The fulfillment of measurement invariance is considered a prerequisite for meaningfully proceeding with substantive cross-group comparisons. In the multiple-group CFA approach to invariance testing, two potential limitations related to model identification have unfortunately received little attention: (1) the specification of a referent variable (i.e., standardization) in the test of factor loading invariance and (2) the lack of a statistical test for intercept invariance. A multiple-indicator multiple-cause (MIMIC) model with moderated effects (i.e., a MIMIC-interaction modeling approach) to detect uniform and nonuniform measurement biases in tandem was proposed to identify credible referent variables. The performance of two search strategies, constrained baseline and free baseline methods, were evaluated. A Monte Carlo simulation study was carried out to determine the effects of different configurations of number of noninvariant variables, location and magnitude of noninvariance, magnitude of group differences in factor means and variances, as well as sample size. Results showed that the constrained baseline method generally outperformed the free baseline method for identifying a credible referent variable, functioning well when up to one-third of the observed variables were noninvariant.