title: What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups.
abstract: Scalar invariance is an unachievable ideal that in practice can only be approximated; often using potentially questionable approaches such as partial invariance based on a stepwise selection of parameter estimates with large modification indices. Study 1 demonstrates an extension of the power and flexibility of the alignment approach for comparing latent factor means in large-scale studies (30 OECD countries, 8 factors, 44 items, N = 249,840), for which scalar invariance is typically not supported in the traditional confirmatory factor analysis approach to measurement invariance (CFA-MI). Importantly, we introduce an alignment-within-CFA (AwC) approach, transforming alignment from a largely exploratory tool into a confirmatory tool, and enabling analyses that previously have not been possible with alignment (testing the invariance of uniquenesses and factor variances/covariances; multiple-group MIMIC models; contrasts on latent means) and structural equation models more generally. Specifically, it also allowed a comparison of gender differences in a 30-country MIMIC AwC (i.e., a SEM with gender as a covariate) and a 60-group AwC CFA (i.e., 30 countries × 2 genders) analysis. Study 2, a simulation study following up issues raised in Study 1, showed that latent means were more accurately estimated with alignment than with the scalar CFA-MI, and particularly with partial invariance scalar models based on the heavily criticized stepwise selection strategy. In summary, alignment augmented by AwC provides applied researchers from diverse disciplines considerable flexibility to address substantively important issues when the traditional CFA-MI scalar model does not fit the data. (PsycINFO Database Record
authors.affiliation: Institute of Positive Psychology and Education, Australian Catholic University.
authors.forename: Herbert W
authors.initials: HW
authors.lastname: Marsh
authors.affiliation: Institute of Positive Psychology and Education, Australian Catholic University.
authors.forename: Jiesi
authors.initials: J
authors.lastname: Guo
authors.affiliation: Institute of Positive Psychology and Education, Australian Catholic University.
authors.forename: Philip D
authors.identifier: 0000-0002-4604-8566
authors.initials: PD
authors.lastname: Parker
authors.affiliation: Hector Research Institute of Education Sciences and Psychology, University of Tübingen.
authors.forename: Benjamin
authors.identifier: 0000-0001-9868-8322
authors.initials: B
authors.lastname: Nagengast
authors.affiliation: Muthén & Muthén.
authors.forename: Tihomir
authors.initials: T
authors.lastname: Asparouhov
authors.affiliation: Muthén & Muthén.
authors.forename: Bengt
authors.initials: B
authors.lastname: Muthén
authors.affiliation: Institute of Positive Psychology and Education, Australian Catholic University.
authors.forename: Theresa
authors.identifier: 0000-0001-8868-2242
authors.initials: T
authors.lastname: Dicke
mesh_terms: D003627:Data Interpretation, Statistical; D005163:Factor Analysis, Statistical; D006801:Humans; D015233:Models, Statistical; D011584:Psychology / Q000379:methods*