Confirmatory factor analysis models of factorial invariance: A multifaceted approach

Typical confirmatory factor analysis studies of factorial invariance test parameter (factor loadings, factor variances/covariances, and uniquenesses) invariance across only two groups (e.g., males and females) or, perhaps, across more than two groups reflecting different levels of a single design facet (e.g., age). The present investigation extends this approach by considering invariance across groups from a two‐facet design. Data consist of multiple dimensions of self‐concept collected from eight groups of students (total N = 4,000) representing a 2 (Gender) × 4 (Age) design. The gender‐stereotypic model posits a particular pattern of gender differences in structure that varies with age. Adopting analysis‐of‐variance terminology, the model posits that structural differences will vary as a function of gender but that this gender effect interacts with age. In testing this model, I consider the lack of invariance in different sets of parameters attributable to gender, age, and their interaction.