| The aim of the study is to find a theoretically justified method to estimate the item parameters, including the guessing parameter, for the compensatory Multidimensional Item Response Theory (MIRT) model. The Markov Chain Monte Carlo (MCMC) method is reproduced first in this study. Results show MCMC gives accurate estimation for the item discriminations and difficulties and fairly good estimation for the guessing parameters. However, its heavy computational burden is a major obstacle for practical application. Based on Classical Test Theory (CTT) and conditional covariance theory an initial estimation method for the item parameters is proposed, which gives good approximations of the item parameters as the starting points for the expectation-maximization method. This study then extends Tsutakawa's unidimensional IRT estimation method to two dimensions; and simulation results show the estimate for the Item Response Function (IRF) is accurate using the initial estimation results as prior information according to an Empirical Bayes method. Finally, a 5-parameter mixed bivariate normal distribution is proposed for the abilities in the Marginal Maximization Likelihood (MML) method. |
