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Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis–Hastings Robbins–Monro Algorithm

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Listed:
  • Ji Seung Yang

    (University of Maryland)

  • Li Cai

    (University of California)

Abstract

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis–Hastings Robbins–Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard errors efficiently. Simulations, with various sampling and measurement structure conditions, were conducted to obtain information about the performance of nonlinear multilevel latent variable modeling compared to traditional hierarchical linear modeling. Results suggest that nonlinear multilevel latent variable modeling can more properly estimate and detect contextual effects than the traditional approach. As an empirical illustration, data from the Programme for International Student Assessment were analyzed.

Suggested Citation

  • Ji Seung Yang & Li Cai, 2014. "Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis–Hastings Robbins–Monro Algorithm," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 550-582, December.
    • Handle: RePEc:sae:jedbes:v:39:y:2014:i:6:p:550-582
    DOI: 10.3102/1076998614559972
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    References listed on IDEAS

    as
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    2. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    3. Asim Ansari & Kamel Jedidi, 2000. "Bayesian factor analysis for multilevel binary observations," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 475-496, December.
    4. Li Cai, 2010. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 307-335, June.
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