Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

The Buss–Perry Aggression Questionnaire: Some unfinished business

This article gauges the extent to which items and sum scores of the Buss–Perry Aggression Questionnaire (BPAQ) are contaminated with social desirability response set (SDR), and the extent to which that contamination results in biased findings. Special validity coefficients are introduced for that purpose. Although the SDR confound was quite substantial across all items (with one exception), it is argued on the basis of the size of the introduced validity coefficients and other, logical considerations that paradoxically the confound had minimally distorting effects in estimating the BPAQ models selected for probing the extent of bias.     

The communality-bonus effect for male transformational leaders – leadership style,gender, and promotability

Women have made considerable inroads into the workforce but remain underrepresented in leadership positions. Even though studies show that men and women hardly differ in their leadership behaviours, we argue that male and female leaders are evaluated differentially contingent on the gender-congruence of their leadership style. Drawing arguments from expectancy violation theory, we investigate evaluations of men and women who show transformational leadership (a style consisting of communal behaviours in line with stereotypes about women) and autocratic leadership (a style consisting of agentic behaviours in line with stereotypes about men). We employed a three-study research design combining two experimental studies and a two-wave field study with business leaders (overall N = 344). Overall transformational leadership resulted in higher evaluations of promotability due to higher perceptions of leaders’ communality and leadership effectiveness. Importantly, these effects were stronger for men, and men showing transformational leadership were evaluated to be more promotable than women. This implies a communality-bonus effect for male transformational leaders. There was no difference in promotability evaluations for women versus men showing autocratic leadership. This effect was mediated by agency and effectiveness perceptions for women but not for men. Implications are discussed.     

A numerical approach to the approximate and the exact minimum rank of a covariance matrix

A concept of approximate minimum rank for a covariance matrix is defined, which contains the (exact) minimum rank as a special case. A computational procedure to evaluate the approximate minimum rank is offered. The procedure yields those proper communalities for which the unexplained common variance, ignored in low-rank factor analysis, is minimized. The procedure also permits a numerical determination of the exact minimum rank of a covariance matrix, within limits of computational accuracy. A set of 180 covariance matrices with known or bounded minimum rank was analyzed. The procedure was successful throughout in recovering the desired rank.The authors are obliged to Paul Bekker for stimulating and helpful comments.     

Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.     

Nest membership determines the levels of aggression and cooperation between females of a supposedly communal digger wasp

Females of communal and eusocial Hymenoptera differ greatly in the treatment of conspecifics: communal species lack the nest membership-bias treatment via nestmate (NM) recognition, which is typical of eusocial Hymenoptera. Therefore, an analysis of social interactions can suggest whether a given bee or wasp is communal or eusocial. For this reason, we observed females of the digger wasp Cerceris rubida in experimental dyadic encounters. Because this species had previously been labeled "communal," we expected to find little evidence of a NM bias with respect to cooperation or aggression when paired with NMs and non-nestmates (NNM). Contrary to expectation, females were highly cooperative toward NMs and highly aggressive toward NNMs. Variation in the intensity of aggression toward NNMs partially stems from the degree to which the paired females differed in size. From these results and quantitative comparisons with studies on solitary, communal, and eusocial bee species, it appears that C. rubida has a more complex social organization than previously believed and, in particular, that females of this species exhibit NM recognition, a trait associated with eusociality.     

Asymptotic distributions of the estimators of communalities in factor analysis

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300. This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).     

Internal consistency of tests: Analyses old and new

A coefficient derived from communalities of test parts has been proposed as greatest lower bound to Guttman's immediate retest reliability. The communalities have at times been calculated from covariances between itemsets, which tends to underestimate appreciably. When items are experimentally independent, a consistent estimate of the greatest defensible internal-consistency coefficient is obtained by factoring item covariances. In samples of modest size, this analysis capitalizes on chance; an estimate subject to less upward bias is suggested. For estimating alternate-forms reliability, communality-based coefficients are less appropriate than stratified alpha.I thank Edward Haertel for comments and suggestions, and Andrew Comrey for data.