Addressing missing data in specification search in measurement invariance testing with Likert-type scale variables: A comparison of two approaches

In measurement invariance testing, when a certain level of full invariance is not achieved, the sequential backward specification search method with the largest modification index (SBSS_LMFI) is often used to identify the source of non-invariance. SBSS_LMFI has been studied under complete data but not missing data. Focusing on Likert-type scale variables, this study examined two methods for dealing with missing data in SBSS_LMFI using Monte Carlo simulation: robust full information maximum likelihood estimator (rFIML) and mean and variance adjusted weighted least squared estimator coupled with pairwise deletion (WLSMV_PD). The result suggests that WLSMV_PD could result in not only over-rejections of invariance models but also reductions of power to identify non-invariant items. In contrast, rFIML provided good control of type I error rates, although it required a larger sample size to yield sufficient power to identify non-invariant items. Recommendations based on the result were provided.