A Bayesian Multilevel Multidimensional Item Response Theory Model for Testing a Key Assumption of the Bifactor Model

• In Event: Marriott Roundtable Session 29
  In Roundtable Session: Estimation and Reporting of Multidimensional Item Response Theory Models

Abstract

The Bifactor item response theory (IRT) model and its variants have seen increase use in the analysis of educational and psychological test data. These models assume the dimensions of the bifactor structure are orthogonal to each other and do not test this assumption because of indeterminacy issues in the correlations. This indeterminacy issue, however, can be overcome in the Bayesian framework. The recently introduced Bayesian multilevel multidimensional IRT (BMMIRT) model is used to show that the orthogonality of the dimensions of a bifactor structure can be directly tested. Simulation show that: 1) the BMMIRT model can detect violations in the orthogonal assumptions; and 2) ignoring the correlations among the dimensions leads to artificially inflated item discriminations and measurement reliability estimates.

Author

• Ken A. Fujimoto, Loyola University Chicago