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Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification

Authors

  • Charles E. McCulloch,

    Corresponding author
    1. Division of Biostatistics, Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, California 94107, U.S.A.
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  • John M. Neuhaus

    Corresponding author
    1. Division of Biostatistics, Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, California 94107, U.S.A.
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email:chuck@biostat.ucsf.edu

email:john@biostat.ucsf.edu

Abstract

Summary Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with the assumption that the random effects follow a Gaussian distribution. Via theoretical and numerical calculations and simulation, we investigate the impact of misspecification of this distribution on both how well the predicted values recover the true underlying distribution and the accuracy of prediction of the realized values of the random effects. We show that, although the predicted values can vary with the assumed distribution, the prediction accuracy, as measured by mean square error, is little affected for mild-to-moderate violations of the assumptions. Thus, standard approaches, readily available in statistical software, will often suffice. The results are illustrated using data from the Heart and Estrogen/Progestin Replacement Study using models to predict future blood pressure values.

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