SPECIFICATION AND ESTIMATION OF LOGICALLY CONSISTENT LINEAR MODELS

The implications of constrained dependent and independent variables for model parameters are examined. In the context of linear model systems, it is shown that polyhedral constraints on the dependent variables will hold over the domain of the independent variables when a set of polyhedral constraints is satisfied by the model parameters. This result may be used in parameter estimation, in which case all predicted values of the dependent variables are consistent with constraints on the actual values. Also, the implicit constraints that define the set of parameters for many commonly used linear stochastic models with an error term yield values of the dependent variables consistent with the explicit constraints. Models possessing these properties are termed “logically consistent”.     

Unclaimed Prize Information Biases Perceptions of Winning in Scratch Card Gambling

Unclaimed prize information (i.e., the number of prizes still available to be won) is information commonly provided to scratch card gamblers. However, unless the number of tickets remaining to be purchased is also provided, this information is uninformative. Despite its lack of utility in assisting gamblers in choosing the most favourable type of scratch card to play, we hypothesized that unclaimed prize information would bias participants’ judgments within a scratch card gambling context. In Experiment 1 (N?=?201), we showed that participants are influenced by this information such that they felt more likely to win, were more excited to play, and preferred to hypothetically purchase more of the scratch card with the greatest number of unclaimed prizes. In Experiment 2 (N?=?201), we attempted to ameliorate this bias by providing participants with the number of tickets remaining to be purchased and equating the payback percentages of all three games. The bias, although attenuated, still persisted in these conditions. Finally, in Experiment 3 (N?=?200), we manipulated the hypothetical scratch cards such that games with the highest number of unclaimed prizes were the least favourable, and vice versa. As in Experiment 2, participants still favoured cards with greater numbers of unclaimed prizes. Possible mechanisms underlying this bias are discussed. In conclusion, across three experiments, we demonstrate that salient unclaimed prize information is capable of exerting a strong effect over judgments related to scratch card games.     

On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses

Statistical experiments, more commonly referred to as Monte Carlo or simulation studies, are used to study the behavior of statistical methods and measures under controlled situations. Whereas recent computing and methodological advances have permitted increased efficiency in the simulation process, known as variance reduction, such experiments remain limited by their finite nature and hence are subject to uncertainty; when a simulation is run more than once, different results are obtained. However, virtually no emphasis has been placed on reporting the uncertainty, referred to here as Monte Carlo error, associated with simulation results in the published literature, or on justifying the number of replications used. These deserve broader consideration. Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. The issues and methods are demonstrated with two simple examples, one evaluating operating characteristics of the maximum likelihood estimator for the parameters in logistic regression and the other in the context of using the bootstrap to obtain 95% confidence intervals. The results suggest that in many settings, Monte Carlo error may be more substantial than traditionally thought.     

THE USE OF ARCS AND NODES FOR THE DETERMINATION OF CRITICAL PATHS IN PERT/CPM NETWORKS

The critical path in a PERT/CPM network is determined in various textbooks by finding the path with associated minimal slack for the network arcs or by finding the path with associated minimal slack for the network nodes. This paper points out that the use of nodes can result in a network path being incorrectly identified as a path of maximum length.     

Characterization of Unacceptable Solutions in LP Discriminant Analysis*

Many linear programming models have been proposed for performing discriminant analysis. Partial characterizations for unacceptable solutions have been presented and new models proposed to circumvent these problems. In this paper those conditions leading to unacceptable solutions for all two-group models are characterized.     

Learning by Objectives for Adaptive Shop-Floor Scheduling*

Effective production scheduling requires consideration of the dynamics and unpredictability of the manufacturing environment. An automated learning scheme, utilizing genetic search, is proposed for adaptive control in typical decentralized factory-floor decision making. A high-level knowledge representation for modeling production environments is developed, with facilities for genetic learning within this scheme. A multiagent framework is used, with individual agents being responsible for the dispatch decision making at different workstations. Learning is with respect to stated objectives, and given the diversity of scheduling goals, the efficacy of the designed learning scheme is judged through its response under different objectives. The behavior of the genetic learning scheme is analyzed and simulation studies help compare how learning under different objectives impacts certain aggregate measures of system performance.     

Unacceptable Solutions and the Hybrid Discriminant Model

A new family of linear programming (LP) discriminant models, the hybrid discriminant model, was recently presented with claims that it avoids all the problems of its predecessor LP models. However, this note shows that it does not avoid unacceptable solutions.     

Chi–square tests for comparing vectors of proportions for several cluster samples

Test statistics are developed for comparing vectors of proportions obtained from several independent two–stage cluster samples. It is assumed that clusters are selected with probability proportional to size for each sample. Wald's general method of constructing quadratic forms is used to obtain a large sample chi–square test. More easily evaluted chi–square tests are derived from the Dirichlet–multinnomial model. Corresponding goodness–of–fit test for the Dirichlet–multinomial model are also derived.     

Limiting median lines frequently determine the yolk

In two-dimensional Euclidean spatial voting models the yolk is the smallest circle which intersects all median lines. It has been assumed that limiting median lines, which intersect two voter ideal points, are sufficient to determine the yolk but recently counter examples have been reported. This note describes the impact of those findings on the results of computation of the location and size of yolk.I wish to acknowledge a number of helpful conversations with Craig Tovey and Nicholas Miller. Any errors which remain are my own.