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

Youjin Sung1, Youngjin Han1, Yang Liu1

  • 1Department of Human Development and Quantitative Methodology, https://ror.org/047s2c258University of Maryland, College Park, MD, USA.

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|August 7, 2025
PubMed
Summary
This summary is machine-generated.

Conventional goodness-of-fit tests for common factor models may miss crucial misfit. Generalized residuals offer a flexible approach to detect issues in distributional and functional assumptions for better measurement model assessment.

Keywords:
common factor modelgeneralized residualsgoodness-of-fit assessment

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Conventional goodness-of-fit (GOF) assessments in common factor models primarily analyze mean and covariance structures.
  • This focus may overlook critical aspects of model misfit, potentially leading to inaccurate conclusions.
  • Generalized residuals, previously applied to categorical data, offer a pathway to more comprehensive fit evaluation.

Purpose of the Study:

  • To extend the theory of generalized residuals to general measurement models.
  • To propose novel fit test statistics for evaluating parametric assumptions in common factor models.
  • To enhance the detection of model misfit often missed by traditional GOF methods.

Main Methods:

  • Extension of generalized residual theory to general measurement models.
  • Development of fit test statistics targeting distributional and functional form assumptions.
  • Evaluation through simulation studies and empirical data analysis.

Main Results:

  • Generalized residuals effectively detect misfit in measurement models.
  • The proposed statistics identify issues often masked by conventional GOF testing.
  • Simulation and empirical results support the utility of the extended framework.

Conclusions:

  • Generalized residuals provide a powerful and flexible tool for assessing common factor model fit.
  • This approach offers a more thorough evaluation beyond traditional mean and covariance structures.
  • The findings suggest improved accuracy and reliability in measurement model assessment.