Approximating Bifactor IRT True-Score Equating With a Projective Item Response Model

Item response theory (IRT) true-score equating for the bifactor model is often conducted by first numerically integrating out specific factors from the item response function and then applying the unidimensional IRT true-score equating method to the marginalized bifactor model. However, an alternative procedure for obtaining the marginalized bifactor model is through projecting the nuisance dimensions of the bifactor model onto the dominant dimension. Projection, which can be viewed as an approximation to numerical integration, has an advantage over numerical integration in providing item parameters for the marginalized bifactor model; therefore, projection could be used with existing equating software packages that require item parameters. In this paper, IRT true-score equating results obtained with projection are compared to those obtained with numerical integration. Simulation results show that the two procedures provide very similar equating results.