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Efficient maximum likelihood estimation of multiple membership linear mixed models, with an application to educational value-added assessments

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  • Karl, Andrew T.
  • Yang, Yan
  • Lohr, Sharon L.

Abstract

The generalized persistence (GP) model, developed in the context of estimating “value added” by individual teachers to their students’ current and future test scores, is one of the most flexible value-added models in the literature. Although developed in the educational setting, the GP model can potentially be applied to any structure where each sequential response of a lower-level unit may be associated with a different higher-level unit, and the effects of the higher-level units may persist over time. The flexibility of the GP model, however, and its multiple membership random effects structure lead to computational challenges that have limited the model’s availability. We develop an EM algorithm to compute maximum likelihood estimates efficiently for the GP model, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. We give examples of the computations and illustrate the gains in computational efficiency achieved by our estimation procedure.

Suggested Citation

  • Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2013. "Efficient maximum likelihood estimation of multiple membership linear mixed models, with an application to educational value-added assessments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 13-27.
    • Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:13-27
    DOI: 10.1016/j.csda.2012.10.004
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    References listed on IDEAS

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    1. M. Jamshidian & R. I. Jennrich, 2000. "Standard errors for EM estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 257-270.
    2. Jennifer Broatch & Sharon Lohr, 2012. "Multidimensional Assessment of Value Added by Teachers to Real-World Outcomes," Journal of Educational and Behavioral Statistics, , vol. 37(2), pages 256-277, April.
    3. Louis T. Mariano & Daniel F. McCaffrey & J. R. Lockwood, 2010. "A Model for Teacher Effects From Longitudinal Data Without Assuming Vertical Scaling," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 253-279, June.
    4. Derek C. Briggs & Jonathan P. Weeks, 2011. "The Persistence of School-Level Value-Added," Journal of Educational and Behavioral Statistics, , vol. 36(5), pages 616-637, October.
    5. Harvey Goldstein & Jon Rasbash & William Browne & Geoffrey Woodhouse & Michel Poulain, 2000. "Multilevel Models in the Study of Dynamic Household Structures," European Journal of Population, Springer;European Association for Population Studies, vol. 16(4), pages 373-387, December.
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    1. Andrew T. Karl & Yan Yang & Sharon L. Lohr, 2013. "A Correlated Random Effects Model for Nonignorable Missing Data in Value-Added Assessment of Teacher Effects," Journal of Educational and Behavioral Statistics, , vol. 38(6), pages 577-603, December.
    2. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.

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