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Fitting the Rasch Model to Account for Variation in Item Discrimination

Naval Postgraduate School, ronweitzman{at}redshift.com

Building on the Kelley and Gulliksen versions of classical test theory, this article shows that a logistic model having only a single item parameter can account for varying item discrimination, as well as difficulty, by using item–test correlations to adjust incorrect–correct (0–1) item responses prior to an initial model fit. The fit occurs through the application of least squares to the logits of the adjusted item responses. Iteration transforms each of the item–test correlations to an item– correlation, of which the discrimination parameter a is shown to be a function. Comparing this response-adjusted model with the traditional Rasch model, a simulation study involving 10-, 20-, and 30-item tests showed that correlations of estimates with their true values were uniformly higher for this model than for the Rasch model, whereas the reverse was true regarding b estimates. A hybrid of the two models proved to have the estimation advantages of both. Particularly notable in this study is that the correlation of estimates with their true values was higher in the 20-item test using the response-adjusted or the hybrid model than in the 30-item test using the Rasch model for parameter estimation.

Key Words: Rasch model • single-parameter logistic model • item discrimination • classical test theory • modern test theory

This version was published on April 1, 2009

Educational and Psychological Measurement, Vol. 69, No. 2, 216-231 (2009)
DOI: 10.1177/0013164408322022


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