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Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach

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  • Renjun Ma
  • Bent Jørgensen

Abstract

Summary. We introduce a new class of generalized linear mixed models based on the Tweedie exponential dispersion model distributions, accommodating a wide range of discrete, continuous and mixed data. Using the best linear unbiased predictor of random effects, we obtain an optimal estimating function for the regression parameters in the sense of Godambe, allowing an efficient common fitting algorithm for the whole class. Although allowing full parametric inference, our main results depend only on the first‐ and second‐moment assumptions of unobserved random effects. In addition, we obtain consistent estimators for both regression and dispersion parameters. We illustrate the method by analysing the epilepsy data and cake baking data. Along with simulations and asymptotic justifications, this shows the usefulness of the method for analysis of clustered non‐normal data.

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  • Renjun Ma & Bent Jørgensen, 2007. "Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 625-641, September.
    • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:625-641
    DOI: 10.1111/j.1467-9868.2007.00603.x
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    Cited by:

    1. M. Tariqul Hasan & Gary Sneddon & Renjun Ma, 2012. "Regression analysis of zero-inflated time-series counts: application to air pollution related emergency room visit data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 467-476, June.
    2. Changli Lu & Yuqin Sun & Yongge Tian, 2018. "Two competing linear random-effects models and their connections," Statistical Papers, Springer, vol. 59(3), pages 1101-1115, September.
    3. Lee Youngjo & Gwangsu Kim, 2020. "Properties of h‐Likelihood Estimators in Clustered Data," International Statistical Review, International Statistical Institute, vol. 88(2), pages 380-395, August.
    4. Xiaoming Lu & Zhaozhi Fan, 2020. "Generalized linear mixed quantile regression with panel data," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.
    5. Yongge Tian, 2017. "Transformation approaches of linear random-effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 583-608, November.
    6. Tiago R. Pellegrini & M. Tariqul Hasan & Renjun Ma, 2017. "Modeling of paired zero-inflated continuous data without breaking down paired designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2427-2443, October.
    7. Bellio, Ruggero & Grassetti, Luca, 2011. "Semiparametric stochastic frontier models for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 71-83, January.
    8. Youngjo Lee & Gwangsu Kim, 2016. "H-likelihood Predictive Intervals for Unobservables," International Statistical Review, International Statistical Institute, vol. 84(3), pages 487-505, December.

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