Journal
VOX SANGUINIS
Volume 98, Issue -, Pages 33-57Publisher
WILEY
DOI: 10.1007/S11336-009-9136-X
Keywords
stochastic approximation; SA; item response theory; IRT; Markov chain Monte Carlo; MCMC; numerical integration; categorical factor analysis; latent variable modeling; structural equation modeling
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Funding
- Educational Testing Service
- National Science Foundation [SES-0717941]
- US Department of Education's Institute of Education Sciences (IES), National Center for Research on Evaluation, Standards and Student Testing (CRESST) [R305A050004]
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A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The accuracy of the proposed algorithm is demonstrated with simulations. As an illustration, the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children. It is shown that when the dimensionality is high, MH-RM has advantages over existing methods such as numerical quadrature based EM algorithm. Extensions of the algorithm to other modeling frameworks are discussed.
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