A comparison of methods to detect invariant reference indicators in structural equation modelling

Abstract

Measurement invariance via multiple-group methods in structural equation modelling is becoming more widely tested by applied researchers. When conducting invariance tests, the selection of an invariant reference indicator is an important concern because it has implications when attempting to detect non-invariance at other levels within a model. Cheung and Rensvold (1999) and Yoon and Millsap (2007) have proposed two methods, respectively, which may be used to select an invariant reference indicator. This study compared these two reference indicator selection methods under varied conditions to assess their accuracy with respect to identifying non-invariant and invariant factor loadings. The two methods performed more optimally in certain conditions. Overall, the method proposed by Yoon and Millsap (2007) performed more accurately when detecting non-invariant indicators whereas the method proposed by Cheung and Rensvold (1999) performed more accurately when detecting invariant indicators. Implications and recommendations are provided.