Finding clusters of groups with measurement invariance: Unraveling intercept non-invariance with mixture multigroup factor analysis

Comparisons of latent constructs across groups are ubiquitous in behavioral research and, nowadays, often numerous groups are involved. Measurement invariance of the constructs across the groups is imperative for valid comparisons and can be tested by multigroup factor analysis. Metric invariance (invariant factor loadings) often holds, whereas scalar invariance (invariant intercepts) is rarely supported across many groups. Scalar invariance is a prerequisite for comparing latent means, however. One may inspect group-specific intercepts to pinpoint non-invariances, but this is a daunting task in case of many groups. This paper presents mixture multigroup factor analysis (MMG-FA) for clustering groups based on their intercepts. Clusters of groups with scalar invariance are obtained by imposing cluster-specific intercepts and invariant loadings whereas unique variances, factor means and factor (co)variances can differ between groups. Thus, MMG-FA ties down the number of intercepts to inspect and generates clusters of groups wherein latent means can be validly compared.