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

Abstract

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.

Keywords

Affiliated Institutions

• University of Ottawa CA

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