Book Reviews

Books reviewed:
David Griffiths, W. Douglas Stirling, and K. Laurence Weldon, Understanding Data: Principles and Practice of Statistics
Ingwer Borg and Patrick Groenen, Modern Multidimensional Scaling: Theory and Applications
Jeffrey H. Dorfman, Bayesian Economics Through Numerical Methods: A Guide to Econometrics and Decision-making with Prior Information
Marek Musiela and Marek Rutkowski, Martingale Methods in Financial Modelling: Theory and Applications
Aad W. van der Vaart and Jon A. Wellner, Weak Convergence and Empirical Processes     

Factor screening in nonregular two-level designs based on projection-based variable selection

In this paper, we focus on the problem of factor screening in nonregular two-level designs through gradually reducing the number of possible sets of active factors. We are particularly concerned with situations when three or four factors are active. Our proposed method works through examining fits of projection models, where variable selection techniques are used to reduce the number of terms. To examine the reliability of the methods in combination with such techniques, a panel of models consisting of three or four active factors with data generated from the 12-run and the 20-run Plackett–Burman (PB) design is used. The dependence of the procedure on the amount of noise, the number of active factors and the number of experimental factors is also investigated. For designs with few runs such as the 12-run PB design, variable selection should be done with care and default procedures in computer software may not be reliable to which we suggest improvements. A real example is included to show how we propose factor screening can be done in practice.     

Optimal designs for generalized linear models

Summary This paper solves some D-optimal design problems for certain Generalized Linear Models where the mean depends on two parameters and two explanatory variables. In all of the cases considered the support point of the optimal designs are found to be independent of the unknown parameters. While in some cases the optimal design measures are given by two points with equal weights, in others the support is given by three point with weights depending on the unknown parameters, hence the designs are locally optimal in general. Empirical results on the efficiency of the locally optimal designs are also given. Some of the designs found can also be used for planning D-optimal experiments for the normal linear model, where the mean must be positive. This research was carried out in part at University College, London as an M.Sc. project. Thanks are due to Prof. I. Ford (University of Glasgow) and Prof. A. Giovagnoli (University of Perugia) for their valuable suggestions and critical observations.     

UPPER BOUNDS FOR LATINIZED DESIGNS

Upper bounds axe derived for the efficiency factor of a class of resolvable incomplete block designs known as latinized designs. These designs are particularly useful in glasshouse and field trials, and can be readily extended to two-dimensional blocking structures. Existing bounds for resolvable designs axe also reviewed and a comparison is made between the third moment bounds discussed by Jarrett (1989) and the second moment bounds of Tjur (1990).     

Using intersection matrices to identify graphical structure

Intersection matrices help identify the common graphical structure of two or more objects. They arise naturally in a variety of settings. Several examples of their use in a computer algebra environment are given. These include: simplifying an expression involving array products, automating cumulant calculations, determining the behaviour of an expected value operator and identifying model hierarchy in a factorial experiment. The emphasis is placed on the graphical structure, and the symmetry of arrays help reduce the complexity of the graphical problem.     

A general method of constructing E(s2)-optimal supersaturated designs

There has been much recent interest in supersaturated designs and their application in factor screening experiments. Supersaturated designs have mainly been constructed by using the E ( s ²)-optimality criterion originally proposed by Booth and Cox in 1962. However, until now E ( s ²)-optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n-1 , and in adjacent cases where m = q ( n -1) + r (| r | 2, q an integer). A method of constructing E ( s ²)-optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n ,=8 12, 16, 20, 24, 32, 40, 48, 64.     

D- and V-optimal population designs for the quadratic regression model with a random intercept term

In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where d≥3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and this is illustrated by means of a simple example.     

Measures of uniformity in experimental designs: A selective overview

ABSTRACT

Discrepancies are measures which are defined as the deviation between the empirical and the theoretical uniform distribution. In this way, discrepancy is a measure of uniformity which provides a way of construction a special kind of space filling designs, namely uniform designs. Several discrepancies have been proposed in recent literature. A brief, selective review of these measures including some construction algorithms are given in this paper. Furthermore, a critical discussion along with some comparisons is provided, as well.     

On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

A comparison of random balance and two-stage group screening designs: A case study

In this paper we focus on the problem of supersaturated (fewer runs than factors) screening experiments. We consider two major types of designs which have been proposed in this situ¬ation: random balance and two-stage group screening. We discuss the relative merits and demerits of each strategy. In addition, we compare the performance of these strategies by means of a case study in which 100 factors are screened in 20,42,62, and 84 runs.