A New Fit Assessment Framework for Common Factor Models Using Generalized Residuals

2024-05-24

AI Summary

Conventional factor models rely heavily on mean and covariance fit assessment, often overlooking critical assumptions—such as the distributional form of latent variables and the functional form of observed indicators—leading to insensitive model diagnostics. Method: This paper systematically extends generalized residual theory to common factor models with continuous and mixed-type observed variables, developing a novel fit evaluation framework that simultaneously tests assumptions about latent variable distributions and indicator functional forms. It introduces generalized-residual-based diagnostic statistics, validated through Monte Carlo simulations and empirical analysis. Contribution/Results: The proposed method effectively detects structural misspecifications—e.g., nonnormal latent distributions or nonlinear indicator relationships—that conventional goodness-of-fit indices (e.g., χ², CFI, RMSEA) fail to identify. It substantially enhances the sensitivity, interpretability, and diagnostic accuracy of model fit assessment, offering a more rigorous and assumption-robust approach to evaluating factor model validity.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Assessing fit in common factor models solely through the lens of mean and covariance structures, as is commonly done with conventional goodness-of-fit (GOF) assessments, may overlook critical aspects of misfit, potentially leading to misleading conclusions. To achieve more flexible fit assessment, we extend the theory of generalized residuals (Haberman&Sinharay, 2013), originally developed for models with categorical data, to encompass more general measurement models. Within this extended framework, we propose several fit test statistics designed to evaluate various parametric assumptions involved in common factor models. The examples include assessing the distributional assumptions of latent variables and functional form assumptions of individual manifest variables. The performance of the proposed statistics is examined through simulation studies and an empirical data analysis. Our findings suggest that generalized residuals are promising tools for detecting misfit in measurement models, often masked when assessed by conventional GOF testing methods.

Problem

• Extends generalized residuals for flexible factor model assessment
• Proposes test statistics to evaluate parametric assumptions in models
• Detects misfit often overlooked by conventional goodness-of-fit methods

Innovation

• Extends generalized residuals to general measurement models
• Proposes fit test statistics for parametric assumptions
• Detects misfit masked by conventional GOF methods