One hundred years have passed since the birth of factor analysis, during which time there have been some major developments and extensions to the methodology. Unfortunately, one issue where the widespread accumulation of knowledge has been rather slow concerns identification. This article provides a didactic discussion of the topic in an attempt…

Bifactor and second-order factor models are two alternative approaches for representing general constructs comprised of several highly related domains. Bifactor and second-order models were compared using a quality of life data set (N = 403). The bifactor model identified three, rather than the hypothesized four, domain specific factors beyond the…

Schools of United States fall short of providing high quality mathematics and science education to all the students. The factors distinguishing the most effective lessons from the least effective ones are stated.

We illustrate testing measurement invariance in a second-order factor model using a quality of life dataset (n = 924). Measurement invariance was tested across 2 groups at a set of hierarchically structured levels: (a) configural invariance, (b) first-order factor loadings, (c) second-order factor loadings, (d) intercepts of measured variables,…

The purpose of this article is to illustrate a mixed-method approach (i.e., combining qualitative and quantitative methods) for advancing the study of construct validation in cross-cultural research. The article offers a detailed illustration of the approach using the responses 612 Sri Lankan adolescents provided to an ethnographic survey. Such…

The purpose of the study was to investigate whether the six-factor structure of the Frost Multidimensional Perfectionism Scale could be replicated in a community-based sample. A sample of 255 adult participants (55.7% female, 44.3% male) ranging in age from 18 to 78 (mean = 37.0) completed the questionnaire. Based on the screen test and parallel…

Ensuring construct comparability is a prerequisite for testing cross-group differences, yet this assumption is rarely tested in mentoring research. More studies testing for factorial invariance are needed for the construct validation of mentoring. Multiple group confirmatory factor analyses (CFAs) were used to investigate the factorial stability…

The factor analysis of ordered-categorical measures has been described in the literature on factor analysis, but the extension of the analysis to the multiple-population case is less well-known. For example, a comprehensive statement of identification conditions for the multiplepopulation case seems absent in the literature. We review this…

We consider a general type of model for analyzing ordinal variables with covariate effects and 2 approaches for analyzing data for such models, the item response theory (IRT) approach and the PRELIS-LISREL (PLA) approach. We compare these 2 approaches on the basis of 2 examples, 1 involving only covariate effects directly on the ordinal variables…

There is evidence of higher prevalence rates for alcohol use among rural adolescents relative to urban adolescents. Strategies aimed at preventing adolescent alcohol use typically include the development of social skills to resist peer pressure; among the social skills frequently targeted is assertiveness. Self-report data were collected from a…

The Attributional Style Questionnaire (ASQ; C. Peterson et al., 1982) has been the subject of some debate challenging its usefulness in research. This study examines the ASQ component structure for Central American immigrants to the United States. Research and cultural implications are discussed.

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

This study of person fit in attitude surveys was undertaken in order to investigate the influence of the inclusion of misfitting persons on item parameter estimates in analyses using the Partial Credit extension of the Rasch measurement model. It was hypothesised that the inclusion of misfitting persons in data sets used for the calibration of…

Given the proliferation of factor analysis applications in the literature, the present article examines the use of factor analysis in current published research across four psychological journals. Notwithstanding ease of analysis due to computers, the appropriate use of factor analysis requires a series of thoughtful researcher judgments. These…

The gains of scores on standardized intelligence tests (i.e., Flynn effect) have been the subject of extensive debate concerning their nature, causes, and implications. The aim of the present study is to investigate whether five intelligence tests are measurement invariant with respect to cohort. Measurement invariance implies that gains over the…