Generalized Structured Component Analysis (GSCA)
Generalized structured component analysis (GSCA; Hwang & Takane, 2004, 2014) is a component-based approach to structural equation modeling (SEM). It is a multivariate method that lets researchers specify and estimate path relationships between observed variables and components, that is, weighted sums of observed variables known as composite indicators. GSCA constructs these components from composite indicators so that they explain as much of the total variance of all dependent variables in the model as possible.
How GSCA Works
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 considers 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
| Step | What it involves |
|---|---|
| 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 strength 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), and Hwang et al. (2021) provide additional information on GSCA and its extensions. For example, Hwang et al. (2023) and Hwang et al. (2024) provide illustrative GSCA tutorials.
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 lets you define individual initial outer weights for every indicator in the PLS path model. For example, a particularly important indicator can obtain a +1 (e.g., when a strong positive relationship with the latent variable is assumed a priori), 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 visible 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.
Frequently Asked Questions
What is GSCA?
Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling. It estimates path relationships between observed variables and components, which are weighted sums of observed variables also known as composite indicators.
How does GSCA estimate model parameters?
GSCA uses an optimization procedure based on alternating least squares (ALS). This method iteratively estimates the weights linking composites to their indicators while considering the relationships between composites, so as to maximize overall model fit by minimizing unexplained variance in the indicators and dependent composites.
Which fit indices does GSCA use to assess model fit?
GSCA reports global fit indices such as FIT, adjusted FIT (AFIT), and the Goodness of Fit Index (GFI), which collectively indicate how well the model accounts for the observed data.
Can GSCA handle both reflective and formative measurement models?
Yes. GSCA is flexible enough to accommodate reflective and formative measurement models, as well as more complex structural relationships such as mediation.
How does SmartPLS determine the initial outer weights for GSCA?
By default, SmartPLS sets all initial outer weights to +1 (Standard). Alternatively, you can define individual initial outer weights for each indicator (Individual), for example assigning +1 to an indicator with an a priori assumed strong positive relationship with its construct and 0 to the others.
Can I change the number of iterations or the stop criterion for the GSCA algorithm?
No. These settings are not visible in SmartPLS 4. The algorithm permanently runs with a maximum of 3,000 iterations and a stop criterion of 10^-7^.
Related SmartPLS Methods
References
- Cho, G., & 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., & 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., & 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.
- Cho, G., Lee, J., Hwang, H., Sarstedt, M., & 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., & 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., & 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., & 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., & Choo, H. (2024). GSCA Pro—Free stand-alone software for structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 31(4), 696–711.
- Hwang, H., Cho, G., Jung, K., Falk, C. F., Flake, J. K., Jin, M. J., & 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., & 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., & Ringle, C. M. (2023). A primer on integrated generalized structured component analysis. European Business Review, 35(3), 261–284.
- Hwang, H., & Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69(1), 81–99.
- Hwang, H., & Takane, Y. (2014). Generalized structured component analysis: A component-based approach to structural equation modeling. Chapman & Hall.
- More literature ...
Cite correctly
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
