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MCMC stopping rules in latent variable modelling.

Sunbeom Kwon1, Susu Zhang1, Hans Friedrich Köhn1

  • 1University of Illinois, Urbana-Champaign, Urbana, Illinois, USA.

The British Journal of Mathematical and Statistical Psychology
|October 10, 2024
PubMed
Summary
This summary is machine-generated.

Choosing the right Markov chain Monte Carlo (MCMC) stopping rule is crucial for accurate latent variable models. Single-chain approaches generally yield better item parameter accuracy than multiple-chain methods.

Keywords:
DINA modelGelman–Rubin diagnosticGeweke's diagnosticMCMC algorithmMonte Carlo standard errorbifactor IRT modeleffective sample size

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Area of Science:

  • Computational Statistics
  • Psychometrics
  • Educational Measurement

Background:

  • Bayesian analysis frequently employs the Markov chain Monte Carlo (MCMC) algorithm for posterior distribution sampling.
  • Accurate convergence diagnostics are essential for reliable MCMC results, particularly in complex latent variable models.

Purpose of the Study:

  • To compare the performance of various MCMC stopping rules within latent variable models.
  • To provide practical guidelines for determining optimal MCMC algorithm termination points.
  • To evaluate stopping rules in the context of the DINA and bifactor item response theory models.

Main Methods:

  • Simulation studies were conducted to assess four MCMC stopping rules: potential scale reduction factor (PSRF), fixed-width stopping rule, Geweke's diagnostic, and effective sample size.
  • Performance was evaluated based on item and person parameter accuracy in specified latent variable models.

Main Results:

  • Single-chain MCMC approaches demonstrated superior item parameter accuracy compared to multiple-chain approaches.
  • The impact of stopping rules on person parameter estimates was less pronounced than on item parameters.
  • Over-reliance on the univariate PSRF can lead to premature algorithm termination and biased item parameter estimates.

Conclusions:

  • Practitioners should exercise caution when using the univariate PSRF, carefully selecting cut-off values to avoid bias.
  • The study offers guidance for selecting appropriate MCMC stopping rules to enhance precision in latent variable modeling.
  • Understanding stopping rule performance is vital for reliable results in educational and psychological measurement.