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Estimating correlations across tasks in experimental psychology.

Shanglin Yang1, Jeffrey N Rouder2

  • 1Department of Cognitive Science, University of California, Irvine, CA, 92697, USA.

Behavior Research Methods
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PubMed
Summary

Bayesian hierarchical models estimate individual differences by modeling measurement error. The LKJ prior offers the most accurate correlation estimates, while the SIW provides a faster, practical alternative for large models.

Keywords:
Bayesian analysisCorrelationsHierarchical modelsIndividual differencesPrior selection

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Area of Science:

  • Psychology
  • Statistics
  • Computational Modeling

Background:

  • Individual-difference psychology relies on understanding performance covariation across tasks.
  • Pearson correlation is scale-invariant but susceptible to measurement noise.
  • Bayesian hierarchical models (BHMs) directly model measurement error for improved accuracy.

Purpose of the Study:

  • Compare the robustness of three common priors (inverse Wishart [IW], scaled inverse Wishart [SIW], LKJ) in BHMs.
  • Assess the impact of prior specification and variable inclusion on correlation estimates.
  • Evaluate trade-offs between accuracy and computational speed.

Main Methods:

  • Simulation studies to evaluate prior performance under various conditions.
  • Visualization of prior distributions.
  • Analysis of posterior estimates for correlation recovery and bias.

Main Results:

  • All priors accurately recover correlations in low-dimensional settings when correctly specified.
  • Inverse Wishart (IW) priors exhibit significant bias when variance is misspecified.
  • LKJ priors are robust to scale misspecification and generally provide accurate estimates.
  • SIW priors show similar bias patterns to IW but less severe.
  • Adding variables stabilizes IW but causes shrinkage in SIW and LKJ.
  • LKJ priors are computationally intensive compared to IW and SIW.

Conclusions:

  • The LKJ prior is recommended for accurate correlation estimation in BHMs.
  • The SIW prior offers a computationally efficient alternative for large-scale analyses.
  • Prior choice significantly impacts BHM results, necessitating careful consideration.