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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Small sample structural equation modeling (SEM) often faces estimation challenges like convergence failures and unstable parameters.
  • Existing research compares SEM solutions to unconstrained maximum likelihood (ML), but less is known about direct comparisons between different solutions.

Purpose of the Study:

  • To compare the performance of constrained ML, Bayesian methods (MCMC), and fixed reliability single indicator (SI) approaches for small sample SEM.
  • To evaluate the impact of parameterizations, constraints, and priors on estimation quality and parameter stability.

Main Methods:

  • A simulation study was conducted to compare the accuracy and stability of parameter estimates across different SEM approaches.
  • Bayesian methods utilized Markov chain Monte Carlo (MCMC) techniques with various prior distributions.

Main Results:

  • Bayesian methods excelled in accuracy under low reliability conditions, surpassing constrained ML and fixed SI approaches.
  • Constrained ML performed well under high reliability conditions.
  • Bayesian and constrained ML methods demonstrated acceptable Type I error rates, while fixed SI approaches showed undercoverage and inflated error rates.
  • Bayesian estimates showed stability even with slightly inaccurate prior information.

Conclusions:

  • The choice of analytical method significantly impacts small sample SEM results, particularly concerning parameter accuracy and error rates.
  • Bayesian methods offer a robust alternative for small sample SEM, especially when dealing with low reliability.
  • Fixed reliability SI approaches should be used with caution due to their tendency for inflated Type I error rates.