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D-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor

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Listed:
  • Oluwole A Nuga
  • Abba Zakirai Abdulhamid
  • Shobanke Emmanuel Omobola Kayode

Abstract

This study examines design preference in Completely Randomized (CR) split-plot experiments involving random whole plot factor effect and fixed sub-plot factor effect. Many previous works on optimally designing split-plot experiments assumed only factors with fixed levels. However, the cases where interests are on random factors have received little attention. These problems have similarities with optimal design of experiments for fixed parameters of non-linear models because the solution rely on the unknown parameters. Design Space (DS) containing exhaustive list of balanced designs for a fixed sample size were compared for optimality using the product of determinants of derived information matrices of the Maximum Likelihood (ML) estimators equivalent to random and fixed effect in the model. Different magnitudes of components of variance configurations where variances of factor effects are larger than variances of error term were empirically used for the comparisons. The results revealed that the D-optimal designs are those with whole plot factor levels greater than replicates within each level of whole plot.

Suggested Citation

  • Oluwole A Nuga & Abba Zakirai Abdulhamid & Shobanke Emmanuel Omobola Kayode, 2022. "D-Optimal Split-plot Designs With Random Whole Plot Factor and Fixed Sub-plot Factor," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(1), pages 1-1, March.
    • Handle: RePEc:ibn:ijspjl:v:11:y:2022:i:1:p:1
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    References listed on IDEAS

    as
    1. Giovagnoli, Alessandra & Sebastiani, Paola, 1989. "Experimental designs for mean and variance estimation in variance components models," Computational Statistics & Data Analysis, Elsevier, vol. 8(1), pages 21-28, May.
    2. André I. Khuri, 2000. "Designs for Variance Components Estimation: Past and Present," International Statistical Review, International Statistical Institute, vol. 68(3), pages 311-322, December.
    3. Loeza-Serrano, S. & Donev, A.N., 2014. "Construction of experimental designs for estimating variance components," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1168-1177.
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    1. Loeza-Serrano, S. & Donev, A.N., 2014. "Construction of experimental designs for estimating variance components," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1168-1177.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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