EFFICIENT FULL INFORMATION MAXIMUM LIKELIHOOD ESTIMATION FOR MULTIDIMENSIONAL IRT MODELS

Abstract

ABSTRACTMaximum marginal likelihood estimation of multidimensional item response theory (IRT) models has been hampered by the calculation of the multidimensional integral over the ability distribution. However, the researcher often has a specific hypothesis about the conditional (in)dependence relations among the latent variables. Exploiting these relations may result in more efficient estimation algorithms. A well‐known example is the bi‐factor model, in which each item measures a general dimension and one of K other dimensions, for which Gibbons and Hedeker (1992) showed that full information maximum likelihood estimation only requires the integration over two‐dimensional integrals. In this paper, it is shown how the approach of Gibbons and Hedeker (1992) can be placed into a graphical model framework. The advantage of the graphical model framework is that efficient estimation schemes can be derived in a fully automatic way by applying algorithms to the graphical representation of a statistical model. This renders the approach fairly generally applicable, and tedious derivations by hand are no longer involved. The generality of the approach is demonstrated by applying it to a multidimensional IRT model with a second order dimension. It turns out that full information maximum likelihood estimation for such a model also requires the evaluation of two‐dimensional integrals only.