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.

方差分析和一般的混合模型是分析心理学实验数据的流行工具。这些模型的贝叶斯推理越来越受欢迎，因为它可以轻松处理复杂的实验设计和数据依赖结构。在处理响应变量的对数时，对方差参数使用标准先验可能会产生推理问题，即在数据的原始规模中不存在参数的后验矩和预测分布。提出使用广义逆高斯分布并仔细选择超参数作为方差参数先验的通用选项。理论和模拟结果激发了该提议。还讨论了实现该分析的软件包。由于在对响应时间建模时经常应用响应变量的对数变换，因此报告了该领域的经验数据分析。