Using Parameter Expansion to Improve the Performance of the EM Algorithm for Multidimensional IRT Population-Survey Models

Abstract

Several large-scale educational surveys use item response theory (IRT) models to summarize complex cognitive responses and relate them to educational and demographic variables. The IRT models are often multidimensional with prespecified traits, and maximum likelihood estimates (MLEs) are found using an EM algorithm, which is typically very slow to converge. We show that the slow convergence is due primarily to missing information about the correlations between latent traits relative to the information that would be present if these traits were observed (“complete data”). We show how to accelerate convergence using parameter extended EM (PX-EM), a recent modification of the EM algorithm. The PX-EM modification is simple to implement for the IRT survey model and reduces the number of required iterations by approximately one-half without adding any appreciable computation to each EM-iteration.