Zhang Boyao, Griesbach Colin, Bergherr Elisabeth
Chair of Spatial Data Science and Statistical Learning, Georg-August-Unversität Göttingen, Göttingen, Germany.
Int J Biostat. 2022 Dec 2;20(1):123-141. doi: 10.1515/ijb-2022-0029. eCollection 2024 May 1.
Selection of relevant fixed and random effects without prior choices made from possibly insufficient theory is important in mixed models. Inference with current boosting techniques suffers from biased estimates of random effects and the inflexibility of random effects selection. This paper proposes a new inference method "BayesBoost" that integrates a Bayesian learner into gradient boosting with simultaneous estimation and selection of fixed and random effects in linear mixed models. The method introduces a novel selection strategy for random effects, which allows for computationally fast selection of random slopes even in high-dimensional data structures. Additionally, the new method not only overcomes the shortcomings of Bayesian inference in giving precise and unambiguous guidelines for the selection of covariates by benefiting from boosting techniques, but also provides Bayesian ways to construct estimators for the precision of parameters such as variance components or credible intervals, which are not available in conventional boosting frameworks. The effectiveness of the new approach can be observed via simulation and in a real-world application.
在混合模型中，在可能缺乏足够理论依据的情况下，选择相关的固定效应和随机效应而不进行事先选择非常重要。当前的增强技术在进行推断时，会出现随机效应估计有偏差以及随机效应选择缺乏灵活性的问题。本文提出了一种新的推断方法“贝叶斯增强”，该方法将贝叶斯学习器集成到梯度增强中，同时在线性混合模型中估计和选择固定效应和随机效应。该方法引入了一种新颖的随机效应选择策略，即使在高维数据结构中，也能在计算上快速选择随机斜率。此外，新方法不仅通过受益于增强技术克服了贝叶斯推断在为协变量选择提供精确且明确指导方面的缺点，还提供了贝叶斯方法来构建诸如方差分量或可信区间等参数精度的估计量，而这些在传统增强框架中是不可用的。通过模拟和实际应用可以观察到新方法的有效性。
