An investigation of a Bayesian decision-theoretic procedure in the context of mastery tests

Abstract

The purpose of this study was to extend Glas and Vos's (1998) Bayesian procedure to the 3PL IRT model by using the MCMC method. In the context of fixedlength mastery tests, the Bayesian decision-theoretic procedure was compared with two conventional procedures (conventional-Proportion Correct and conventional-EAP) across different simulation conditions. Several simulation conditions were investigated, including two loss functions (linear and threshold loss function), three item pools (high discrimination, moderate discrimination and real item pool) and three test lengths (20, 40 and 60). Different loss parameters were manipulated in the Bayesian decision-theoretic procedure to examine the effectiveness of controlling false positive and false negative errors. The degree of decision accuracy for the Bayesian decision-theoretic procedure using both the 3PL and 1PL models was also compared. Four criteria, including the percentages of correct classifications, false positive error rates, false negative error rates, and phi correlations between the true and observed classification status, were used to evaluate the results of this study. According to these criteria, the Bayesian decision-theoretic procedure appeared to effectively control false negative and false positive error rates. The differences in the percentages of correct classifications and phi correlations between true and predicted status for the Bayesian decision-theoretic procedures and conventional procedures were quite small. The results also showed that there was no consistent advantage for either the linear or threshold loss function. In relation to the four criteria used in this study, the values produced by these two loss functions were very similar.