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1.
John A. Eccleston Deborah J. Street 《Australian & New Zealand Journal of Statistics》1994,36(3):371-378
This paper presents an algorithm for the construction of optimal or near optimal change-over designs for arbitrary numbers of treatments, periods and units. Previous research on optimality has been either theoretical or has resulted in limited tabulations of small optimal designs. The algorithm consists of a number of steps:first find an optimal direct treatment effects design, ignoring residual effects, and then optimise this class of designs with respect to residual effects. Poor designs are avoided by judicious application of the (M, S)-optimality criterion, and modifications of it, to appropriate matrices. The performance of the algorithm is illustrated by examples. 相似文献
2.
The optimality of two-factor experimental designs is studied in the dual senses of estimating contrasts in the parameters for each of the factors. The outline of comparison employed allows one to judge the performance of different designs for estimating contrasts of one set of parameters directly with the performance of the complementary set without going through a common intermediary step of considering all the parameters. The results hold for a wide class of optimality criteria (not merely D-, A- and E-optimality), which must satisfy a functional equation obtained in connection with our method. Also we investigate the optimality of row–column designs which satisfy an ‘adjusted orthogonality’ condition. Our point of departure is the paper by Shah, Raghavarao and Khatri (1976) and that of Mitchell and John (1977). 相似文献
3.
In this paper a method for the construction of a class of row-column designs with good statistical properties and high efficiency is presented. The class of designs produced is shown to exhibit balance, orthogonality and adjusted orthogonality. The efficiencies of these designs are investigated in detail, and they are shown to be very high, and possibly maximal in some cases. 相似文献
4.
Row-column designs may be considered to have two blocking schemes, namely the treatments by rows and treatments by columns component block designs. The (M,S)-optimality criterion is applied to row-column designs, and che connection between the (M,S)-optimal design and its component block designs is demonstrated. 相似文献
5.
I.W. Saunders J.A. Eccleston R.J. Martin 《Australian & New Zealand Journal of Statistics》1995,37(3):353-365
Saunders & Eccleston (1992) presented an approach to the design of 2-level factorial experiments for continuous processes. It determined sets of contrasts between the observations that could be well estimated, and then selected a design so that those contrasts estimated the parameters of interest. This paper shows that a well-estimated contrast must have a large number of changes of sign or level, and also be ‘paired’ in a particular sense. It develops an algorithm which constructs designs that must have a large number of changes of sign, evenly spread among the contrasts and optimal or near optimal. When such designs exist they are often preferable to those produced by the reverse foldover algorithm of Cheng & Steinberg (1991). 相似文献
6.
J.A. Eccleston 《Journal of statistical planning and inference》1980,4(3):291-297
The construction of experimental designs by recursive techniques is studied in this paper. Formulae for the recursive addition or deletion of data from a design are derived for a typical sub-hypothesis situation of a general experimental design. These results are used to consider the recursive construction of experimental designs with respect to different optimality criteria. This approach to the construction of designs is quite different to that of the well-established theory of optimal design. 相似文献
7.
T.H. Waterhouse D.C. Woods J.A. Eccleston S.M. Lewis 《Journal of statistical planning and inference》2008
The aim of an experiment is often to enable discrimination between competing forms for a response model. We investigate the selection of a continuous design for a non-sequential strategy when there are two competing generalized linear models for a binomial response, with a common link function and the linear predictor of one model nested within that of the other. A new criterion, TE-optimality, is defined, based on the difference in the deviances from the two models, and comparisons are made with T-, Ds- and D-optimality. Issues are raised through the study of two examples in which designs are assessed using simulation studies of the power to reject the null hypothesis of the smaller model being correct, when the data are generated from the larger model. Parameter estimation for discrimination designs is also discussed and a simple method is investigated of combining designs to form a hybrid design in order to achieve both model discrimination and estimation. This method has a computational advantage over the use of a compound criterion and the similar performance of the designs obtained from the two approaches is illustrated in an example. 相似文献
8.
Barbara S.P. Chan & J.A. Eccleston 《Australian & New Zealand Journal of Statistics》2003,45(1):97-106
Nearest–neighbour balance is considered a desirable property for an experiment to possess in situations where experimental units are influenced by their neighbours. This paper introduces a measure of the degree of nearest–neighbour balance of a design. The measure is used in an algorithm which generates nearest–neighbour balanced designs and is readily modified to obtain designs with various types of nearest–neighbour balance. Nearest–neighbour balanced designs are produced for a wide class of parameter settings, and in particular for those settings for which such designs cannot be found by existing direct combinatorial methods. In addition, designs with unequal row and column sizes, and designs with border plots are constructed using the approach presented here. 相似文献
9.
An algorithm is described for the optimal rearrangement of the treatments within each block of a Balanced Incomplete Block Design when a specified “nearest neighbour” correlation structure exists among observations from plots in the same block. The procedure uses results obtained by Kiefer & Wynn (1981). Designs obtained using the algorithm are found to compare favourably with those produced by combinatorial methods given in Cheng (1983). The algorithm produces optimal designs for all BIBD parameter sets, including those not covered by the results of Kiefer & Wynn or Cheng. 相似文献
10.
David G. Butler John A. Eccleston Brian R. Cullis 《Australian & New Zealand Journal of Statistics》2008,50(4):295-307
The design of large‐scale field trials where the residuals are correlated has been of recent interest, in large part because of advances in statistical and computational methods of analysis. The construction of designs for correlated data has typically used A‐optimality and is computationally intensive. This involves calculating the inverse of the information matrix for treatments under the supervision of an optimization strategy that explores the design space. We propose an approximation to A‐optimality, using nearest‐neighbour balance, that is less computationally demanding and can achieve at least 95% efficiency relative to A‐optimality in many practical situations. 相似文献