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An Importance Sampling EM Algorithm for Latent Regression Models

Reporting methods used in large-scale assessments such as the National Assessment of Educational Progress (NAEP) rely on latent regression models. To fit the latent regression model using the maximum likelihood estimation technique, multivariate integrals must be evaluated. In the computer program MGROUP used by the Educational Testing Service for fitting the latent regression model to data from NAEP and other assessments, the integral is computed either by numerical quadrature or approximated. CGROUP, the current operational version of MGROUP used in NAEP for problems with more than two dimensions, uses Laplace approximation that may not provide fully satisfactory results, especially if the number of items per scale is small. This article examines a stochastic expectation-maximization (EM) method that uses importance sampling to NAEP-like settings. A simulation study and a real data analysis show that the importance sampling EM method provides a viable alternative to CGROUP for fitting multivariate latent regression models.