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Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors

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Abstract

This paper is concerned with the problem of pseudo-Bayesian D-optimal designs for the first-order Poisson mixed model for longitudinal data with time-dependent correlated errors. A standard approximate covariance matrix of the parameter estimation is obtained based on the quasi-likelihood method. Furthermore, to overcome the dependence of pseudo-Bayesian D-optimal designs on the choice of the prior mean, a hierarchical pseudo-Bayesian D-optimal designs based on the hierarchical prior distribution of unknown parameters is proposed. The results show that the optimal number of time points depends on both the interclass autoregressive coefficients and different cost constraints. The relative efficiency of equidistant designs compared with the hierarchical pseudo-Bayesian D-optimal designs is also discussed.

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Authors and Affiliations

  1. College of Mathematics and Science, Shanghai Normal University, Shanghai, 200234, China

    Hong-Yan Jiang & Rong-Xian Yue

  2. Department of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, 223003, Jiangsu, China

    Hong-Yan Jiang

  3. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China

    Rong-Xian Yue

Authors
  1. Hong-Yan Jiang
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  2. Rong-Xian Yue
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Corresponding author

Correspondence to Rong-Xian Yue.

Additional information

This work was supported by NSFC Grants 11471216 and 11871143.

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Jiang, HY., Yue, RX. Pseudo-Bayesian D-optimal designs for longitudinal Poisson mixed models with correlated errors. Comput Stat 34, 71–87 (2019). https://doi.org/10.1007/s00180-018-0834-7

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  • DOI: https://doi.org/10.1007/s00180-018-0834-7

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