Bayesian Analysis of ANOVA and Mixed Models on the Log-Transformed Response Variable

Enrico Fabrizi, Aldo Gardini, Carlo Trivisano

Research output: Contribution to journalArticlepeer-review

Abstract

The analysis of variance, and mixed models in general, are popular tools for analyzing experimental data in psychology. Bayesian inference for these models is gaining popularity as it allows to easily handle complex experimental designs and data dependence structures. When working on the log of the response variable, the use of standard priors for the variance parameters can create inferential problems and namely the non-existence of posterior moments of parameters and predictive distributions in the original scale of the data. The use of the generalized inverse Gaussian distributions with a careful choice of the hyper-parameters is proposed as a general purpose option for priors on variance parameters. Theoretical and simulations results motivate the proposal. A software package that implements the analysis is also discussed. As the log-transformation of the response variable is often applied when modelling response times, an empirical data analysis in this field is reported.
Original languageEnglish
Pages (from-to)619-641
Number of pages23
JournalPsychometrika
Volume86
DOIs
Publication statusPublished - 2021

Keywords

  • Generalized inverse Gaussian
  • Log-normal distribution
  • Markov chain Monte Carlo
  • Response times
  • Bayes Theorem
  • Markov Chains
  • Monte Carlo Method
  • Psychometrics
  • Analysis of Variance

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