The effect of agency and communality on self-esteem: Gender differences in longitudinal data

Prior studies have noted a positive relationship between masculinity (M) and self-esteem (S-E) for both males and females. However, during adolescence, males and females have been described as experiencing a divergence into two domains: agency for males and communality for females. The present study hypothesized that, contrary to the cross-sectional positive correlational relationship between M and S-E for both males and females, an agentic orientation during adolescence would predict heightened S-E at young adulthood for males only. Conversely, a communal orientation was hypothesized to predict heightened S-E for females only at young adulthood. Using structural equation models with latent variables to analyze data from a community sample of 654 subjects (M=192, F=462; White=432; Black=97; Hispanic=64; Asian=61), these hypotheses were confirmed. In addition, as found in typical masculinity-femininity (M-F) studies, both males and females evidenced a positive relationship between S-E and M, as measured on the Personal Attributes Questionnaire and essentially no relationship between F and S-E. Possible reasons for this complexity and implications for future research are discussed.     

Linear structural equations with latent variables

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017) and a research grant (DA01070) from the U. S. Public Health Service.     

Statistical aspects of a three-mode factor analysis model

A special case of Bloxom's version of Tucker's three-mode model is developed statistically. A distinction is made between modes in terms of whether they are fixed or random. Parameter matrices are associated with the fixed modes, while no parameters are associated with the mode representing random observation vectors. The identification problem is discussed, and unknown parameters of the model are estimated by a weighted least squares method based upon a Gauss-Newton algorithm. A goodness-of-fit statistic is presented. An example based upon self-report and peer-report measures of personality shows that the model is applicable to real data. The model represents a generalization of Thurstonian factor analysis; weighted least squares estimators and maximum likelihood estimators of the factor model can be obtained using the proposed theory.This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and a research grant (DA01070) from the U. S. Public Health Service. The very helpful comments of several anonymous reviewers are gratefully acknowledged.     

Function invariant and parameter scale-free transformation methods

The parameter matrices of factor analysis and principal component analysis are arbitrary with respect to the scale of the factors or components; typically, the scale is fixed so that the factors have unit variance. Oblique transformations to optimize an objective statement of a principle such as simple structure or factor simplicity yield arbitrary solutions, unless the criterion function is invariant with respect to the scale of the factors, or the parameter matrix is scale free with respect to the factors. Criterion functions that are factor scale-free have a number of invariance characteristics, such as being equally applicable to primary pattern or reference structure matrices. A scale-invariant simple structure function of previously studied function components is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing.Aspects of this paper were presented at the 1970 and 1974 annual meetings, Society of Multivariate Experimental Psychology, and the 1975 annual meeting, Psychometric Society. This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and research grants (MH24149 and DA01070) from the U. S. Public Health Service. The assistance of Bonnie Barron, Sik-Yum Lee, and several extremely helpful reviewers is gratefully acknowledged.     

Alpha,Dimension-Free,and Model-Based Internal Consistency Reliability

As pointed out by Sijtsma (in press), coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score. Better estimators of internal consistency are available. In addition to those mentioned by Sijtsma, an old dimension-free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency. The various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items. Research supported in part by grants DA00017 and DA01070 from the National Institute on Drug Abuse. This paper is based in part on Bentler (2003).