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Item response theory (IRT) is a mathematical model for creating, conducting and analyzing test items. In this model, both item difficulties and examinee’s latent trait are mesured on the same scale. Item response theory required the assumption of local independence between items. This assumption means that the response to an item is independent from responses to other items when ith examinee’s ability parameter θ i is given. However, we often conduct a test which is broken the assumption of local independence. Although complex IRT models have been proposed to solve this problem, we hope to use a simpler IRT model in real test cases if available. Testlet model is one of simpler models. A testlet is an item group items of which have relationship each other. By counting the number of correct answers in a testlet, items with local dependence can be analyzed by using GRM. Therefore it is meaningful to investigate to what extent a simpler IRT model and GRM are applicable to items with local dependence. The purpose of this study is to examine the effects of the number of examinees and the combination of item difficulties on the estimation of ability parameters in such situations. As simpler IRT models we employe the two-parameter logistic model (2PLM) and the testlet model, we assume to item response patterns items of which have local dependence. In the dependent pattern, we set that correct answers do not follow incorrect answers. The number of examinee is set to be 100, 200, 500, and 1000. Item discriminations are set at fixed values of 0.3, 0.9, and 1.5. Item difficulties are set in eleven patterns. The indices of differences between the true ability values and their estimates are Bias, RMSE, and corθ . Simulation results showed the low item discrimination was precision of estimation generally poor. When the values of the item difficulties parameter decrease in a testlet, precision of estimate was also poor. When the values of the item difficulties parameter increase in a testlet, and the number of examinee was 200 the testlet model works well although it requires high item discrimination.When the values of the item difficulties parameter increase in a testlet and the number of examinee more than or equal to 500, the testlet model was applicable, while the 2PLM was acceptable. Therefore we can conclude that simpler IRT models such as 2PLM and testlet model can be applied to analyze test data items of which have local dependence if the values of the item difficulties parameter increase in a testlet and the number of examinee more than or equal to 200. |
