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Comparison of procedures for the estimation of ability parameter in the three-parameter item response model
Abstract
Item response theory has improved the area of educational and psychological measurement significantly. However, the effectiveness of the applications of item response theory is dependent on the adequacy of techniques of parameter estimation. When item parameters are precalibrated and treated as known, the ability estimation is relatively straightforward. Currently, several competing estimators of the ability parameters in item response models are available. These are: Maximum Likelihood estimator (ML), the Bayesian Modal estimator (BM), the Expected A Posterior estimator (EAP), and the Mean of the likelihood function (abbreviated as "MM" to differentiate from ML, above). The primary purpose of the study was to examine and compare the properties of the above ability estimators when item parameters were precalibrated and treated as known. In particular, the properties of the ability estimators, such as distribution, bias, and accuracy were investigated. The secondary purpose of this study was to investigate the asymptotic properties of the ML ability estimator with respect to accuracy, bias, and the asymptotic normal distribution. In addition, the effects of test lengths and ability levels were studied in the three-parameter item response model. Simulated data were generated under various test lengths and ability levels in the three-parameter models. In order to accomplish the purpose of this study analyses such as: (1) accuracy of the ability estimators; (2) bias of the ability estimators; (3) distributional property of the ability estimators; and (4) the asymptotic properties of the ML ability estimators were carried out. The results of this study indicate that the ML ability estimator tends to be better than the MM, BM, and EAP ability estimators in the three-parameter item response model. This is particularly true in the proficiency test data set based on the three-parameter item response model. In general, the ML, BM, MM, and EAP ability estimators are normally distributed except when the true ability levels are at both of the extremes and tests are short (n $\le$ 40). The ML ability estimator is asymptotically normally distributed with tests longer than 20 items and when true ability is in the range ($-$1, 1).
Subject Area
Educational tests & measurements|Social studies education|Mathematics education|Statistics|Educational evaluation
Recommended Citation
Zhou, Yu-Hui Alison, "Comparison of procedures for the estimation of ability parameter in the three-parameter item response model" (1991). Doctoral Dissertations Available from Proquest. AAI9207480.
https://scholarworks.umass.edu/dissertations/AAI9207480