Using Item Mean Squares To Evaluate Fit to the Rasch Model.Report as inadecuate

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In the mid to late 1970s, considerable research was conducted on the properties of Rasch fit mean squares, resulting in transformations to convert the mean squares into approximate t-statistics. In the late 1980s and the early 1990s, the trend seems to have reversed, with numerous researchers using the untransformed fit mean squares as a means of testing fit to the Rasch measurement models, citing as the principal motivation the influence sample size has on the sensitivity of the t-converted mean squares. The historical development of these fit indices and the various transformations are traced, and the impact of sample size on both the fit mean squares and the t-transformations of those mean squares is examined. Because the sample size problem has little influence on the person mean square problem, due to the relatively short length (100 items or fewer), this paper focuses on the item fit mean squares, where it is common to find the statistics used with sample sizes ranging from 30 to 10,000. Simulation results indicate that the critical value for the mean square used to detect misfit is affected both by the type of the mean square and the number of persons in the calibration. Four tables present analysis results. (Contains 11 references.) (SLD)

Descriptors: Evaluation Methods, Goodness of Fit, Item Response Theory, Sample Size, Simulation, Test Items

Author: Smith, Richard M.; And Others


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