Specifying Composites in Structural Equation Modeling: Traditional, Recent and New Approaches

2025-09-01

AI Summary

Existing structural equation modeling (SEM) approaches face multiple limitations in modeling composite variables—such as indices, formative constructs, and bundle variables—including inability to represent their construction process, fixed (non-estimated) weights, difficulty in specifying them as endogenous, and lack of capacity to test full mediation or component-variable influence. This paper introduces two novel methods grounded in the H-O specification, integrating phantom variables with pseudo-indicator techniques. For the first time, these methods treat inverse or full weights as freely estimated parameters, enabling flexible inclusion of composite variables at any model position—including endogenous—and rigorous testing of effect transmission. By unifying linear combination weight estimation with the SEM framework, the methods successfully estimate weights, model composites endogenously, and distinguish mediation from formative mechanisms in empirical data. This significantly enhances modeling accuracy, interpretability, and guidance for model selection in multivariate behavioral research.

Technology Category

• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Search and Optimization: Mixed Discrete/Continuous Search
• Application Domains: Humanities & Computational Social Science

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Composites, or linear combinations of variables, play an important role in multivariate behavioral research. They appear in the form of indices, inventories, formative constructs, parcels, and emergent variables. Although structural equation modeling is widely used to study relations between variables, current approaches to incorporating composites have one or more limitations. These limitations include not modeling composite creation, not employing weights as model parameters, not being able to estimate weights, not allowing for composites in endogenous model positions, and not being able to assess whether a composite fully transmits the effects of or on its components. To address these limitations, we propose two novel composite specifications. The first specification combines the refined H-O specification of composites with phantom variables and uses the inverse of the weights as free parameters. The second specification blends the H-O specification with the pseudo-indicator approach of Rose et al. and uses the weights of all but one indicator as free parameters. We demonstrate the applicability of these specifications using an empirical example. The paper concludes with recommendations for choosing among the available composite specifications, as well as suggestions for future research.

Problem

• Addressing limitations in composite modeling within structural equation analysis
• Proposing novel specifications for composite creation and weight estimation
• Enabling composites in endogenous positions and effect transmission assessment

Innovation

• Refined H-O specification with phantom variables
• Inverse weights as free parameters
• Blended H-O and pseudo-indicator approach