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

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. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11336-021-09769-y.