It Matters: Reference Indicator Selection in Measurement Invariance Tests

Abstract

Conventional approaches for selecting a reference indicator (RI) could lead to misleading results in testing for measurement invariance (MI). Several newer quantitative methods have been available for more rigorous RI selection. However, it is still unknown how well these methods perform in terms of correctly identifying a truly invariant item to be an RI. Thus, Study 1 was designed to address this issue in various conditions using simulated data. As a follow-up, Study 2 further investigated the advantages/disadvantages of using RI-based approaches for MI testing in comparison with non-RI-based approaches. Altogether, the two studies provided a solid examination on how RI matters in MI tests. In addition, a large sample of real-world data was used to empirically compare the uses of the RI selection methods as well as the RI-based and non-RI-based approaches for MI testing. In the end, we offered a discussion on all these methods, followed by suggestions and recommendations for applied researchers.

Selecting scaling indicators in structural equation models (sems).

“…Some references advise selecting the most reliable and valid indicator of the latent variable as the scaling indicator while warning of the adverse consequences of choosing an indicator that is not invariant (e.g., Bollen & Curran, 2006, p. 255). Others even suggest that scaling indicators are sometimes chosen at random (e.g., Thompson et al, 2021, p. 6).…”

“…The results of these tests inform the decision regarding which indicator should be chosen as the scaling indicator. One option, called Min χ 2 by Thompson et al (2021), is to choose that indicator with the smallest LR χ 2 test statistic (Woods, 2009). The method allows the LR χ 2 to be statistically significant as long as it is the smallest LR χ 2 .…”

“…The method allows the LR χ 2 to be statistically significant as long as it is the smallest LR χ 2 . Another option, termed MaxL by Thompson et al (2021), is similar except it chooses an indicator with a nonsignificant LR χ 2 and the largest standardized loading (Lopez Rivas et al, 2009; Meade & Wright, 2012; Stark et al, 2006). Variants of these methods that contain corrections for multiple significance testing are available (e.g., Raykov et al, 2013).…”

Mental Health of Refugee and Non-refugee Migrant Young People in European Secondary Education: The Role of Family Separation, Daily Material Stress and Perceived Discrimination in Resettlement

“…Seventh, testing for measurement invariance between groups, we consistently used the first item of the measure as the reference indicator for the latent variable. Future work, however, could engage in a more nuanced consideration of the reference indicator selection when testing for measurement invariance (e.g., Thompson et al, 2021). Lastly, the outcomes and conclusions presented apply only to the countries in which the data for this study were collected.…”

An Italian adaptation of the Child-Adolescent Perfectionism Scale: Testing measurement invariance across grade levels and exploring associations with academic achievement

“…Several studies have indeed shown that using items that are not invariant across groups could lead to misleading results [62,63]. The best possible invariant indicators were therefore identified by adopting the Minχ 2 approach, as recommended by Thompson, Song, Shi & Liu [64]. We first fitted a baseline model, in which factor loadings and intercepts were all constrained to be equal across groups.…”