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.     

Liability in child welfare

Child welfare workers and agencies are vulnerable to lawsuits. Recent court rulings have more clearly defined the liability of workers. The distinguishing variable is custody. Children injured while in the custody of the state are entitled to sue for damages. Children injured by their parent, even if under the supervision of a child welfare agency, are not entitled to claim a violation of their 14th Amendment rights. These cases are reviewed and strategies designed to minimize vulnerability are offered.     

Inside two commercially available statistical expert systems

A decade of research into the applications of artificial intelligence in statistics has finally resulted in the appearance of commercially available statistical expert systems. This paper takes a closer look at two of these systems, which are now commercially available on microcomputers, and shows what knowledge they actually contain and how they operate. It is concluded that although the technology and concepts that drive these systems could still benefit from further improvement, the real challenge lies in defining and constructing the statistical knowledge and strategy that should be incorporated and in presenting the results to the user's full advantage.     

A measure of slope-rotatability for second order response surface experimental designs

In the design of experiments for estimating the slope of a response surface, slope-rotatability is a desirable property. In this paper, a measure is introduced that enables us to assess the degree of slope-rotatability for a given response surface design. The measure takes the value zero if and only if the design is slope-rotatable, and becomes larger as the design deviates from a slope-rotatable design. Examples of applying this measure to some response surface designs are also given.     

Statistical software packages for PCs — A market survey

The increase of statistical software applications for PCs is caused by decreasing hardware costs and dramatically enhanced PC performance. Whereas in the past the domain of statistical computing has been reserved to mainframe solutions, a great number of new software packages for PCs have come out in the last five years. Therefore, the producers of established mainframe software were also forced to offer PC-based solutions. By limiting a market analysis to products with a medium set of well known statistical methods, the immense number of available products is reduced to about fifty systems. We ordered an evaluation copy of these systems to test the numerical quality, the system speed, and the performance of several procedures. Seventeen packages were made available for an extensive examination. This paper will (1) discuss the problems and the solutions of obtaining a complete and correct datamatrix that describes the entire market and (2) present the results of a comparative market analysis.     

Analytical approximations for iterated bootstrap confidence intervals

Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991). Our technique significantly reduces the computational expense of iterated bootstrap calculations. A formal algorithm for the construction of our approximate iterated bootstrap confidence intervals is presented, and some crucial practical issues arising in its implementation are discussed. Our procedure is illustrated in the case of constructing confidence intervals for ratios of means using both real and simulated data. We repeat an experiment of Schenker (1985) involving the construction of bootstrap confidence intervals for a variance and demonstrate that our technique makes feasible the construction of accurate bootstrap confidence intervals in that context. Finally, we investigate the use of our technique in a more complex setting, that of constructing confidence intervals for a correlation coefficient.     

TOWARD A SOCIOLOGY OF CULT FILMS: Reading Rocky Horror

This article provides a sociological reading of cult films, in particular, The Rocky Horror Picture Show. Cult films are secular documents, celebrated as sacred texts by audiences and used as shared foci to collectively create rituals and belief systems. They differ from popular re-releases, fad films, films with cult qualities, and critical cult films in that they involve typical people in atypical situations, sympathetic deviance, challenges to traditional authority, reflections of societal strains, and paradoxical and interpretable resolutions. Examination of the Rocky Horror text and the cult activities that occur during its viewing, reveal it as a paradoxical indictment and validation of traditional societal arrangements.     

A subjectivist approach to consecutive conflict

An easily applied approach is developed to provide one participant in a sequence of conflicts with an optimal strategy. A goal of this article is to demonstrate that it is mathematically feasible to incorporate a decision maker's subjective distributions over the effects his actions will have on the outcomes of future conflicts. Unlike many other approaches, the model of this article does not restrict the beliefs that the participant is allowed to express. The participant, not the decision theorist, decides on what is relevent. Model assumptions required for updating rules, such as Bayesian updating, are not required unless they really are appropriate for the situation.Thanks are due to J. B. Kadane for suggesting the problem and for many helpful discussions.