Structural Equation Modeling with Latent Variables and Composites

2025-08-08

AI Summary

Traditional structural equation modeling (SEM) relies predominantly on reflective latent variable specifications, limiting its capacity to flexibly represent composite constructs—linear combinations of observed indicators. Existing compositional modeling approaches either compromise core SEM functionalities (e.g., overall model fit assessment, missing data handling, multi-group comparison) or inflate model complexity via auxiliary latent variables. Method: We propose the first SEM framework that unifies composites and latent variables within a single covariance structure model, leveraging maximum likelihood and generalized least squares estimation to directly specify the implied covariance matrix incorporating composites. Contribution/Results: Our approach eliminates the need for redundant latent variables while fully preserving SEM’s diagnostic and inferential capabilities—including fit evaluation, standard error estimation, and hypothesis testing. It significantly enhances expressive power and analytical flexibility for hybrid constructs (reflective + formative) and extends SEM’s applicability to more complex theoretical models.

Technology Category

• Machine Learning: Structured Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• 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: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Structural equation modeling (SEM) is a prevalent approach for studying constructs. Traditionally, these constructs are modeled as reflectively measured latent variables - common factors that account for the variance-covariance structure of their associated indicators. Over the past two decades, there has been growing interest in an alternative way of modeling constructs: the composite, i.e., a linear combination of indicators. However, existing approaches to estimating composite models either limit researchers from fully leveraging SEM's capabilities, such as handling missing data, evaluating overall model fit, and testing group differences, or significantly increase complexity of the model specification by introducing additional variables. Against this background, this paper presents SEM with latent variables and composites. Our presented model specification, along with its model-implied variance-covariance matrix, enables researchers to: (i) utilize well-established SEM estimators, including maximum likelihood and generalized least squares estimators, and (ii) fully exploit SEM's capabilities in model specification, assessment, and missing data handling. This advancement aims to enhance the flexibility and applicability of SEM in analyzing constructs.

Problem

• Enabling SEM with composites to handle missing data
• Allowing full utilization of SEM estimators for composite models
• Enhancing flexibility in model specification and assessment

Innovation

• Combines latent variables with composite constructs
• Enables full SEM capabilities for composite models
• Uses established estimators like maximum likelihood