Invariance Of Factor Loadings Research Articles

Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance.

Addresses issues related to partial measurement in variance using a tutorial approach based on the LISREL confirmatory factor analytic model. Specifically, we demonstrate procedures for (a) using sensitivity to establish stable and substantively well-fitting baseline models, (b) determining partially invariant measurement parameters, and (c) testing for the invariance of factor covariance and mean structures, given partial measurement invariance. We also show, explicitly, the transformation of parameters from an all-^fto an all-y model specification, for purposes of testing mean structures. These procedures are illustrated with multidimensional self-concept data from low (« = 248) and high (n = 582) academically tracked high school adolescents. An important assumption in testing for mean differences is that the measurement (Drasgow & Kanfer, 1985; Labouvie, 1980; Rock, Werts, & Haugher, 1978) and the structure (Bejar, 1980; Labouvie, 1980; Rock etal., 1978) of the underlying construct are equivalent across groups. One methodological strategy used in testing for this equivalence is the analysis of covariance structures using the LISREL confirmatory factor analytic (CFA) model (Joreskog, 1971). Although a number of empirical investigations and didactic expositions have used this methodology in testing assumptions of factorial invariance for multiple and single parameters, the analyses have been somewhat incomplete. In particular, researchers have not considered the possibility of partial measurement invariance. The primary purpose of this article is to demonstrate the application of CFA in testing for, and with, partial measurement invariance. Specifically, we illustrate (a) testing, independently, for the invariance of factor loading (i.e., measurement) parameters, (b) testing for the invariance of factor variance-covariance (i.e., structural) parameters, given partially invariant factor loadings, and (c) testing for the invariance of factor mean structures.1 Invariance testing across groups, however, assumes wellfitting single-group models; the problem here is to know when to stop fitting the model. A secondary aim of this article, then, is to demonstrate sensitivity that can be used to establish stable and substantively meaningful baseline models.

A COMPARISON OF THE STRUCTURAL RELATIONSHIPS AMONG READING, LISTENING, WRITING, AND SPEAKING COMPONENTS OF THE AP FRENCH LANGUAGE EXAMINATION FOR AP CANDIDATES AND COLLEGE STUDENTS1,2

ABSTRACTYearly the Advanced Placement Program administers an examination to high school students measuring French language skills that students might acquire after six semesters of college French Language courses. The dimensional structure of the 1987 AP French Language exam was tested in four populations using a series of confirmatory linear factor analysis models. In order to mitigate problems associated with the linear factor analysis of multiple‐choice items, the linear factor analysis of item parcel scores, made up of small mutually exclusive collections of items hypothesized to measure the same underlying dimension, was utilized. Six confirmatory factor analysis models were tested within each of five samples of data. Two samples contained high school AP candidates with no out‐of‐school French Language experience. A third sample contained AP candiates which had spent a significant amount of time in a French speaking counry. A fourth sample contained AP candidates who regularly spoke or heard French at home. The final sample contained students with no out‐of‐class French language experience enrolled in third year French classes at one of sixteen colleges. In all samples the exam appears to measure four major dimensions which are associated with the language skills of listening, reading, writing and speaking. For the student groups lacking out‐of‐school French language experience, the structure of the exam displays invariance of factor loadings and errors of measurement. Factor structures were most similar for groups with similar out‐of‐school French language experiences.

Arousability, trait anxiety and the worry and emotionality components of test anxiety

Abstract Eleventh- and twelfth-grade high-school students (or equivalent subjects in Saudi Arabia, Egypt and Brazil) participated in this study. All subjects were administered the Test Anxiety Inventory and the Anxiety/Arousability Inventory in their native language. A confirmatory factor analysis yielded the following conclusions: (1) the measures of trait anxiety arousability, test anxiety (worry), and test anxiety (emotionality) demonstrated high reliability, factorial validity and discriminant validity in each of the four samples; (2) as hypothesized, significant positive correlations were found between all four measures in each of the four samples; (3) analyses of invariance supported the invariance of factor loadings and factor true variances across three cultural groups: Egypt, Brazil and the USA. (Saudi Arabia was eliminated from the invariance analysis because the sample was all male.) Analyses of invariance did not support the invariance of error/uniquenesses and factor correlations.

The mathematical theory of factorial invariance under selection

It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.