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Bayesian mixed models are popular in psychology. Using generalized inverse Gaussian priors for variance parameters solves problems with log-transformed data, enabling valid inference on the original response scale.

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Area of Science:

  • Psychology
  • Statistics
  • Computational Statistics

Background:

  • Analysis of variance (ANOVA) and mixed models are widely used in psychological research.
  • Bayesian inference offers advantages for complex experimental designs and data structures.
  • Log-transforming response variables can lead to issues with standard priors on variance parameters, causing non-existent posterior moments.

Purpose of the Study:

  • To address inferential challenges with standard priors on variance parameters in Bayesian mixed models when using log-transformed response variables.
  • To propose a robust and generalizable prior distribution for variance parameters.
  • To facilitate accurate Bayesian inference on the original data scale.

Main Methods:

  • Utilizing generalized inverse Gaussian distributions as priors for variance parameters.
  • Careful selection of hyper-parameters for the proposed priors.
  • Theoretical derivations and simulation studies to validate the approach.
  • Development of accompanying software for implementation.

Main Results:

  • The proposed generalized inverse Gaussian priors resolve issues of non-existent posterior moments and predictive distributions in the original data scale.
  • Theoretical and simulation results confirm the effectiveness of the proposed method.
  • A practical software package is available for applying the analysis.

Conclusions:

  • Generalized inverse Gaussian distributions provide a suitable and general solution for priors on variance parameters in Bayesian mixed models with log-transformed data.
  • This approach enables valid posterior inference and prediction on the original response scale, particularly relevant for response time data.
  • The developed methodology and software enhance the application of Bayesian mixed models in psychological research.