Computational Statistics

, Volume 33, Issue 2, pp 903–931 | Cite as

Robust population designs for longitudinal linear regression model with a random intercept

  • Xiao-Dong Zhou
  • Yun-Juan Wang
  • Rong-Xian Yue
Original Paper


In this paper, optimal population designs for linear regression model with a random intercept for longitudinal data are considered. The design space is assumed to be a set of equally spaced time points. Taking the sampling scheme for each subject as a multidimensional point in the space of admissible sampling sequence, we determine the optimal number and allocation of sampling times in order to estimate the fixed effects model as accurately as possible. To make comparisons between different designs in a meaningful manner, we take experimental costs into account when defining the D-optimal design criterion function. We take a Bayesian method to overcome the uncertainty of the parameters in the design criterion to derive Bayesian optimal population designs. For complicated cases, we propose a hybrid algorithm to find optimal designs. Meanwhile, we apply the Equivalence Theorem to check the global optimality of these designs.


Optimal design Mixed effects models Equivalence theorem Particle swarm optimization 



This work was partially supported by NSFC Grant (11301332, 11471216), China.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Statistics and InformationShanghai University of International Business and EconomicsShanghaiChina
  2. 2.School of Mathematics and StatisticsShanghai University of Engineering ScienceShanghaiChina
  3. 3.College of Mathematics and ScienceShanghai Normal UniversityShanghaiChina

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