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On the determination of optimal designs for an interference model

Author

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  • Kunert, Joachim
  • Martin, R. J.

Abstract

This paper generalizes Kushner's (1997) method for finding optimal repeated measurements designs to optimal designs under an interference model. The model we assume is for a onedimensional layout without guard plots and with different left and right neighbour effects. The resulting optimal designs may need many blocks or may not even exist as a finite design. The results give lower bounds for optimality criteria on finite designs, and the design structure can be used to suggest efficient small designs.

Suggested Citation

  • Kunert, Joachim & Martin, R. J., 2000. "On the determination of optimal designs for an interference model," Technical Reports 2000,17, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200017
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    File URL: https://www.econstor.eu/bitstream/10419/77265/2/2000-17.pdf
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    Citations

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    Cited by:

    1. Vasiliki Koutra & Steven G. Gilmour & Ben M. Parker, 2021. "Optimal block designs for experiments on networks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 596-618, June.
    2. Filipiak, Katarzyna, 2012. "Universally optimal designs under an interference model with equal left- and right-neighbor effects," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 592-598.
    3. Miltiadis S. Chalikias, 2023. "Optimal Designs for Direct Effects: The Case of Two Treatments and Five Periods," Mathematics, MDPI, vol. 11(24), pages 1-12, December.
    4. Kunert, Joachim & Mersmann, Sabine, 2009. "Optimal designs for an interference model," Technical Reports 2009,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Katarzyna Filipiak & Dietrich Rosen, 2012. "On MLEs in an extended multivariate linear growth curve model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1069-1092, November.
    6. Adrian Wilk & Joachim Kunert, 2015. "Optimal crossover designs in a model with self and mixed carryover effects with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 161-174, February.
    7. Vasiliki Koutra & Steven G. Gilmour & Ben M. Parker & Andrew Mead, 2023. "Design of Agricultural Field Experiments Accounting for both Complex Blocking Structures and Network Effects," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(3), pages 526-548, September.
    8. Futao Zhang & Xiangshun Kong, 2023. "Optimal Designs for Proportional Interference Models with Different Guarding Strategies," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    9. Akram Fakhari-Esferizi & Saeid Pooladsaz, 2022. "Universally optimal balanced block designs for interference model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 1049-1061, November.
    10. Ben M. Parker & Steven G. Gilmour & John Schormans, 2017. "Optimal design of experiments on connected units with application to social networks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 455-480, April.
    11. K. Filipiak & A. Markiewicz, 2007. "Optimal designs for a mixed interference model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 369-386, May.
    12. Katarzyna Filipiak & Augustyn Markiewicz, 2017. "Universally optimal designs under mixed interference models with and without block effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 789-804, November.
    13. Filipiak, K. & Markiewicz, A., 2004. "Optimality of type I orthogonal arrays for general interference model with correlated observations," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 259-265, July.

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