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

TL;DR

This paper introduces an extended framework of generalized residuals for more comprehensive fit assessment of common factor models, revealing misfits overlooked by traditional methods through simulation and empirical analysis.

Contribution

It extends generalized residual theory to broader measurement models and proposes new fit test statistics for assessing model assumptions.

Findings

Generalized residuals effectively detect model misfit.

Proposed tests outperform traditional GOF methods in simulations.

Empirical analysis confirms the utility of the new approach.

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.