AN EXTENSION OF THE IRT TO A NETWORK MODEL

抄録

The traditional Item Response Theory (IRT) models assume local independence, which is equivalent to the assumption of unidimensionality. This assumption states that a subject's responses to different items in a test are statistically independent. For the assumption to be true, a subject's performance on one item must not affect. either for better or for worse, his or her responses to any other items in the test. The main purpose of this paper is to relax the local independence assumption in the traditional IRT models by extending to a network model. A new IRT model is defined which assumes probabilistic network structures for the assumption of local independence. Another unique feature of the model proposed is that it is a new probabilistic network model with the conditional probability parameters depending on a latent trait variable. Information criteria AIC and BIC are used to evaluate the performance of the model proposed, using actual test data. It shows that the proposed model provides better results than the traditional model. In addition, this paper proposes an item selection criterion from the decision theoretic approach. The amount of test information is defined as the amount of mutual information between a variable for the item and all variables over the test, to maximize the prediction efficiency of the subject's responses. The new item selection method is used to compare the prediction efficiency between the proposed model and the traditional IRT model. The proposed model is shown to be more efficient.