Generalized Structured Component Analysis (GSCA)

Abstract

The generalized structured component analysis (GSCA; Hwang & Takane, 2004; Hwang & Takane, 2014) represents a component-based approach to structural equation modeling (SEM). GSCA s a multivariate method that allows you to specify and estimate path relationships between observed variables and components (i.e. weighted sums of observed variables). Observed variables that form components are referred to as composite indicators. GSCA constructs components from composite indicators such that the components can explain the total variances of all dependent variables in the model as much as possible.

Description

In the measurement model, GSCA requires the operationalization of composites as weighted combinations of their observed indicators. Additionally, the relationships between these composites must be explicitly specified in the structural model. To estimate the model parameters using the available empirical data, GSCA employs an optimization procedure based on alternating least squares (ALS). This method iteratively estimates the weights linking composites to their indicators and considering the relationships between composites to maximize the overall model fit, typically by minimizing the proportion of unexplained variance in the indicators and dependent composites. Model fit is assessed using indices such as FIT, adjusted FIT (AFIT), and the Goodness of Fit Index (GFI), which collectively measure how well the model accounts for the observed data. GSCA uses bootstrapping to test the significance of path relationships, providing a robust means of statistical inference. Notably, GSCA is very flexible, accommodating both reflective and formative measurement models, as well as more complex structural relationships like mediation.

Steps in GSCA:

Model Specification: Define the structural and measurement models, including the relationships between latent variables (structural model) and the relationships between latent variables and their indicators (measurement model).
Weight Estimation: GSCA uses alternating least squares (ALS) to estimate the weights for creating latent variables as linear combinations of their indicators.
Model Assessment: Evaluate the model using global fit indices (e.g., FIT, AFIT) and path coefficients. Check the significance of weights and path coefficients, often via bootstrapping.
Interpretation: Assess the strengths of the relationships in the structural model and the reliability of the measurement model.

For details on the GSCA algorithm and evaluation criteria, see Hwang and Takane (2004) and Hwang and Takane (2014). Authors such as Cho and Hwang (2024), Cho et al. (2020), Cho et al. (2022a, 2022b, 2022c), Cho et al. (2023), Hwang and Cho (2020), Hwang et al. (2020), Hwang et al. (2021), and Hwang et al. (2023) provide addtional information on GSCA and its extensions.

GSCA Algorithm Settings in SmartPLS

Initial Outer Weights

Standard: As the default (i.e., the SmartPLS settings), the initial outer weights are set to +1.
Individual: SmartPLS to define individual initial outer weights for every indicator in the PLS path model. For example, are particularly important indicator can obtain a +1 (e.g., when the strong a positive relationship with the latent variable is assumed a prior), while the other indicators of the same measurement model obtain a 0.

Maximum Iterations

This option to change the settings for running the GSCA algorithm is not visible in SmartPLS 4. The permanent setting is 3,000 iterations.

Stop Criterion

This option to change the settings for running the GSCA algorithm is not vible in SmartPLS 4. The permanent setting is 10^-7^.

GSCA Bootstrapping Settings in SmartPLS

For GSCA bootstrapping, see the different options that are available for bootstrapping in general in SmartPLS.

References

Cho, G., and Hwang, H. (2024). Generalized Structured Component Analysis Accommodating Convex Components: A Knowledge-Based Multivariate Method with Interpretable Composite Indexes. Psychometrika, 89(1), 241-266.
Cho, G., Hwang, H., Sarstedt, M., and Ringle, C. M. (2020). Cutoff Criteria for Overall Model Fit Indexes in Generalized Structured Component Analysis. Journal of Marketing Analytics, 8, 189-202.
Cho, G., Hwang, H., Sarstedt, M., and Ringle, C. M. (2022a). A Prediction-Oriented Specification Search Algorithm for Generalized Structured Component Analysis. Structural Equation Modeling: A Multidisciplinary Journal, 29(4), 611-619. https://doi.org/10.1080/10705511.2022.2057315
Cho, G., Lee, J., Hwang, H., Sarstedt, M., and Ringle, C. M. (2023). A Comparative Study of the Predictive Power of Component-based Approaches to Structural Equation Modeling. European Journal of Marketing, 57(6), 1641-1661.
Cho, G., Sarstedt, M., and Hwang, H. (2022b). A Comparative Evaluation of Factor- and Component-based Structural Equation Modelling Approaches Under (In)Correct Construct Representations. British Journal of Mathematical and Statistical Psychology, 75(2), 220-251.
Cho, G., Schlägel, C., Hwang, H., Choi, Y., Sarstedt, M., and Ringle, C. M. (2022c). Integrated Generalized Structured Component Analysis: On the Use of Model Fit Criteria in International Management Research. Management International Review, 62, 569-609.
Hwang, H., and Cho, G. (2020). Global Least Squares Path Modeling: A Full-Information Alternative to Partial Least Squares Path Modeling. Psychometrika, 85(4), 947-972.
Hwang, H., Cho, G., Jung, K., Falk, C. F., Flake, J. K., Jin, M. J., and Lee, S. H. (2021). An Approach to Structural Equation Modeling with Both Factors and Components: Integrated Generalized Structured Component Analysis. Psychological Methods, 26(3), 273-294.
Hwang, H., Sarstedt, M., Cheah, J. H., and Ringle, C. M. (2020). A Concept Analysis of Methodological Research on Composite-based Structural Equation Modeling: Bridging PLSPM and GSCA. Behaviormetrika, 47, 219–241.
Hwang, H., Sarstedt, M., Cho, G., Choo, H., and Ringle, C. M. (2023). A Primer on Integrated Generalized Structured Component Analysis. European Business Review, 35(3), 261-284.
Hwang, H., and Takane, Y. (2004). Generalized Structured Component Analysis. Psychometrika, 69(1), 81-99.
Hwang, H., and Takane, Y. (2014). Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling. Chapman & Hall: New York, NY.
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Please always cite the use of SmartPLS!

Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com