Investigation of the Orthogonality Assumption in the Bifactor Item Response Theory

Purpose: This study aims to investigate the orthogonality assumption, which restricts the use of Bifactor item response theory under different conditions. Method: Data of the study have been obtained in accordance with the Bifactor model. It has been produced in accordance with two different models (Model 1 and Model 2) in a simulated way. Results: As a result of the research, it was found out that the case that two factors were correlated (Model 1) and that all factors were correlated (Model 2) had the same effect on the accuracy of both person and item parameter estimations. While estimating the discrimination parameters, as the orthogonality violation increased, it was concluded that the bias increased, too. As the test length increased, the accuracy of estimations of discrimination and difficulty parameters, namely the reliability decreased. Increasing the number of items increased the accuracy of person parameters, which was the reliability. Implication for Research and Practice: As test length increases, the Bifactor theory can better tolerate the orthogonality violation in estimation of person parameters. The practitioners who want to use this theory are recommended to work with large item pools. At all correlation levels, the accuracy of the parameter estimations was approximately the same. New studies can be repeated with intermediate correlation levels. Among all the parameters, the parameters whose estimation reliability is the lowest were found to be person parameters