although, the Monte Carlo p-values are always approximate, a stability study conducted in this dissertation reveals, that they show remarkable stability with respect to the number of simulated matrices. It is shown, that for moderately sized response matrices a satisfactorily stable p-value can be obtained within a reasonable computing time, making the newly proposed technique available to the test developing community.