Two-Step Approach to Partial Factorial Invariance: Selecting a Reference Variable and Identifying the Source of Noninvariance

• Published in: Structural equation modeling Vol. 24; no. 1; pp. 65 - 79
• Main Authors: Jung, Eunju, Yoon, Myeongsun
• Format: Journal Article
• Language: English
• Published: Hove Routledge 02.01.2017; Psychology Press
• Subjects: Discriminant analysis; Factorial experiments; modification index; multiple-group confirmatory factor analysis; partial factorial invariance; reference variable
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705511.2016.1251845

To date, no effective empirical method has been available to identify a truly invariant reference variable (RV) in testing measurement invariance under a multiple-group confirmatory factor analysis. This study proposes a method that, in selecting an RV, uses the smallest modification index (min-mod). The method's performance is evaluated using 2 models: (a) a full invariance model, and (b) a partial invariance model. Results indicate that for both models the min-mod successfully identifies a truly invariant RV (Study 1). In Study 2, we use the RV found in Study 1 to further evaluate the performance of item-by-item Wald tests at locating a noninvariant variable. The results indicate that Wald tests overall performed better with an RV selected in a partial invariance model than an RV selected in a full invariance model, although in certain conditions their performances were rather similar. Implications and limitations of the study are also discussed.