On choosing between fixed and random block effects in some no-interaction models

The purpose of this article is to strengthen the understanding of the relationship between a fixed-blocks and random-blocks analysis in models that do not include interactions between treatments and blocks. Treating the block effects as random has been recommended in the literature for balanced incomplete block designs (BIBD) because it results in smaller variances of treatment contrasts. This reduction in variance is large if the block-to-block variation relative to the total variation is small. However, this analysis is also more complicated because it results in a subjective interpretation of results if the block variance component is non-positive. The probability of a non-positive variance component is large precisely in those situations where a random-blocks analysis is useful – that is, when the block-to-block variation, relative to the total variation, is small. In contrast, the analysis in which the block effects are fixed is computationally simpler and less subjective. The loss in power for some BIBD with a fixed effects analysis is trivial. In such cases, we recommend treating the block effects as fixed. For response surface experiments designed in blocks, however, an opposite recommendation is made. When block effects are fixed, the variance of the estimated response surface is not uniquely estimated, and in practice this variance is obtained by ignoring the block effect. It is argued that a more reasonable approach is to treat the block effects to be random than to ignore it.     

Designing selection experiments with bernoulli populations

This paper is concerned with a fixed size subset selection problem for Bernoulli populations in the framework of the indifference zone approach. The goal is to select s populationswhich contain at least c of those with the t largest success probabilities. In order to control the probability of correct selection over the preference zone extensive tables of exact minimum sample sizes have been prepared to implement the single-stage procedure generalized from the well-known Sobel-Huyett procedure. It is shown how the tables can also be employed to design certain closedsequential procedures. These procedures curtail the sampling process of the single-stage procedureand may differ in their sampling rules. Two procedures working with play-the-winner rules are described in detail     

Maximum Likelihood Estimation for Multinomial‐Poisson Models: A Generalization of Birch's Numerical Invariance Results

Abstract. This study gives a generalization of Birch's log‐linear model numerical invariance result. The generalization is given in the form of a sufficient condition for numerical invariance that is simple to verify in practice and is applicable for a much broader class of models than log‐linear models. Unlike Birch's log‐linear result, the generalization herein does not rely on any relationship between sufficient statistics and maximum likelihood estimates. Indeed the generalization does not rely on the existence of a reduced set of sufficient statistics. Instead, the concept of homogeneity takes centre stage. Several examples illustrate the utility of non‐log‐linear models, the invariance (and non‐invariance) of fitted values, and the invariance (and non‐invariance) of certain approximating distributions.     

ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

The asymptotic covariance structure of log-linear model estimated parameters for the multiple recapture census

This paper presents a matrix formulation for log-linear model analysis of the incomplete contingency table which arises from multiple recapture census data. Explicit matrix product expressions are given for the asymptotic covariance structure of the maximum likelihood estimators of both the log-linear model parameter vector and the predicted value vector for the observed and missing cells. These results are illustrated for data pertaining to a population of children possessing a common congenital anomaly.     

Approximate and exact distributions of rank tests for balanced incomplete block designs

Judges rank k out of t objects according to m replic ations of abasic balanced incomplete block design with bblocks. In Alvo and Cabilio(1991),it is shown that the Durbin test, which is the usual test in this situation, can be written in terms of Spearman correlations between the blocks, and using a Kendall correlation, they generated a new statistic for this situation.This Kendall tau based statistic has a richer support than the Durbin statistic, and is at least as efficient.In the present paper,exact and simulation based tables are generated for both statistics, and various approximations to these null distributions are considered and compared.     

A class of single replicate orthogonal designs

A simple method is given to calculate the number of degrees of freedom confounded with blocks of a specific factorial effect in a single replicate orthogonal design. Two classes of designs having partial orthogonality are also discussed     

Contingency tables with structural zeros

In this paper, the method of Hocking and Oxspring (1971) to estimate multinomial probabilities when full and partial data are available for some cells is extended to estimate the cell probabilities of a contingency table with structural zeros. The estimates are maximum likelihood, and the process is sequential. The gain in precision is due to the use of partial data and the bias of the estimates is also investigated.     

In Memoriam: Frank Wilcoxon

A mosaic is a graphical display of cross-classified data in which each count is represented by a rectangle of area proportional to the count. The positions and sides of the rectangles are set to encourage comparisons between counts in the figures. Mosaics are useful for discovering unusually high or small counts and for discovering dependencies between variables. In principle, mosaics may be used for any number of cross-classifying variables, but six seems to be a practical maximum. A mosaic is given for a four-way classification of Nielsen ratings.     

多专家判断的模糊偏好信息集结规划方法

本文给出了一种群决策中通过专家判断矩阵集结专家判断信息的方法。在考虑各专家具有不同强度的偏好效用和容许部分专家给出不完整信息的情况下,将专家判断信息集结转化为一类模糊规划问题,通过最大化群组满意度获得最终的群决策结果。最后,本文通过一个算例说明该方法的可行性及有效性。