Inequalities among lower bounds to reliability: With applications to test construction and factor analysis

A chain of lower-bound inequalities leading to the greatest lower bound to reliability is established for the internal consistency of a composite of unit-weighted components. The chain includes the maximum split-half coefficient, the lowest coefficient consistent with nonimaginary common factors, and the lowest coefficient consistent with nonimaginary common and unique factors. Optimization theory is utilized to determine the conditions that are requisite for the inequalities. Convergence proofs demonstrate that the coefficients can be attained. Rapid algorithms obtain estimates of the coefficients with sample data. The theory yields methods for splitting items into maximally similar sets and for exploratory factor analysis based on a theoretical solution to the communality problem.     

Covariance structure analysis of ordinal ipsative data

Data are ipsative if they are subject to a constant-sum constraint for each individual. In the present study, ordinal ipsative data (OID) are defined as the ordinal rankings across a vector of variables. It is assumed that OID are the manifestations of their underlying nonipsative vector y, which are difficult to observe directly. A two-stage estimation procedure is suggested for the analysis of structural equation models with OID. In the first stage, the partition maximum likelihood (PML) method and the generalized least squares (GLS) method are proposed for estimating the means and the covariance matrix of A_cy, where A_c is a known contrast matrix. Based on the joint asymptotic distribution of the first stage estimator and an appropriate weight matrix, the generalized least squares method is used to estimate the structural parameters in the second stage. A goodness-of-fit statistic is given for testing the hypothesized covariance structure. Simulation results show that the proposed method works properly when a sufficiently large sample is available.This research was supported by National Institute on Drug Abuse Grants DA01070 and DA10017. The authors are indebted to Dr. Lee Cooper, Dr. Eric Holman, Dr. Thomas Wickens for their valuable suggestions on this study, and Dr. Fanny Cheung for allowing us to use her CPAI data set in this article. The authors would also like to acknowledge the helpful comments from the editor and the two anonymous reviewers.     

Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis

An alpha-O coefficient of internal consistency is defined for an observed score composite. Maximizing alpha-O leads to a system of psychometric (vs. statistical) factor analysis in which successive factors describe dimensions of successively less internal-consistency. Factoring stops when alpha-O is zero or less. In contrast to Kaiser-Caffrey's alpha-C analysis, when the factored matrix is rank 1, alpha-O does not reach unity; it can approach unity only as the number of variables reach infinity. The relative usefulness and domains of generalization of alpha-C and alpha-O are compared. Basically, alpha-C analysis is concerned with the representativeness of factors while alpha-O analysis is concerned with the assessibility of factors. Consequently, either system of factoring can and should be summarized by both the alpha-C and alpha-O coefficients. Not surprisingly, alpha-O analysis is computationally analogous to Rao's canonical factor analysis.     

Substance use and abuse among children and teenagers

During the past several years, there has been a renewed national concern about drug abuse, culminating in the current "war on drugs." In this review, we emphasize that even though child or teenage drug use is an individual behavior, it is embedded in a sociocultural context that strongly determines its character and manifestations. Our focus is on psychoactive substances both licit (cigarettes and alcohol) and illicit (e.g., cannabis and cocaine). We feel that it is critical to draw a distinction between use and abuse of drugs and to do so from a multidimensional perspective that includes aspects of the stimulus (drug), organism (individual), response, and consequences. Our selective review of substance use and abuse among children and adolescents covers epidemiology (patterns and extent of drug use), etiology (what generates substance use), prevention (how to limit drug use), treatment (interventions with drug users), and consequences (effects and outcomes of youthful drug use).     

Adolescent socialization and use of licit and illicit substances: Impact on adult health

Abstract

This study examined the impact of adolescent substance use on young adult health. Longitudinal data from 825 participants were assessed when the participants were junior high school and high school students (1969-1973) and again in 1981. Latent variable models were used to determine what effect adolescent drug use had on later health. General substance use, which included tobacco, alcohol, stimulants, sedatives, and other hard drugs, had a small effect on adult health problems associated with substance use, and also predicted accidents related to substance use. In addition, the specific use of tobacco and cannabis in adolescence predicted later respiratory problems, while cigarette smoking during adolescence also predicted decreased physical hardiness. Lower adolescent socialization predicted post high school accidents (automobile and other) serious enough to require medical attention, and predicted increased psychosomatic and seizure symptoms, as well as general psychiatric distress. Implications of these results for the successful prevention or intervention of drug use are discussed. In addition to these results, gender differences are also examined.     

SEM with simplicity and accuracy

Professor Iacobucci has provided a useful introduction to the computer program LISREL, as well as to several technical topics in structural equation modeling (SEM). However, SEM has not been synonymous with LISREL for several decades, and focusing on LISREL's 13 Greek matrices and vectors is not the most intuitive way to learn SEM. It is possible today to do model specification via a path diagram without any need for filling in matrix elements. The simplest alternative is based on the Bentler–Weeks model, whose basic concepts are reviewed. Selected additional SEM topics are discussed, including some recent developments and their practical implications. New simulation results on model fit under null and alternative hypotheses are also presented that are consistent with statistical theory but in part seem to contradict those reported by Iacobucci.     

An EM algorithm for fitting two-level structural equation models

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a variety of two-level structural equation models. As a result, the proposed EM algorithm is widely applicable in practice. A practical example illustrates the performance of the EM algorithm and the maximum likelihood statistic.We are thankful to the reviewers for their constructive comments that have led to significant improvement on the first version of this paper. Special thanks are due to the reviewer who suggested a comparison with the LISREL program in the saturated means model, and provided its setup and output. This work was supported by National Institute on Drug Abuse grants DA01070, DA00017, and a UNH 2002 Summer Faculty Fellowship.     

Structural equation modeling with heavy tailed distributions

Data in social and behavioral sciences typically possess heavy tails. Structural equation modeling is commonly used in analyzing interrelations among variables of such data. Classical methods for structural equation modeling fit a proposed model to the sample covariance matrix, which can lead to very inefficient parameter estimates. By fitting a structural model to a robust covariance matrix for data with heavy tails, one generally gets more efficient parameter estimates. Because many robust procedures are available, we propose using the empirical efficiency of a set of invariant parameter estimates in identifying an optimal robust procedure. Within the class of elliptical distributions, analytical results show that the robust procedure leading to the most efficient parameter estimates also yields a most powerful test statistic. Examples illustrate the merit of the proposed procedure. The relevance of this procedure to data analysis in a broader context is noted. The authors thank the editor, an associate editor and four referees for their constructive comments, which led to an improved version of the paper.     

Exploratory Bi-Factor Analysis

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this paper is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific bi-factor model a priori. The result of an exploratory bi-factor analysis, however, can be used as an aid in defining a specific bi-factor model. Our exploratory bi-factor analysis is simply exploratory factor analysis using a bi-factor rotation criterion. This is a criterion designed to produce perfect cluster structure in all but the first column of a rotated loading matrix. Examples are given to show how exploratory bi-factor analysis can be used with ideal and real data. The relation of exploratory bi-factor analysis to the Schmid-Leiman method is discussed.