Abstract
The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA framework, methods have been proposed to trace such non-invariant items, but these methods have some disadvantages in that they require researchers to run a multitude of analyses and in that they imply assumptions that are often questionable. In this paper, we propose an alternative strategy which builds on clusterwise simultaneous component analysis (SCA). Clusterwise SCA, being an exploratory technique, assigns the groups under study to a few clusters based on differences and similarities in the component structure of the items, and thus based on the covariance matrices. Non-invariant items can then be traced by comparing the cluster-specific component loadings via congruence coefficients, which is far more parsimonious than comparing the component structure of all separate groups. In this paper we present a heuristic for this procedure. Afterwards, one can return to the multigroup CFA framework and check whether removing the non-invariant items or removing some of the equality restrictions for these items, yields satisfactory invariance test results. An empirical application concerning cross-cultural emotion data is used to demonstrate that this novel approach is useful and can co-exist with the traditional CFA approaches.
Highlights
IntroductionTo assess the quality of psychological instruments (e.g., surveys, questionnaires, etc.), confirmatory factor analysis (CFA; Lawley and Maxwell, 1962) is often applied
To assess the quality of psychological instruments, confirmatory factor analysis (CFA; Lawley and Maxwell, 1962) is often applied
To detect non-invariant items, we propose to apply the following procedure5, which consists of four steps: 1. Rotate cluster-specific loadings toward the postulated factor structure: Since clusterwise simultaneous component analysis (SCA)-P solutions have rotational freedom, the comparability of the cluster-specific component loadings is optimized by orthogonally rotating them toward a target matrix that corresponds to the factor model specification that was used in the measurement invariance testing
Summary
To assess the quality of psychological instruments (e.g., surveys, questionnaires, etc.), confirmatory factor analysis (CFA; Lawley and Maxwell, 1962) is often applied. CFA tests whether or not a particular latent variable model, specifying which latent variables (i.e., factors) are measured by which items, complies with the observed item scores. When the instrument is used among several groups, quality testing becomes more intricate, as the equality of different aspects of the latent variable model has to be verified (i.e., the configuration and size of the loadings of the items on the factors, item intercepts, unique variances), before the factor scores of the different groups can be compared meaningfully. We propose a new procedure to detect which items violate configural and/or weak measurement invariance. The novel procedure is rooted in component analysis and circumvents some disadvantages of the existing solutions in the multigroup CFA framework
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