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In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an alternative method for testing factorial invariance and evaluates the performance of the method in specification searches based on the modification index. The results of the study showed that the proposed specification searches performed well when the number of noninvariant variables was relatively small and this performance improved as sample size increased and the size of group differences increased. When the number of noninvariant variables was relatively large, however, the method rarely succeeded in detecting the noninvariant items in the specification searches. Implications of the findings are discussed along with the limitations of the study.
Yoon et al. (Tue,) studied this question.