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Graphical technique for comparing designs for random models

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  • Juneyoung Lee
  • Andre Khuri

Abstract

Methods for comparing designs for a random (or mixed) linear model have focused primarily on criteria based on single-valued functions. In general, these functions are difficult to use, because of their complex forms, in addition to their dependence on the model's unknown variance components. In this paper, a graphical approach is presented for comparing designs for random models. The one-way model is used for illustration. The proposed approach is based on using quantiles of an estimator of a function of the variance components. The dependence of these quantiles on the true values of the variance components is depicted by plotting the so-called quantile dispersion graphs (QDGs), which provide a comprehensive picture of the quality of estimation obtained with a given design. The QDGs can therefore be used to compare several candidate designs. Two methods of estimation of variance components are considered, namely analysis of variance and maximum-likelihood estimation.

Suggested Citation

  • Juneyoung Lee & Andre Khuri, 1999. "Graphical technique for comparing designs for random models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 933-947.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:8:p:933-947
    DOI: 10.1080/02664769921945
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    References listed on IDEAS

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    1. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    2. 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.
    3. A. I. Khuri, 1997. "Quantile dispersion graphs for analysis of variance estimates of variance components," Journal of Applied Statistics, Taylor & Francis Journals, vol. 24(6), pages 711-722.
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