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Stochastic Approximation Methods for Latent Regression Item Response Models

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  • Matthias von Davier
  • Sandip Sinharay

Abstract

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates serving as predictors of the conditional distribution of ability. Applications to estimating latent regression models for National Assessment of Educational Progress (NAEP) data from the 2000 Grade 4 mathematics assessment and the Grade 8 reading assessment from 2002 are presented and results of the proposed method are compared to results obtained using current operational procedures.

Suggested Citation

  • Matthias von Davier & Sandip Sinharay, 2010. "Stochastic Approximation Methods for Latent Regression Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 35(2), pages 174-193, April.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:2:p:174-193
    DOI: 10.3102/1076998609346970
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    References listed on IDEAS

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    1. Neal Thomas, 2002. "The role of secondary covariates when estimating latent trait population distributions," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 33-48, March.
    2. Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    3. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
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    Cited by:

    1. Norman Rose & Matthias Davier & Benjamin Nagengast, 2017. "Modeling Omitted and Not-Reached Items in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 795-819, September.
    2. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.

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