FOUR APPROACHES TO THE CLASSIFICATION PROBLEM IN DISCRIMINANT ANALYSIS: AN EXPERIMENTAL STUDY*

Four discriminant models were compared in a simulation study: Fisher's linear discriminant function [14], Smith's quadratic discriminant function [34], the logistic discriminant model, and a model based on linear programming [17]. The study was conducted to estimate expected rates of misclassification for these four procedures when observations were sampled from a variety of normal and nonnormal distributions. In contrast to previous research, data were taken from four types of Kurtotic population distributions. The results indicate the four discriminant procedures are robust toward data from many types of distributions. The misclassification rates for both the logistic discriminant model and the formulation based on linear programming consistently decreased as the kurtosis in the data increased. The decreases, however, were of small magnitude. None of these procedures yielded statistically significant lower rates of misclassification under nonnormality. The quadratic discriminant function produced significantly lower error rates when the variances across groups were heterogeneous.     

A TEACHING NOTE ON THE USE OF ASSUMPTIONS IN CASE STUDY

This note describes a modification in the conventional case method of instruction. The modification, which deals with the problem caused by each student making a different set of assumptions for a given case, has successfully met the test of classroom use.     

AN EMPIRICAL ASSESSMENT OF COMPUTER-ASSISTED DECISION ANALYSIS*

Decision analysis tools often are used in semistructured and ill-structured situations. While some researchers have argued that computerized decision analysis programs may improve decision quality in such situations, research support for this assertion is weak. In this laboratory study, business students used a computerized decision-analysis program with short strategic-management cases to prepare decision reports. Independent raters' perceptions of aided and unaided decision performance were contrasted, attitudes of students toward the program were assessed, individual differences were correlated with attitudes, and the program's impact on students' perceptions of their decision processes and performance was examined. Student attitudes toward the computerized aid were favorable, and individual differences in reactions generally were as predicted. However, the program did not improve the independent ratings of students' decision reports and recommendations. These findings suggest that computerized decision aids should be adopted cautiously. If such aids result in positive user affect and heightened decision confidence without corresponding improvements in decision quality, they may be dysfunctional. Rigorous research methodologies which incorporate independent evaluations of analyses and decisions are recommended for use in future research on computerized decision-analysis programs.     

A NOTE ON MODELING PROJECT INTERDEPENDENCE IN RESEARCH AND DEVELOPMENT*

This note is concerned with the problem of resource allocation under uncertainty in a research and development laboratory. A distinction is defined between project interrelationships that are specific (or internal) to certain projects and interrelationships resulting from external environmental factors. Formulations are introduced that allow both types of interrelationships to be formally included in a resource allocation optimization model. In the case of external environmental factors, an example is presented and analyzed.     

A NOTE ON THE USE OF SELECTED NONFINANCIAL RATIO VARIABLES TO PREDICT SMALL-BUSINESS LOAN PERFORMANCE*

Small business loan applications have not been evaluated successfully by traditional methods. This paper explores the possibility of using three types of nonfinancial ratio variables (owner, firm, and loan characteristics) to predict whether a small business will pay off or default its loan. The owner and loan variables were better predictors of loan success than the firm variables.     

A NOTE ON A MULTIVARIATE GENERALIZATION OF THE KRUSKAL-WALLIS TEST

Marketers are often interested in testing whether the mean vectors of multivariate distributions are equal. The test usually applied, one-way MANOVA, assumes the distributions are multinormal. Unfortunately, this assumption is not supported in many studies. As an alternative, a nonparametric multivariate one-way analysis of variance procedure is presented.     

A NOTE ON THE RELATIONSHIPS AMONG FINENESS,GARBLING, AND SUFFICIENCY FOR THE COMPARISON OF INFORMATION SYSTEMS*

Choice among competing information systems is an important problem for both the providers and users of information. When the attributes of the decision makers and decision problems for which information is produced are unknown or heterogeneous, it is difficult to choose among alternative information sources. Three criteria for such comparisons of information systems are available in the theory of information economics. These criteria may be distinguished by the differing restrictions that they impose on the generality of the studies in which they are used. This note explicates the relationships among these criteria and discusses the various limitations that they impose on generality.     

ON THE IMPLICATIONS OF SPECIFICATION UNCERTAINTY IN FORECASTING*

Forecasters typically select a statistical forecasting model from among a set of alternative models. Subsequently, forecasts are generated with the chosen model and reported to management (forecast consumers) as if specification uncertainty did not exist (i.e., as if the chosen model were the “true” model of the forecast variable). In this note, a well-known Bayesian model-comparison procedure is used to illustrate some of the ambiguities and distortions of forecasts that do not reflect specification uncertainty. It is shown that a single selected forecasting model (however chosen) will generally misstate measures of forecast risk and lead to point and interval forecasts that are misplaced from a decision-theoretic point of view.     

A NOTE ON AN APPLICATION OF THE ANALYTIC HIERARCHY PROCESS

This note is a response to an article by Zahedi [2] published in the Winter 1985 issue of Decision Sciences. It demonstrates that there is no need to calculate eigenvalues for consistent pairwise comparison matrices in order to calculate normalized values of attributes.     

PRACTICAL SIGNIFICANCE AND PARTITIONING VARIANCE IN DISCRIMINANT ANALYSIS

This note sets forth a method for obtaining viable estimates of total discriminatory power in a discriminant analysis. In addition, a technique based upon this methodisgiven for assessing the overall relative importance of each predictor variable regardless of the number of discriminant functions. Two examples are given to illustrate application of the method.     

ON USING LINEAR PROGRAMMING IN DISCRIMINANT PROBLEMS

This commentary evaluates the usefulness of the Freed and Glover [6] linear programming approach to the discriminant problem, relates linear programming to other parametric and nonparametric approaches, and evaluates the linear programming approach.     

A NOTE ON PROCEDURES FOR TESTING THE QUALITY OF A CLUSTERING OF A SET OF OBJECTS

Despite the increased application of cluster analysis in decision sciences, few attempts have been made to derive hypothesis-testing procedures for the evaluation of clustering solutions. In fact, the present paper shows that at least one such attempt failed to specify a meaningful sampling distribution for the test procedure. An alternative index based on the concept of point-biserial correlation is proposed as a possible recovery measure. The index is subsequently used to form the basis of a valid statistical test for the existence of cluster structure.     

A NEW CLASS OF MODELS FOR THE DISCRIMINANT PROBLEM

Discriminant analysis is relevant to business decision making in a variety of contexts, such as when one decides to make or buy a specified component, fund a venture project, or hire a particular person. Potential applications in artificial intelligence, particularly in the area of pattern recognition, have further underscored the importance of the field. A recent innovation in discriminant analysis is provided by special linear programming (LP) models, which offer attractive alternatives to classical statistical approaches. The scope of application in which discriminant analysis can be advantageously employed is broadened by the flexibility to tailor parameters in the LP approaches to reflect diverse goals and by the power to explore the sensitivity of these parameters. In spite of the promise of the LP formulations, however, limitations to their effectiveness have been uncovered in certain settings. A recent advance involving a normalization construct removes some of the limitations but entails solving the LP model twice (to allow for different signs of a normalization constant) and does not yield equivalent solutions for different rotations of the problem data. This paper introduces a new model and a new class of normalizations that remedy both remaining limitations, making it possible to take advantage of the modeling capabilities of the LP formulations without the attendant shortcomings encountered by earlier investigations. Our development shows by empirical testing and illustrative analysis that the quality of solutions from LP discriminant approaches is more favorable (relative to the classical model) than previously supposed.     

ON THE USE OF VERBAL PROTOCOLS IN CONJOINT ANALYSIS STUDIES

A recent study by Olshavsky and Acito helped gain insight into (a) the decision process used by respondents when asked to do a conjoint task, (b) the predictive validity of conjoint models compared to models derived from verbal protocols, and (c) the reasons for prediction errors. In this article, the author argues that the Olshavsky and Acito results do not lead one to believe that the compensatory conjoint models can be potentially more misleading than models that try to represent more accurately the underlying evaluation process with noncompensatory and compensatory rules. Hence, it does not seem necessary to try to identify noncompensatory rules in a conjoint study.