Abstract
In this paper we define a class of unbalanced designs, denoted by Ck,s,t, for estimating the components of variance in a k-stage nested random effects linear model. This class contains many of the designs proposed in the literature for nested components of variance models. We focus on the three-state model and discuss the determination of locally optimal designs within this class using a systematic computer search. For large sample sizes we show that approximate optimal designs may be obtained using a limit argument combined with numerical optimization. A comparison of our designs with previously published designs suggests that, in many cases, our designs result in substantial gains in efficiency.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Anderson, R. L. (1960) Uses of variance component analysis in the interpretation of biological experiments. Bulletin of the International Statistical Institute, 32(3), 71–90.
Anderson, R. L. and Bancroft, T. A. (1952) Statistical Theory in Research. McGraw-Hill, New York.
Bainbridge, T. R. (1963) Staggered nested designs for estimating variance components. In American Society for Quality Con-trol: Annual Conference Transactions, pages 93–103.
Box, G. E. P., Hunter, W. G. and Hunter, J. S. (1978) Statistics for Experimenters, An Introduction to Design, Data Analysis and Model Building. John Wiley, New York.
Calvin, L. D. and Miller, J. D. (1961) A sampling design with incomplete dichotomy. Agronomy Journal, 53, 325–28.
Delgado, J. (1997) Optimal Design of Experiments in Nested Variance-Components Models. PhD thesis, Colorado State University, Fort Collins, Colorado.
Goldsmith, C. H. (1969) Three Stage Nested Designs for Esti-mating Variance Components. PhD thesis, North Carolina State University, Raleigh, North Carolina.
Goldsmith, C. H. and Gaylor, D. W. (1970) Three stage nested designs for estimating variance components. Technometrics, 12, 487–98.
IMSL Inc. (1987) IMSL MATH/LIBRARY User's Manual. Houston, TX.
Prairie, R. R. (1961) Some results concerning the reduction of product variability through the use of variance components. In Proc. Seventh Conf. on the Design of Experiments in Army Research Development and Testing, pages 655–688, Fort Monmouth, New Jersey.
Prairie, R. R. (1962) Optimal Designs to Estimate Variance Components and Reduce Product Variability for Nested Classifications. PhD thesis, North Carolina State University, Raleigh, North Carolina.
Searle, S. R. (1961) Variance components in the unbalanced 2-way nested classification. Annals of Mathematical Statistics, 32, 161–66.
Rights and permissions
About this article
Cite this article
Delgado, J., Iyer, H. Search for optimal designs in a three stagenested random model. Statistics and Computing 9, 187–193 (1999). https://doi.org/10.1023/A:1008913829056
Issue Date:
DOI: https://doi.org/10.1023/A:1008913829056