Accessing the impact of unmodeled systematic error variance on measurement invariance tests

Systematic error variance (SEV) is one of sources that make a measurement noninvariant (DeShon, 2004). In the confirmatory factor analysis (CFA), researchers use the bifactor or correlated uniqueness (CU) model to control the SEV. This study aims to examine the impacts of SEVs on the multiple groups mean comparison, and evaluate the methods used to control the SEVs in the framework of multiple group CFA. In Monte Carlo simulation, multiple groups data contaminated by different SEV distributions are generated, then, the bifactor and the CU model were used to fit the data. The original model, which assumed no SEVs, was also used as the baseline model. Results show that uncontrolled SEV could affect the estimation of mean difference. Among three models, the bifactor overperformed the other two models in most conditions if it yields converged results. This study also provided an empirical example to demonstrate how to select appropriate methods in multiple group CFA. Implications of these results for applied researchers are discussed