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Design and cost optimization for hierarchical data

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  • Kari Tokola
  • Andreas Lundell
  • Jaakko Nevalainen
  • Hannu Oja

Abstract

type="main"> In this paper, we consider balanced hierarchical data designs for both one-sample and two-sample (two-treatment) location problems. The variances of the relevant estimates and the powers of the tests strongly depend on the data structure through the variance components at each hierarchical level. Also, the costs of a design may depend on the number of units at different hierarchy levels, and these costs may be different for the two treatments. Finally, the number of units at different levels may be restricted by several constraints. Knowledge of the variance components, the costs at each level, and the constraints allow us to find the optimal design. Solving such problems often requires advanced optimization tools and techniques, which we briefly explain in the paper. We develop new analytical tools for sample size calculations and cost optimization and apply our method to a data set on Baltic herring.

Suggested Citation

  • Kari Tokola & Andreas Lundell & Jaakko Nevalainen & Hannu Oja, 2014. "Design and cost optimization for hierarchical data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(2), pages 130-148, May.
    • Handle: RePEc:bla:stanee:v:68:y:2014:i:2:p:130-148
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    File URL: http://hdl.handle.net/10.1111/stan.12026
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    References listed on IDEAS

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    1. Tokola, K. & Larocque, D. & Nevalainen, J. & Oja, H., 2011. "Power, sample size and sampling costs for clustered data," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 852-860, July.
    2. Moonseong Heo & Andrew C. Leon, 2008. "Statistical Power and Sample Size Requirements for Three Level Hierarchical Cluster Randomized Trials," Biometrics, The International Biometric Society, vol. 64(4), pages 1256-1262, December.
    3. Spyros Konstantopoulos, 2009. "Incorporating Cost in Power Analysis for Three-Level Cluster-Randomized Designs," Evaluation Review, , vol. 33(4), pages 335-357, August.
    4. Xiaofeng Liu, 2003. "Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization," Journal of Educational and Behavioral Statistics, , vol. 28(3), pages 231-248, September.
    5. Mirjam Moerbeek & Gerard J. P. van Breukelen & Martijn P. F. Berger, 2000. "Design Issues for Experiments in Multilevel Populations," Journal of Educational and Behavioral Statistics, , vol. 25(3), pages 271-284, September.
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