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PC priors for residual correlation parameters in one-factor mixed models
Statistical Methods & Applications ( IF 1 ) Pub Date : 2019-11-21 , DOI: 10.1007/s10260-019-00501-w
Massimo Ventrucci , Daniela Cocchi , Gemma Burgazzi , Alex Laini

Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models, discussing several correlation structures for the within group residuals. All the considered group models are parametrized in terms of a single correlation (hyper-)parameter, controlling the shrinkage towards the case of independent residuals (iid). We derive a penalized complexity (PC) prior for the correlation parameter of a generic group model. This prior has desirable properties from a practical point of view: (i) it ensures appropriate shrinkage to the iid case; (ii) it depends on a scaling parameter whose choice only requires a prior guess on the proportion of total variance explained by the grouping factor; (iii) it is defined on a distance scale common to all group models, thus the scaling parameter can be chosen in the same manner regardless the adopted group model. We show the benefit of using these PC priors in a case study in community ecology where different group models are compared.



中文翻译:

一元混合模型中残差相关参数的PC先验

线性回归残差的缺乏独立性促使在许多应用领域中使用随机效应模型。我们从单向方差模型开始,并将其扩展到一类单因子贝叶斯混合模型,讨论组内残差的几种相关结构。所有考虑的组模型均根据单个相关性(超)参数进行参数化,控制朝着独立残差(iid)的方向收缩。我们先得出通用组模型的相关参数的惩罚复杂度(PC)。从实践的角度来看,该先有技术具有理想的性能:(i)确保对iid盒进行适当的收缩;(ii)取决于缩放参数,其选择仅需要事先对由分组因子解释的总方差的比例进行猜测;(iii)它是在所有组模型通用的距离尺度上定义的,因此无论采用哪种组模型,都可以相同的方式选择尺度参数。我们在社区生态学的案例研究中显示了使用这些PC先验的好处,该案例研究比较了不同的群体模型。

更新日期:2019-11-21
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