Abstract
Measurement equivalence/invariance (ME/I) is a condition that should be met before meaningful
comparisons of survey results across groups can be made. As an alternative to the likelihood ratio
test (LRT), the change in comparative fit index (DCFI) rules of thumb, and the modification index
(MI), this teaching note demonstrates the procedures for establishing bias-corrected (BC) bootstrap
confidence intervals for testing ME/I. Unlike the LRT and DCFI methods, which need a different
model estimation per item, the BC bootstrap confidence intervals approach can examine itemlevel
ME/I tests using a single model. This method greatly simplifies the search for an invariant item
as the reference indicator in the factor-ratio test. Also demonstrated here is how the factor-ratio
test and the list-and-delete method can be extended from the metric invariance test to the scalar
invariance test. Finally, the BC bootstrap confidence interval procedures for comparing uniqueness
variances, factor variances, factor covariances, and latent means across groups are shown.
Keywords
measurement equivalence/invariance, factor-ratio test, latent mean comparisons, bootstrapping,
structural equation modeling




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