Model Evaluation in Generalized Structured Component Analysis Using Confirmatory Tetrad Analysis.

Ji Hoon Ryoo,Heungsun Hwang

doi:10.3389/fpsyg.2017.00916

Abstract

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.

Highlights

Generalized structured component analysis (GSCA; Hwang and Takane, 2004) is a component-based approach to structural equation modeling (SEM), where weighted composites or components of observed variables serve as proxies for latent variables
By conducting confirmatory tetrad analysis (CTA) for each model, we found that Model 0 includes 22 vanishing tetrads whereas Model 3 includes 15 vanishing tetrads, which shows that Model 3 is possibly tetradnested in Model 0
CTA can be used as a model evaluation in GSCA, we were unable to conclude that CTA is more applicable to GSCA than FIT, Adjusted FIT (AFIT), GFI, and SRMR because CTA does not work for non-tetrad nested models

Summary

Introduction

Generalized structured component analysis (GSCA; Hwang and Takane, 2004) is a component-based approach to structural equation modeling (SEM), where weighted composites or components of observed variables serve as proxies for latent variables. It estimates parameters via least squares (LS; Hwang and Takane, 2014) and does not require the multivariate normality assumption of indicators and seldom suffers from non-convergence, even in small samples. As will be shown shortly, GSCA expresses all sub-models into a single model formation, which in turn facilitates the derivation of a global optimization criterion that is consistently minimized to estimate parameters It can deal with more complex analyses (e.g., constrained multiple-group analysis, analysis of discrete indicators, etc.) in a straightforward and coherent manner, minimizing a single optimization criterion. We propose to apply confirmatory tetrad analysis

Methods

Results

Discussion

Conclusion