Stuart J. Allen

An empirical comparison of alternative methods for principal component extraction

Abstract A major problem confronting users of principal component analysis is the determination of how many components to extract from an empirical correlation matrix. Using 30 such matrices obtained from marketing and psychology sources, the authors provide a comparative assessment of the extraction capabilities exhibited by five principal component decision rules. These are the Kaiser-Guttman, scree, Bartlett, Horn, and random intercepts procedures. Application of these rules produces highly discrepant results. The random intercepts and Bartlett formulations yield unacceptable component solutions by grossly under- and overfactoring respectively. The Kaiser-Guttman and scree rules performed equivalently, yet revealed tendencies to overfactor. In comparison Horns test acquitted itself with distinction, and warrants greater attention from applied researchers.

Controlling the Risk for an Agricultural Harvest

Gathering the harvest represents a complex managerial problem for agricultural cooperatives involved in harvesting and processing operations: balancing the risk of overinvestment with the risk of underproduction. The rate to harvest crops and the corresponding capital investment are critical strategic decisions in situations where poor weather conditions present a risk of crop loss. In this article, we discuss a case study of the Concord grape harvest and develop a mathematical model to control harvest risk. The model involves differentiation of a joint probability distribution that represents risks associated with the length of the harvest season and the size of the crop. This approach is becoming popular as a means of dealing with complex problems involving operational and supply chain risk. Significant cost avoidance, in the millions of dollars, results from practical implementation of the Harvest Model. Using real data, we found that the Harvest Model provides lower-cost solutions in situations involving moderate variability in both the length of season and the crop size as compared to solutions based on imposed risk policies determined by management.

Notes and Commentary: Regression Equations for the Latent Roots of Random Data Correlation Matrices with Unities on the Diagonal

In order to make parallel analysis more accessible to researchers employing principal component techniques, regression equations are presented for the logarithms of the latent roots of random data correlation matrices with unities on the diagonal. These regression equations have as independent variables logarithms of: the single variable degrees of freedom; Bartlett-Lawley degrees of freedom; the next lowest ordered eigenvalue. The multiple correlation coefficients are at least 0.96 in all cases.

A Cautionary Note on the Use of Principal Components Analysis Supportive Empirical Evidence

In a recent edition of this journal, Borgatta et al. (1986), using hypothetical data, illustrated how the results produced by principal components analysis can be substantially different from those of common factor analysis. The present article, using seven well-known data sets, extends their work into the empirical domain, and also compares the results of the maximum likelihood factor analysis model with those of the principal components model. The results strongly support those of Borgatta et al. Indeed, the discrepancies in the empirical results reported here are often larger than their hypothetical example suggests. It was found that, when comparing the performance of the principal components model with the common factor and maximum likelihood models, differences can be expected to occur in (1) the magnitudes of the factor loadings, (2) the signs attached to the factor loadings, and, most important, (3) the interpretation of the factors themselves.

Raw Material Management at Welchs, Inc.

Welchs, a large grape-processing company owned by a grower cooperative, faced complex logistics in planning recipes for products sold in retail stores. The recently installed integrated MRP and cost-accounting systems did not include ways to calculate recipes at optimal cost based on plant-raw-material and capacity constraints. An imbalance of supply and demand further complicated this problem in raw-materials management. The cross-functional team in charge of managing raw materials spent increasing a mounts of time deciding what recipes to use at each plant. We formulated the problem as a linear program model and used spreadsheet optimization to incorporate the model in daily decision making. The company has run the model each month since 1994 to provide senior management with information on the optimal logistics plan. This simple application saved Welchs between

ON THE NUMBER AND NATURE OF COMMON FACTORS EXTRACTED BY THE EIGENVALUE-ONE RULE USING BMDP VS SPSSX '

130,000 to

The Open System for Master Production Scheduling: Information Technology for Semantic Connections between Data and Mathematical Models

170,000 during the first year.

Are Responses Measured with Graphic Rating Scales Subject to Perceptual Distortion

Given nuances in the computer programs, unwary researchers performing a common factor analysis on the same set of data can be expected to arrive at very different conclusions regarding the number and nature of extracted factors if they use the BMDP, as opposed to the SPSSx (or SAS), statistical software package. This is illustrated using six well-known empirical data sets from the psychology literature.

Global RFID: The Value of the EPCglobal Network for Supply Chain Management

Commonly provided by ERP vendors, master production scheduling (MPS) systems often strive to meet the needs of a large user base while limiting software functionality. Subsequently, business process reengineering becomes the means for firms to adapt to MPS software packages. This article develops a flexible approach for MPS delivery as an alternative to packaged software. The article examines the general case of open system architecture to deliver a specific master scheduling model to end-users. The open system approach fulfills a goal to standardize and speed the process of modeling in practice by creating a supply network for mathematical models that is searchable across the Internet with precision. The value lies on quickly putting state-of-the-art modeling in the hands of many users with no local computer implementation other than downloading an Excel spreadsheet.

Regression Equations for the Latent Roots of Random Data Correlation Matrices with Unities on the Diagonal.

No consensus appears to exist as to how long physically a graphic rating scale should be. The present study found no statistical evidence of perceptual distortion in information collected with continuous rating scales of lengths 75 mm, 100 mm, and 125 mm, so such scales seem robust to variations in line length.