The Detection of Influential Observations for Allocation,Separation, and the Determination of Probabilities in a Bayesian Framework

Normal theory separation and allocation problems are discussed from a predictive point of view. Influence statistics are defined and employed to ascertain the impact that particular observations will have on the inferential goals—allocation of future observations, separation between populations, and the determination of probabilities for future cases. Methods are illustrated on a collection of financial data taken from Johnson and Wichern (1982).     

Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power

A Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (Δ), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size (Δ) and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.     

Accent on Teaching Materials

Estimation of covariance components in the multivariate random-effect model with nested covariance structure is discussed. There are two covariance matrices to be estimated, namely, the between-group and the within-group covariance matrices. These two covariance matrices are most often estimated by forming a multivariate analysis of variance and equating mean square matrices to their expectations. Such a procedure involves taking the difference between the between-group mean square and the within-group mean square matrices, and often produces an estimated between-group covariance matrix that is not nonnegative definite. We present estimators of the two covariance matrices that are always proper covariance matrices. The estimators are the restricted maximum likelihood estimators if the random effects are normally distributed. The estimation procedure is extended to more complicated models, including the twofold nested and the mixed-effect models. A numerical example is presented to illustrate the use of the estimation procedure.     

The Consistent System

The Consistent System (CS) is an interactive computer system for researchers in the behavioral and policy sciences and in fields with similar requirements for data management and statistical analysis. The researcher is not expected to be a programmer. The system offers a wide range of facilities and permits the user to combine them in novel ways. In particular, tools for statistical analysis may be used in combination with a powerful relational subsystem for data base management. This paper gives an overview of the objectives, capabilities, status, and availability of the system.     

Statistical Computing: History and Trends

The evolution of computers is currently in a period of rapid change, stimulated by radically cheaper and smaller devices for processing and memory. These changes are certain to provide major opportunities and challenges for the use of computers in statistics. This article looks at history and current trends, in both general computing and statistical computing, with the goal of identifying key features and requirements for the near future. A discussion of the S language developed at Bell Laboratories illustrates some program design principles that can make future work on statistical programs more effective and more valuable.     

Frequency of Selecting Noise Variables in Subset Regression Analysis: A Simulation Study

This article presents the results of a simulation study of variable selection in a multiple regression context that evaluates the frequency of selecting noise variables and the bias of the adjusted R ² of the selected variables when some of the candidate variables are authentic. It is demonstrated that for most samples a large percentage of the selected variables is noise, particularly when the number of candidate variables is large relative to the number of observations. The adjusted R ² of the selected variables is highly inflated.     

Dynamic Graphics for Exploring Spatial Data with Application to Locating Global and Local Anomalies

We explore the application of dynamic graphics to the exploratory analysis of spatial data. We introduce a number of new tools and illustrate their use with prototype software, developed at Trinity College, Dublin. These tools are used to examine local variability—anomalies—through plots of the data that display its marginal and multivariate distributions, through interactive smoothers, and through plots motivated by the spatial auto-covariance ideas implicit in the variogram. We regard these as alternative and linked views of the data. We conclude that the most important single view of the data is the Map View: All other views must be cross-referred to this, and the software must encourage this. The view can be enriched by overlaying on other pertinent spatial information. We draw attention to the possibilities of one-many linking, and to the use of line-objects to link pairs of data points. We draw attention to the parallels with work on Geographical Information Systems.     

A Critical Look at Some Analyses of Major League Baseball Salaries

At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at building parsimonious, understandable models that fit the data well. We also find that common data displays, when applied carefully, are often sufficient for even complex analyses such as this.     

Bayesian Binomial Regression: Predicting Survival at a Trauma Center

Standard methods for analyzing binomial regression data rely on asymptotic inferences. Bayesian methods can be performed using simple computations, and they apply for any sample size. We provide a relatively complete discussion of Bayesian inferences for binomial regression with emphasis on inferences for the probability of “success.” Furthermore, we illustrate diagnostic tools, perform model selection among nonnested models, and examine the sensitivity of the Bayesian methods.     

Nenparametric Two-Group Classification: Concepts and a SAS-Based Software Package

This article introduces BestClass, a set of SAS macros, available in the mainframe and workstation environment, designed for solving two-group classification problems using a class of recently developed nonparametric classification methods. The criteria used to estimate the classification function are based on either minimizing a function of the absolute deviations from the surface which separates the groups, or directly minimizing a function of the number of misclassified entities in the training sample. The solution techniques used by BestClass to estimate the classification rule use the mathematical programming routines of the SAS/OR software. Recently, a number of research studies have reported that under certain data conditions this class of classification methods can provide more accurate classification results than existing methods, such as Fisher's linear discriminant function and logistic regression. However, these robust classification methods have not yet been implemented in the major statistical packages, and hence are beyond the reach of those statistical analysts who are unfamiliar with mathematical programming techniques. We use a limited simulation experiment and an example to compare and contrast properties of the methods included in Best-Class with existing parametric and nonparametric methods. We believe that BestClass contributes significantly to the field of nonparametric classification analysis, in that it provides the statistical community with convenient access to this recently developed class of methods. BestClass is available from the authors.