Abstract
Measurement invariance (MI) entails that measurements in different groups are comparable, and is a logical prerequisite when studying difference or change across groups. MI is commonly evaluated using multi-group structural equation modeling through a sequence of chi-square and chi-square-difference tests. However, under the conventional null hypothesis testing (NHT) one can never be confident enough to claim MI even when all test statistics are not significant. Equivalence testing (ET) has been recently proposed to replace NHT for studying MI. ET informs researchers a size of possible misspecification and allows them to claim that measurements are practically equivalent across groups if the size of misspecification is smaller than a tolerable value. Another recent advancement in studying MI is a projection-based method under which testing the cross-group equality of means of latent traits does not require the intercepts equal across groups. The purpose of this article is to introduce the key ideas of the two advancements in MI and present a newly developed R package equaltestMI for researchers to easily apply the two methods. A real data example is provided to illustrate the use of the package. It is advocated that researchers should always consider using the two methods whenever MI needs to be examined.
Highlights
Reliable and valid measurements are key to social and behavioral sciences
We introduced two recently proposed methods, combined the projection-based method and Equivalence testing (ET), implemented the new methods in an R package, and illustrated the use of the R package via a real data example
We believe that the development will contribute to the use of the cutting-edge methodology in substantive areas where Measurement invariance (MI) is needed in group comparison
Summary
Reliable and valid measurements are key to social and behavioral sciences. When studying difference across groups, an important concept is measurement invariance (MI) or equivalence (Mellenbergh, 1989; Meredith, 1993; Millsap, 2011; Kim et al, 2012), which entails that measurements in different groups are comparable. Equivalent measurements are logical prerequisites to the evaluation of substantive hypotheses, regardless of whether the interest is as simple as a test of mean difference between groups or as complex as a test for possible changes of theoretical constructs across groups (Vandenberg and Lance, 2000). The observed cross-group difference is not interpretable nor valid for quantifying the cross-group difference on the target attribute
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