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Accuracy of parameter estimation on polytomous IRT models

Chung Park, University of Massachusetts Amherst


Procedures based on item response theory (IRT) are widely accepted for solving various measurement problems which cannot be solved using classical test theory (CTT) procedures. The desirable features of dichotomous IRT models over CTT are well known and have been documented by Hambleton, Swaminathan, and Rogers (1991). However, dichotomous IRT models are inappropriate for situations where items need to be scored in more than two categories. For example, in performance assessments, most of the scoring rubrics for performance assessment require scoring of examinee's responses in ordered categories. In addition, polytomous IRT models are useful for assessing an examinee's partial knowledge or levels of mastery. However, the successful application of polytomous IRT models to practical situations depends on the availability of reasonable and well-behaved estimates of the parameters of the models. Therefore, in this study, the behavior of estimators of parameters in polytomous IRT models were examined. In the first study, factors that affected the accuracy, variance, and bias of the marginal maximum likelihood (MML) estimators in the generalized partial credit model (GPCM) were investigated. Overall, the results of the study showed that the MML estimators of the parameters of the GPCM, as obtained through the computer program, PARSCALE, performed well under various conditions. However, there was considerable bias in the estimates of the category parameters under all conditions investigated. The average bias did not decrease when sample size and test length increased. The bias contributed to large RMSE in the estimation of category parameters. Further studies need to be conducted to study the effect of bias in the estimates of parameters on the estimation of ability, the development of item banks, and on adaptive testing based on polytomous IRT models. In the second study, the effectiveness of Bayesian procedures for estimating parameters in the GPCM was examined. The results showed that Bayes procedures provided more accurate estimates of parameters with small data sets. Priors on the slope parameters, while having only a modest effect on the accuracy of estimation of slope parameters, had a very positive effect on the accuracy of estimation of the step difficulty parameters.

Subject Area

Educational evaluation|Psychological tests

Recommended Citation

Park, Chung, "Accuracy of parameter estimation on polytomous IRT models" (1997). Doctoral Dissertations Available from Proquest. AAI9809382.