Advances in Measurement Invariance and Mean Comparison of Latent Variables: Equivalence Testing and A Projection-Based Approach

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 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.

The Sense of Belonging to the Country: Integrative Relationships and Spatiotemporal Commitment

“…Confirmatory factor analysis was conducted using “lavaan” 0.6-6 ( Rosseel, 2012 ) for R (R Project for Statistical Computing, RRID:SCR_001905 ). Model invariance tests were performed using “equaltestMI” 0.6.0 ( Jiang et al, 2017 ) for R (R Project for Statistical Computing, RRID:SCR_001905 ). Testing invariance focused on the weak (metric), strong (scalar), and strict (residual) equivalence of the model across subgroups (e.g., Putnick and Bornstein, 2016 ).…”

Faking Effects on the Factor Structure of a Quasi-Ipsative Forced-Choice Personality Inventory

“…The invariance or equivalence of the measure establishes that measures in two or more groups or in two or more conditions are comparable (Millsap, 2011;Jiang et al, 2017). In the current study, the analysis of measure equivalence was conducted in order to determine if the the Five Factor measure evaluated with a quasiipsative FC inventory changes depending on whether the personality inventory is completed under honest or faking instructions.…”

Failure to Detect Metric Measurement Non-Invariance: How Manifest Residual Variances, Indicator Communalities, and Sample Size affect the χ2-Test Statistic

“…When the χ 2 -difference test is not significant, the metric MI model is retained. A detailed description of this process can be found in, e.g, Jiang, Mai, and Yuan (2017). In this contribution, we only consider the metric MI model, so we do not elaborate on further MI levels.…”