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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 note presents the original Steiger-Lind (1980) handout entitled, “Statistically-Based Tests for the Number of Common Factors”, distributed to all in attendance at the talk given at the annual meeting of the Psychometric Society in Iowa City, Iowa.

Two studies examined the relationship between precollegiate advanced/enriched educational experiences and adult accomplishments in science, technology, engineering, and mathematics (STEM). In Study 1, 1,467 13-year-olds were identified as mathematically talented on the basis of scores 500 (top 0.5%) on the math section of the Scholastic Assessment Test; subsequently, their developmental trajectories were studied over 25 years. Particular attention was paid to high-level STEM accomplishments with low base rates in the general population (STEM PhDs, STEM publications, STEM tenure, STEM patents, and STEM occupations). Study 2 retrospectively profiled the adolescent advanced/enriched educational experiences of 714 top STEM graduate students (mean age 25), and related these experiences to their STEM accomplishments up to age 35. In both longitudinal studies, those with notable STEM accomplishments manifested past histories involving a richer density of advanced precollegiate educational opportunities in STEM (a higher “STEM dose”) than less highly achieving members of their respective cohorts. While both studies are quasi-experimental, they suggest that for mathematically talented and academically motivated young adolescents, STEM accomplishments are facilitated by a rich mix of precollegiate STEM educational opportunities that are designed to be intellectually challenging, even for students at precocious developmental levels. These opportunities appear to be uniformly important for both sexes.

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.

Barrett’s (2007) article on “adjudging model fit” raises some important issues concerning the use of global fit indices to justify weak structural equation models, and recommends prohibition of future use of such indices. In this commentary, I critique Barrett’s presentation, and show that his recommendations are (a) unnecessarily regressive, and (b) likely to be ignored. Then I suggest a constructive alternative in line with the spirit of his concerns.

Trait–State–Occasion (TSO) covariance models represent an important advance in methods for studying the longitudinal stability of latent constructs. Such models have only been examined under fairly restricted conditions (e.g., having only 2 tau-equivalent indicators per wave). In this study, Monte Carlo simulations revealed the effects of having 2 versus 3 indicators per wave and relaxing the within-wave tau equivalence. These modifications were examined under conditions that varied with regard to the within-wave trait variance and the cross-wave stability of occasion influences. In general, the TSO model performed well (i.e., few convergence problems or out-of-range parameter estimates) under most of these conditions; however, the likelihood of improper solutions increased when only 2 indicators were used per wave, when factor loadings were small, when the proportion of trait variance was either very high or very low, and when the occasion factor was highly stable. Based on these findings, recom...

The latent trait-state-error model (TSE) and the latent state-trait model with autoregression (LST-AR) represent creative structural equation methods for examining the longitudinal structure of psychological constructs. Application of these models has been somewhat limited by empirical or conceptual problems. In the present study, Monte Carlo analysis revealed that TSE models tend to generate improper solutions when N is too small, when waves are too few, and when occasion factor stability is either too large or too small. Mathematical analysis of the LST-AR model revealed its limitation to constructs that become more highly auto-correlated over time. The trait-state-occasion model has fewer empirical problems than does the TSE model and is more broadly applicable than is the LST-AR model.

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.

Hayduk and Glaser (2000) asserted that the most commonly used point estimate of the Root Mean Square Error of Approximation index of fit (Steiger & Lind, 1980) has two significant problems: (a) The frequently cited target value of. 05 is not a stable target, but a "sample size adjustment"; and (b) the truncated point estimate Rt = max(R, 0) effectively throws away a substantial part of the sampling distribution of the test statistic with "proper models," rendering it useless a substantial portion of the time. In this article, I demonstrate that both issues discussed by Hayduk and Glaser are actually not problems at all. The first "problem" derives from a false premise by Hayduk and Glaser that Steiger (1995) specifically warned about in an earlier publication. The second so-called problem results from the point estimate satisfying a fundamental property of a good estimator and can be shown to have virtually no negative implications for statistical practice.

Generalization of the Steiger‐Lind root mean square error of approximation fit indexes and interval estimation procedure to models based on multiple independent samples is discussed. In this article, we suggest an approach that seems both reasonable and workable, and caution against one that definitely seems inappropriate.

Contents: Preface. Part I: Overview. L.L. Harlow, Significance Testing Introduction and Overview. Part II: The Debate: Against and For Significance Testing. J.Cohen, The Earth Is Round. F.L. Schmidt, J. Hunter, Eight Objections to the Discontinuation of Significance Testing in the Analysis of Research Data. S.A. Mulaik, N.S. Raju, R. Harshman, There Is a Time and Place for Significance Testing. R.P. Abelson, A Retrospective on the Significance Test Ban of 1999 (If There Were No Significance Tests, They Would Be Invented). Part III: Suggested Alternatives to Significance Testing. R.J. Harris, Reforming Significance Testing via Three-Valued Logic. J.S. Rossi, Spontaneous Recovery of Verbal Learning: A Case Study in the Failure of Psychology as a Cumulative Science. J.H. Steiger, R.T. Fouladi, Noncentrality Interval Estimation and the Evaluation of Statistical Models. R.P. McDonald, Goodness of Approximation in the Linear Model. Part IV: A Bayesian Approach to Hypothesis Testing. R.M. Pruzek, An Introduction to Bayesian Inference and Its Application. D. Rindskopf, Testing 'Small,' Not Null, Hypotheses: Classical and Bayesian Approaches. C.S. Reichardt, H.F. Gollob, When Confidence Intervals Should Be Used Instead of Statistical Significance Tests, and Vice Versa. Part V: Philosophy of Science Issues. W.W. Rozeboom, Good Science Is Abductive, Not Hypothetico-Deductive. P.E. Meehl, The Problem Is Epistemology, Not Statistics: Replace Significance Tests by Confidence Intervals and Quantify Accuracy of Risky Numerical Predictions.

In the late 1970s, 563 intellectually talented 13-year-olds (identified by the SAT as in the top 0.5% of ability) were assessed on spatial ability. More than 30 years later, the present study evaluated whether spatial ability provided incremental validity (beyond the SAT’s mathematical and verbal reasoning subtests) for differentially predicting which of these individuals had patents and three classes of refereed publications. A two-step discriminant-function analysis revealed that the SAT subtests jointly accounted for 10.8% of the variance among these outcomes ( p < .01); when spatial ability was added, an additional 7.6% was accounted for—a statistically significant increase ( p < .01). The findings indicate that spatial ability has a unique role in the development of creativity, beyond the roles played by the abilities traditionally measured in educational selection, counseling, and industrial-organizational psychology. Spatial ability plays a key and unique role in structuring many important psychological phenomena and should be examined more broadly across the applied and basic psychological sciences.

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.

Core Affect is a state accessible to consciousness as a single simple feeling (feeling good or bad, energized or enervated) that can vary from moment to moment and that is the heart of, but not the whole of, mood and emotion. In four correlational studies (Ns = 535, 190, 234, 395), a 12-Point Affect Circumplex (12-PAC) model of Core Affect was developed that is finer grained than previously available and that integrates major dimensional models of mood and emotion. Self-report scales in three response formats were cross-validated for Core Affect felt during current and remembered moments. A technique that places any external variable into the 12-PAC showed that 29 of 38 personality scales and 30 of 30 mood scales are significantly related to Core Affect, but not in a way that revealed its basic dimensions.

Silver and Dunlap (1989) reviewed several tests for the hypothesis of multivariate independence, and, on the basis of Monte Carlo results, recommended a procedure by Brien, Venables, and Mayo (1984) as providing best overall performance. More recently (Silver and Dunlap, 1990), they have distributed computer software implementing this recommendation. In this paper, the writers demonstrate that Brien et al.'s test is not a proper test for multivariate independence, and propose a revised appraisal of the Silver and Dunlap (1989) results.

In practice, the inclusion of correlated residuals in latent-variable models is often regarded as a statistical sleight of hand, if not an outright form of cheating. Consequently, researchers have tended to allow only as many correlated residuals in their models as are needed to obtain a good fit to the data. The current article demonstrates that this strategy leads to the underinclusion of residual correlations that are completely justified on the basis of measurement theory and research design. In many designs, the absence of such correlations will not substantially harm the fit of the model; however, failure to include them can change the meaning of the extracted latent variables and generate potentially misleading results. Recommendations include (a) returning to the full multitrait-multimethod design when measurement theory implies the existence of shared method variance and (b) abandoning the evil-but-necessary attitude toward correlated residuals when they reflect intended features of the research design.

In this article, we identify key trends in the development of statistical, graphical, and word processing software for the social scientist. We examine the trends from the perspective of the social scientist with a typical background in applied statistics, intent on developing a high-power, low-cost personal workstation for data analysis and manuscript production. Keywords: statistics, graphics, word processing, microcomputer software.

This article presents confidence interval methods for improving on the standard F tests in the balanced, completely between-subjects, fixed-effects analysis of variance. Exact confidence intervals for omnibus effect size measures, such as ω 2 and the root-mean-square standardized effect, provide all the information in the traditional hypothesis test and more. They allow one to test simultaneously whether overall effects are (a) zero (the traditional test), (b) trivial (do not exceed some small value), or (c) nontrivial (definitely exceed some minimal level). For situations in which single-degree-of-freedom contrasts are of primary interest, exact confidence interval methods for contrast effect size measures such as the contrast correlation are also provided.

In traditional approaches to structural equations modeling, variances of latent endogenous variables cannot be specified or constrained directly and, consequently, are not identified, unless certain precautions are taken. The usual method for achieving identification has been to fix one factor loading for each endogenous latent variable at unity. An alternative approach is to fix variances using newer constrained estimation algorithms. This article examines the philosophy behind such constraints and shows how their appropriate use is neither as straightforward nor as noncontroversial as portrayed in textbooks and computer manuals. The constraints on latent variable variances can interact with other model constraints to interfere with the testing of certain kinds of hypotheses and can yield incorrect standardized solutions with some popular software.

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 issue of factor indeterminacy, and its meaning and significance for factor analysis, has been the subject of considerable debate in recent years. Interestingly, the identical issue was discussed widely in the literature of the late 1920's and early 1930's, but this early discussion was somehow lost or forgotten during the development and popularization of multiple factor analysis. There are strong parallels between the arguments in the early literature, and those which have appeared in recent papers. Here I review the history of this early literature, briefly survey the more recent work, and discuss these parallels where they are especially illuminating.

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.

Persons' classifications of emotions are viewed as based on an implicit taxonomy of emotions. This implicit taxonomy has sometimes been thought of as a bipolar dimensional system within which are located all the various emotion-descriptive categories (fear, anger, happiness, etc.). A dimensional taxonomy of this kind assumes that all emotion categories are interrelated in a systematic way. More often, however, the implicit taxonomy has been thought of as a list of separate emotions. A taxonomy in the form of a list typically presupposes that emotion categories are either synonymous, independent, or mutually exclusive. McNair, Lorr, and Droppleman's Profile of Mood States (San Diego: Educational and Industrial Testing Service, 1971 ) is one such list of emotion categories and was therefore examined in two studies for the actual interrelationships among its categories. To examine intra individual relationships, 45 subjects rated the emotional state posed in each of 32 videotape segments. Even at the level of the individual subject, results showed that emotion categories are systematically interrelated and can be accounted for reasonably well by a system of three bipolar dimensions: pleasure-displeasure, arousal-sleepiness, and dominance-submissiveness. Evidence for the same bipolar system was also obtained in a second study, which examined inter individual differences in the self-reported emotional states of 343 subjects.

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.

A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.

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).

A series of experiments, using a modification of the Shepard and Metzler mental rotation task, was performed to investigate Shepard’s “holistic rotation” hypothesis. Effective figural complexity was manipulated in the experiments in two distinct ways. In one manipulation, blocks were added to the standard 10-blockfigures. In the other manipulation, the figures used and the direction of angular rotation were restricted so that some featural information in the figures was redundant, that is, unnecessary for the discrimination task at hand. There were two major conclusions. First, when figural complexity is effectively manipulated, it has a powerful effect on the “speed of mental rotation,” as measured by the slope of the curve relating reaction time to angular disparity. Second, it is possible, by ignoring featural redundancy, to construct experimental paradigms in which “complexity” of figures is apparently manipulated but has no effect on speed of mental rotation. This fact provides a possible explanation of why some previous experiments have failed to find a complexity effect in mental rotation.

A theorem is presented which gives the range of possible correlations between a common factor and an external variable (i.e., a variable not included in the test battery factor analyzed). Analogous expressions for component (and regression component) theory are also derived. Some situations involving external correlations are then discussed which dramatize the theoretical differences between components and common factors.

In a variety of situations in psychological research, it is desirable to be able to make statistical comparisons between correlation coefficients measured on the same individuals. For example, an experimenter may wish to assess whether two predictors correlate equally with a criterion variable. In another situation, the experimenter may wish to test the hypothesis that an entire matrix of correlations has remained stable over time. The present article reviews the literature on such tests, points out some statistics that should be avoided, and presents a variety of techniques that can be used safely with medium to large samples. Several illustrative numerical examples are provided.

A partition of the vector space of all deviation score vectors for fixed sample size N is used to show that the (indeterminate) factors of the factor model can always be constructed so as to predict any criterion perfectly, including all those that are entirely uncorrected with the observed variables.

The program presented computes a chi-square statistic for testing pattern hypotheses on correlation matrices. The statistic is based on a multivariate generalization of the Fisher r-to- z transformation. Monte Carlo studies have demonstrated that this statistic has small sample performance which is superior to an analogous likelihood ratio statistic obtained via the analysis of covariance structures.