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


  • Copyright Taylor & Francis Group, LLC. 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 methods 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.

published proceedings


author list (cited authors)

  • Jung, E., & Yoon, M.

citation count

  • 14

complete list of authors

  • Jung, Eunju||Yoon, Myeongsun

publication date

  • January 2017