AUTHOR=Guenole Nigel , Brown Anna TITLE=The consequences of ignoring measurement invariance for path coefficients in structural equation models JOURNAL=Frontiers in Psychology VOLUME=5 YEAR=2014 URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2014.00980 DOI=10.3389/fpsyg.2014.00980 ISSN=1664-1078 ABSTRACT=

We report a Monte Carlo study examining the effects of two strategies for handling measurement non-invariance – modeling and ignoring non-invariant items – on structural regression coefficients between latent variables measured with item response theory models for categorical indicators. These strategies were examined across four levels and three types of non-invariance – non-invariant loadings, non-invariant thresholds, and combined non-invariance on loadings and thresholds – in simple, partial, mediated and moderated regression models where the non-invariant latent variable occupied predictor, mediator, and criterion positions in the structural regression models. When non-invariance is ignored in the latent predictor, the focal group regression parameters are biased in the opposite direction to the difference in loadings and thresholds relative to the referent group (i.e., lower loadings and thresholds for the focal group lead to overestimated regression parameters). With criterion non-invariance, the focal group regression parameters are biased in the same direction as the difference in loadings and thresholds relative to the referent group. While unacceptable levels of parameter bias were confined to the focal group, bias occurred at considerably lower levels of ignored non-invariance than was previously recognized in referent and focal groups.