Abstract
Generalized structured component analysis (GSCA) is a technically well-established approach to component-based structural equation modeling that allows for specifying and examining the relationships between observed variables and components thereof. GSCA provides overall fit indexes for model evaluation, including the goodness-of-fit index (GFI) and the standardized root mean square residual (SRMR). While these indexes have a solid standing in factor-based structural equation modeling, nothing is known about their performance in GSCA. Addressing this limitation, we present a simulation study’s results, which confirm that both GFI and SRMR indexes distinguish effectively between correct and misspecified models. Based on our findings, we propose rules-of-thumb cutoff criteria for each index in different sample sizes, which researchers could use to assess model fit in practice.
Highlights
Component-based structural equation modeling (SEM) is a general multivariate framework for evaluating the relationships between observed variables and their weighted composites
Our analysis aims to assess whether the goodness-of-fit index (GFI) and SRMR differentiate between correct and misspecified models and to identify cutoff values that minimize Types I and II error rates under different conditions
Our simulation study suggests that GFI and SRMR are effective in discriminating between correct and misspecified component models when estimating the models using Generalized structured component analysis (GSCA)
Summary
Component-based structural equation modeling (SEM) is a general multivariate framework for evaluating the relationships between observed variables and their weighted composites (i.e., components). This SEM domain differs from factor-based SEM used to investigate the relationships between observed variables and common factors rather than components (e.g., Jöreskog and Wold 1982; Rigdon 2012; Tenenhaus 2008).. While PLSPM and GSCA share the same aim, which is estimating relationships between observed variables and Rigdon et al (2017) offer a detailed discussion of the conceptual differences between factor-based and component-based SEM and their implications for assessing the methods’ relative merits; see Rhemtulla et al (2020) and Petter (2018)
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