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Abstract
Confirmatory factor analytic tests of measurement invariance (MI) require a referent indicator (RI) for model identification. Although the assumption that the RI is perfectly invariant across groups is acknowledged as problematic, the literature provides relatively little guidance for researchers to identify the conditions under which the practice is appropriate. Using simulated data, this study examined the effects of RI selection on both scale- and item-level MI tests. Results indicated that while inappropriate RI selection has little effect on the accuracy of conclusions drawn from scale-level tests of metric invariance, poor RI choice can produce very misleading results for item-level tests. As a result, group comparisons under conditions of partial invariance are highly susceptible to problems associated with poor RI choice.
Notes
1A literature search was conducted to identify studies that used the CFA framework to test real data for measurement invariance. Search terms were the following: factorial invariance, measurement invariance, measurement equivalence, and alpha, beta, and gamma change. Journals included in the search were Journal of Applied Psychology, Psychological Methods, and Educational and Psychological Measurement.
2We tested several different levels of simulated differences between the Group 1 and Group 2 data for two non-RI items. The .25 value chosen best illustrated the effects of these differences without encountering ceiling or floor effects in the resulting percentage of the analysis found to be significant.
∗p < .01.