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Application of the Stochastic EM Method to Latent Regression Models NAEP

Author(s):
von Davier, Matthias; Sinharay, Sandip
Publication Year:
2004
Report Number:
RR-04-34
Source:
ETS Research Report
Document Type:
Report
Page Count:
33
Subject/Key Words:
CGROUP, National Assessment of Educational Progress (NAEP), Importance Sampling Method, Stochastic Integration, Latent Regression, Expectation-Maximization Algorithms

Abstract

In the computer program MGROUP used by ETS for fitting the latent regression model to data from NAEP and other sources, the integration is currently done either by numerical quadrature (for problems up to two dimensions) or by an approximation of the integral. CGROUP, the current operational version of the MGROUP program used in NAEP and other assessments since 1993, is based on Laplace approximation that may not provide fully satisfactory results, especially if the number of items per scale is small. This paper examines the application of stochastic expectation-maximization (EM) methods (where an integral is approximated by an average over a random sample) to NAEP-like settings. We present a comparison of CGROUP with a promising implementation of the stochastic EM algorithm that utilizes importance sampling. Simulation studies and real data analysis show that the stochastic EM method provides a viable alternative to CGROUP for fitting multivariate latent regression models.

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