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Wayne Velicer is remembered for a mind where mathematical concepts and calculations intrigued him, behavioral science beckoned him, and people fascinated him. Born in Green Bay, Wisconsin on March 4, 1944, he was raised on a farm, although early influences extended far beyond that beginning. His Mathematics BS and Psychology minor at Wisconsin State University in Oshkosh, and his PhD in Quantitative Psychology from Purdue led him to a fruitful and far-reaching career. He was honored several times as a high-impact author, was a renowned scholar in quantitative and health psychology, and had more than 300 scholarly publications and 54,000+ citations of his work, advancing the arenas of quantitative methodology and behavioral health. In his methodological work, Velicer sought out ways to measure, synthesize, categorize, and assess people and constructs across behaviors and time, largely through principal components analysis, time series, and cluster analysis. Further, he and several colleagues developed a method called Testing Theory-based Quantitative Predictions, successfully applied to predicting outcomes and effect sizes in smoking cessation, diet behavior, and sun protection, with the potential for wider applications. With $60,000,000 in external funding, Velicer also helped engage a large cadre of students and other colleagues to study methodological models for a myriad of health behaviors in a widely applied Transtheoretical Model of Change. Unwittingly, he has engendered indelible memories and gratitude to all who crossed his path. Although Wayne Velicer left this world on October 15, 2017 after battling an aggressive cancer, he is still very present among us.

This paper extends results on the distribution of the Fisher transform of the correlation coefficient (Fisher, 1921). Approaches to obtain exact moments of the Fisher transform for both null and non-null correlations are presented. We extend the classic series expansion formulae of Hotelling (1953) for the moments of the Fisher transform. These results are considered in the context of quadratic functions of the Fisher transform. Some applications of these results are discussed in the context of correlational hypothesis tests and confidence intervals, and a Monte Carlo experiment is used to demonstrate how application of these results impact the small sample performance of select tests on correlations.

Dans les differentes procedures existantes pour l'evaluation et les modifications sequentielles des modeles structuraux, l'auteur s'attache a discuter celle connue sous le terme PMM. Plus generalement, les propositions de KAPLAN (1990) sont critiquees dans le detail

Analysis of covariance or correlation structure is characterized, unfortunately, by repetitive suboptimal communication between persons and/or computer programs. After analyzing some aspects of this suboptimality, I suggest some approaches to improving the situation.

(1990). Some Additional Thoughts on Components, Factors, and Factor Indeterminancy. Multivariate Behavioral Research: Vol. 25, No. 1, pp. 41-45.

Structural equation modeling is one of the most widely used statistical techniques in the social sciences, especially psychology. Its popularity and complexity have spawned a large number of “user-friendly” computer programs, training seminars, introductory textbooks, edited volumes, and an internet discussion group (SEMNET). A review of several introductory textbooks and an edited volume raises disturbing questions about the interplay between commercial development, statistical theory, and “practical” statistical education in this field.

A simple numerical example helps illuminate some of the issues discussed by Maraun (1996), and also helps dispel some of the myths connected with the posterior moment position.

Nearly 70 years ago, eminent mathematician Edwin Bidwell Wilson attended a dinner at Harvard where visitor Charles Spearman discussed the "two-factor theory" of intelligence and his just-released book The Abilities of Man. Wilson, having just discovered factor indeterminacy, attempted to explain to Spearman and the assembled guests that Spearman's two-factor theory might have a non-uniqueness problem. Neither Spearman nor the guests could follow Wilson's argument, but Wilson persisted, first through correspondence, later through a series of publications that spanned more than a decade, involving Spearman and several other influential statisticians in an extended debate. Many years have passed since the Spearman-Wilson debates, yet the fascinating statistical, logical, and philosophical issues surrounding factor indeterminacy are very much alive. Equally fascinating are the sociological issues and historical questions surrounding the way indeterminacy has periodically vanished from basic textbooks on factor analysis. In this article, I delineate some of these historical-sociological issues, and respond to a critique from some recent commentators on the history of factor indeterminacy.

Regression component decompositions (RCD) are defined as a special class of component decompositions where the pattern contains the regression weights for predicting the observed variables from the latent variables. Compared to factor analysis, RCD has a broader range of applicability, greater ease and simplicity of computation, and a more logical and straightforward theory. The usual distinction between factor analysis as a falsifiable model, and component analysis as a tautology, is shown to be misleading, since a special case of regression component decomposition can be defined which is not only falsifiable, but empirically indistinguishable from the factor model.

The goodness-of-fit of correlational pattern hypotheses has traditionally been assessed either with a likelihood ratio statistic (in conjunction with maximum likelihood estimation) or with a quadratic form statistic (in conjunction with generalized least squares estimates). In the present paper, several alternative statistics, based on the use of the Fisher r-to-z transform, are proposed, and their performance (as well as that of the traditional statistics) is assessed in a Monte Carlo experiment. The new statistics are shown to have Type I error rate performance at smaller sample sizes which is notably superior to their more traditional counterparts.

The general asymptotic distribution of elements of a correlation matrix is derived. Applications of the result in robust correlational testing are discussed and illustrated with a numerical example.

Schonemann & Steiger (1976, Theorem 5) proved that the common factor model fits a given set of observed variables if and only if a restricted regression component model fits the same variables. In the present paper a number of results, relating factor score estimates and the class of all sets of ‘factor-equivalent’ regression components, are presented. These results clarify and extend a result given by McDonald (1977).