John A. Nelder

Generalized linear models. 2nd ed.

Addresses a class of statistical models that generalizes classical linear models-extending them to include many other models useful in statistical analysis. Incorporates numerous exercises, both theoretical and data-analytic Discusses quasi-likelihood functions and estimating equations, models for dispersion effect, components of dispersion, and conditional likelihoods Holds particular interest for statisticians in medicine, biology, agriculture, social science, and engineering

Taguchi's parameter design: a panel discussion

It is more than a decade since Genichi Taguchis ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchis methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchis methodology for implementing it. The topics covered include the importance of vari...

Analysis of covariance and standardization as instances of prediction.

In this paper, prediction provides the basis for unifying the procedures of covariances adjustment and standardization. Analysis of covariance is a method of forming predictions from a linear model; it is used when qualitative effects are to be studied and the effects of continuous variables are to be adjusted for. An essential feature is the division into effects of interest and effects for which adjustment is required. Covariates may also be qualitative: as such, they are used implicitly in experimental designs with blocks, where treatment effects are adjusted for the effect of blocks. The technique of standardization is well-known in epidemiology and demography as a method of adjusting explicitly for qualitative effects. The same division of effects applies when an analysis that uses generalized linear models is summarized. Two distinct types of prediction, which give identical results in classical linear models, are available: prediction may be conditional on a fixed value of a covariate, or marginal on a distribution of values such as the distribution in the set of data being analysed. Prediction methods are illustrated by the analysis of a table of proportions by use of a logit model.

Conditional and Marginal Models: Another View

There has existed controversy about the use of marginal and conditional models, particularly in the analysis of data from longitudinal studies. We show that alleged differences in the behavior of parameters in so-called marginal and conditional models are based on a failure to compare like with like. In particular, these seemingly apparent differences are meaningless because they are mainly caused by preimposed unidentifiable constraints on the random effects in models. We discuss the advantages of conditional models over marginal models. We regard the conditional model as fundamental, from which marginal predictions can be made.

Robust design via generalized linear models

A single data transformation may fail to satisfy all the required properties necessary for an analysis. With generalized linear models (GLMs), the identification of the mean-variance relationship and the choice of the scale on which the effects are to be measured can be done separately, overcoming the shortcomings of the data-transformation approach. GLMs also provide an extension of the response surface approach. In this paper, we set out the current status of the GLM approach to the analysis of data from quality-improvement experiments and discuss its merits.

Generalized Linear Models for Quality-Improvement Experiments

Since the early 1980s, industry has embraced the use of designed experiments as an effective means for improving quality. For quality characteristics not normally distributed, the practice of first transforming the data and then analyzing them by standa..

The Selection of Terms in Response-Surface Models—How Strong is the Weak-Heredity Principle?

Abstract Model selection under the weak-heredity principle allows models that contain compound terms such as x 1 x 2 to have only one of the corresponding x 1 and x 2 terms In the model It is shown that the conditions required to justify use of the principle are so restrictive as to make It unusable in practice. An example is given to Illustrate this.

Modelling and analysing correlated non-normal data:

We introduce a model class that includes many types of correlation structures for non-Gaussian models. We then show how to check the underlying model assumptions to discriminate between different correlation patterns and demonstrate how to select suitable models. Strawberry data are used to discuss the choice between fixed- and random-effect models for the fertility effect in agricultural experiments. Prostate-cancer data are used to demonstrate the method applied to the analysis of longitudinal studies and Scottish lip-cancer data to illustrate an application to spatial statistics.

Two ways of modelling overdispersion in non‐normal data

For non-normal data assumed to have distributions, such as the Poisson distribution, which have an a priori dispersion parameter, there are two ways of modelling overdispersion: by a quasi-likelihood approach or with a random-effect model. The two approaches yield different variance functions for the response, which may be distinguishable if adequate data are available. The epilepsy data of Thall and Vail and the fabric data of Bissell are used to exemplify the ideas.

The Computer Analysis of Factorial Experiments: In Memoriam—Frank Yates

Abstract The responses to a recent paper by Dallal in this journal are evaluated by reference to the ideas of Frank Yates. It is concluded that much unnecessary complication has been introduced into the computer analysis of linear models by (1) the imposition of constraints on parameters, (2) neglect of marginality relations in forming hypotheses, and (3) confusion between the form of noncentrality parameters and hypotheses.