An iterative strategy for referent variable selection in MIMIC-interaction modeling

Examining cross-group latent differences in various research contexts has brought measurement invariance/equivalence into the spotlight. One major limitation of measurement invariance testing through multiple-group confirmatory factor analysis (MGCFA) has been recognized yet has not received much attention: the selection of a referent observed variable. Recently, multiple-indicator multiple-cause (MIMIC)-interaction modeling with the all-other anchor method (i.e., a constrained baseline approach) has been used to identify referent variables in a repetitive manner. This study proposed an iterative search strategy in MIMIC-interaction models to improve the accuracy of referent variable selection, particularly when the proportion of noninvariance increases. A Monte Carlo simulation design was used to evaluate the effects of the proportion of noninvariance, magnitude of noninvariance, magnitude of latent variable differences, and sample size. The accuracy rate was used to assess the performance of selecting referent variables from among truly invariant observed variables in the population. Results showed that the iterative strategy generally outperformed the repetitive strategy for locating credible referent variables across nearly all conditions, suggesting that the iterative strategy is a reliable and practical approach for referent variable selection in applications. The superiority of the iterative strategy over the repetitive strategy became substantial in the conditions of high proportions of noninvariance, large latent variable differences, or a combination of both. We present an illustrative example to demonstrate the applicability of the iterative strategy for referent variable selection in MIMIC-interaction modeling.