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The E-Step of the MGROUP EM Algorithm. Program Statistics Research Technical Report No. 93-37.

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Bibliographic Details
Title: The E-Step of the MGROUP EM Algorithm. Program Statistics Research Technical Report No. 93-37.
Language: English
Authors: Thomas, Neal, Educational Testing Service, Princeton, NJ.
Peer Reviewed: N
Page Count: 77
Publication Date: 1993
Document Type: Reports - Evaluative
Descriptors: Algorithms, Elementary Secondary Education, Estimation (Mathematics), Evaluation Methods, Item Response Theory, Models, Statistical Distributions
Assessment and Survey Identifiers: National Assessment of Educational Progress
Abstract: 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. Two figures and two tables illustrate the analysis. Six appendixes present various subroutines. (Contains 22 references.) (Author/SLD)
Entry Date: 1995
Accession Number: ED382647
Database: ERIC
Description
Abstract: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. Two figures and two tables illustrate the analysis. Six appendixes present various subroutines. (Contains 22 references.) (Author/SLD)