Model evaluation in generalized structured component analysis using confirmatory tetrad analysis

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM). GSCA regards weighted composites or components of indicators as proxies for latent variables and estimates model parameter via least squares without resorting to a distributional assumption such as multivariate normality of indicators. As with other SEM approaches, model evaluation is a crucial procedure in GSCA that is used to examine whether a hypothesized model is consistent with the data in hand. However, the few descriptive measures of model evaluation available for GSCA are limited to evaluating models in a more confirmatory manner. This study integrates confirmatory tetrad analysis (CTA) into GSCA for model evaluation or comparison. Although CTA has been used in factor-based SEM as an inferential statistic, CTA is actually more compatible with GSCA because it is completely free of the multivariate normality assumption. Utilizing empirical data collected for 18,174 students' social skills in an early childhood longitudinal study of 2010-11 kindergarten cohort, we demonstrate the capability and applicability of CTA in GSCA and compare its performance with existing measures for GSCA.