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.
| Original language | English |
|---|---|
| Pages (from-to) | 933-947 |
| Number of pages | 15 |
| Journal | Journal of Applied Statistics |
| Volume | 26 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 1999 Jan 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Graphical technique for comparing designs for random models. / Lee, Juneyoung; Khuri, André I.
In: Journal of Applied Statistics, Vol. 26, No. 8, 01.01.1999, p. 933-947.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Graphical technique for comparing designs for random models
AU - Lee, Juneyoung
AU - Khuri, André I.
PY - 1999/1/1
Y1 - 1999/1/1
N2 - 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.
AB - 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.
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U2 - 10.1080/02664769921945
DO - 10.1080/02664769921945
M3 - Article
VL - 26
SP - 933
EP - 947
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
SN - 0266-4763
IS - 8
ER -