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The E-Step of the MGROUP EM Algorithm NAEP

Thomas, Neal
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Algorithms, Item Response Models, MGROUP, National Assessment of Educational Progress (NAEP), Statistical Analysis


(76pp.) Mislevy (1984, 1985) introduced an EM algorithm for estimating the parameters of a latent distribution model that is used extensively by the National Assessment of Educational Progress. Second order asymptotic corrections are derived and applied along with more common first order asymptotic corrections to approximate the expectations required by the E-step of the EM algorithm. These corrections produce much more accurate approximations than those produced by two different normal approximations. The asymptotic corrections are applicable in high dimensional models. The number of function evaluations required by these methods grows linearly as dimension increases, in contrast to the exponential growth with dimension of product quadrature rules which yield similar accuracy.

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