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

• Published in: Computational statistics Vol. 34; no. 1; pp. 71 - 87
• Main Authors: Jiang, Hong-Yan, Yue, Rong-Xian
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019; Springer Nature B.V
• Subjects: Bayesian analysis; Covariance matrix; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematical models; Mathematics and Statistics; Original Paper; Parameter estimation; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Time dependence; Within-subjects design; Quasi-likelihood method; Estimating equation; Repeated measures; Longitudinal data; Hierarchical design
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-018-0834-7

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.