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Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity.

Luna Fazio1, Paul-Christian Bürkner1

  • 1Department of Statistics, TU Dortmund University, Dortmund, Germany.

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Summary

This study introduces a new Bayesian framework for structural equation modeling (SEM) to better predict changes in psychological variables, including their variances. This method enhances the analysis of complex psychological theories and latent variables.

Keywords:
Bayesian inferenceStructural equation modelingdistributional regressionheteroscedasticitymeasurement invariance

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Area of Science:

  • Psychology
  • Statistics
  • Computational Social Science

Background:

  • Psychological theories often involve complex relationships between latent variables (e.g., personality, intelligence).
  • Traditional structural equation modeling (SEM) has limitations in modeling changes in the variances of these latent variables.
  • Existing methods inadequately support the modeling of latent variances as a function of other latent variables, known as latent heteroscedasticity.

Purpose of the Study:

  • To develop a novel Bayesian framework for Gaussian distributional SEM.
  • To extend the capabilities of SEM for modeling latent heteroscedasticity.
  • To provide a method that accounts for changes in both means and variances of latent variables.

Main Methods:

  • Development of a Bayesian framework for Gaussian distributional SEM.
  • Statistical simulation across four distinct model structures to validate the framework.
  • Application of the framework to a real-world case study in personality psychology.

Main Results:

  • The proposed Bayesian framework successfully models latent heteroscedasticity.
  • Statistical simulations demonstrated reliable inferences and efficient computation.
  • The framework proved applicable to real-world psychological research questions.

Conclusions:

  • The developed Bayesian distributional SEM framework significantly broadens the scope of feasible models for latent variable analysis.
  • This approach allows for a more comprehensive understanding of psychological theories by modeling both means and variances.
  • The method offers practical utility for researchers in psychology and related fields.