Abstract

Linear mixed models are standard models to analyze repeated measures or longitudinal data under the assumption of normality for random components in the model. Although the mixed models are often used in both frequentist and Bayesian inference, their evaluation from robustness perspective has not received as much attention in Bayesian inference as in frequentist. The aim of this study is to evaluate Bayesian tests in mixed models for their robustness to normality. We use a general class of exponential power distributions, EPD, and particularly focus on testing fixed effects in longitudinal models. The EPD class contains both light and heavy tailed distributions, with normality as a special case. Further, we consider a new paradigm of Bayesian testing decision theory where the hypotheses are formulated as a mixture model, with subsequent testing based on the posterior distribution of the mixture weights. It is shown that the EPD class provides a flexible alternative to normality assumption, particularly in the presence of outliers. Real data applications are also demonstrated.

摘要

线性混合模型是在模型中随机分量的正态假设下分析重复测量或纵向数据的标准模型。尽管混合模型经常用于常客推理和贝叶斯推理，但从鲁棒性角度进行的评估在贝叶斯推理中并没有像常客推理那样受到关注。本研究的目的是评估混合模型中的贝叶斯检验对正态性的稳健性。我们使用一类通用的指数功率分布 EPD，并特别关注纵向模型中的固定效应测试。EPD 类包含轻尾分布和重尾分布，正态性是一个特例。此外，我们考虑了贝叶斯测试决策理论的新范式，其中假设被表述为混合模型，随后基于混合权重的后验分布进行测试。结果表明，EPD 类为正态假设提供了一种灵活的替代方案，特别是在存在异常值的情况下。还演示了真实的数据应用程序。