We present an illustrative study in which we use a mixture of regressions model to improve on an ill-fitting simple linear regression model relating log brain mass to log body mass for 100 placental mammalian species. The slope of the model is of particular scientific interest because it corresponds to a constant that governs a hypothesized allometric power law relating brain mass to body mass. We model these data using an anchored Bayesian mixture of regressions model, which modifies the standard Bayesian Gaussian mixture by pre-assigning small subsets of observations to given mixture components with probability one. These observations (called anchor points) break the relabeling invariance (or label-switching) typical of exchangeable models. In the article, we develop a strategy for selecting anchor points using tools from case influence diagnostics. We compare the performance of three anchoring methodson the allometric data and in simulated settings.

翻译：我们通过一项说明性研究，展示如何使用回归混合模型改进针对100种胎盘哺乳动物物种的脑质量对数与体重对数间拟合不佳的简单线性回归模型。该模型的斜率具有特殊科学意义，因为它对应一个控制脑质量与体重间假设异速生长幂律的常数。我们采用锚定贝叶斯回归混合模型对这些数据进行建模，该模型通过将少量观测值以概率1预先分配给特定混合成分，从而对标准贝叶斯高斯混合模型进行改进。这些观测值（称为锚点）打破了可交换模型典型的重新标记不变性（或称标签交换）。本文基于案例影响诊断工具开发了一种锚点选择策略，并在异速生长数据及模拟场景中比较了三种锚定方法的性能。