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Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures

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  • Minjeong Jeon

    (University of California, Berkeley)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley and Institute of Education, University of London)

Abstract

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be estimated this way is generalized linear mixed models with factor structures. Such models are useful in educational research, for example, for estimation of value-added teacher or school effects with persistence parameters and for analysis of large-scale assessment data using multilevel item response models with discrimination parameters. The authors describe the profile-likelihood approach, implement it in the R software, and apply the method to longitudinal data and binary item response data. Simulation studies and comparison with gllamm show that the profile-likelihood method performs well in both types of applications. The authors also briefly discuss other types of models that can be estimated using the profile-likelihood idea.

Suggested Citation

  • Minjeong Jeon & Sophia Rabe-Hesketh, 2012. "Profile-Likelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures," Journal of Educational and Behavioral Statistics, , vol. 37(4), pages 518-542, August.
  • Handle: RePEc:sae:jedbes:v:37:y:2012:i:4:p:518-542
    DOI: 10.3102/1076998611417628
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    References listed on IDEAS

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    2. Joshua B. Gilbert & James S. Kim & Luke W. Miratrix, 2023. "Modeling Item-Level Heterogeneous Treatment Effects With the Explanatory Item Response Model: Leveraging Large-Scale Online Assessments to Pinpoint the Impact of Educational Interventions," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 889-913, December.
    3. Sun-Joo Cho & Jennifer Gilbert & Amanda Goodwin, 2013. "Explanatory Multidimensional Multilevel Random Item Response Model: An Application to Simultaneous Investigation of Word and Person Contributions to Multidimensional Lexical Representations," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 830-855, October.
    4. Minjeong Jeon & Sophia Rabe-Hesketh, 2016. "An autoregressive growth model for longitudinal item analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 830-850, September.

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