Random effect models have become a mainstream statistical technique over the last decades, and the same can be said for response transformation models such as the Box-Cox transformation. The latter ensures that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for the use of a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. In this vignette, we introduce a new R package, boxcoxmix, that aims to ensure the validity of a normal response distribution using the Box-Cox power transformation in the presence of random effects, thereby not requiring parametric assumptions on their distribution. This is achieved by extending the “Nonparametric Maximum Likelihood” towards a “Nonparametric Profile Maximum Likelihood” technique. The implemented techniques allow to deal with overdispersion as well as two–level data scenarios.

中文翻译：

---

随机效应和方差分量模型的响应变换

在过去的几十年里，随机效应模型已经成为一种主流的统计技术，对于诸如 Box-Cox 变换之类的响应变换模型来说也是如此。后者确保满足响应分布的正态性和同方差性假设，这是使用线性模型或线性混合模型的必要条件。然而，响应转换和同时包含随机效应的方法很少被开发和实施，并且迄今为止仅限于高斯随机效应。在这个小插图中，我们引入了一个新的 R 包 boxcoxmix，旨在确保在存在随机效应的情况下使用 Box-Cox 幂变换的正态响应分布的有效性，从而不需要对其分布进行参数化假设。这是通过将“非参数最大似然”扩展到“非参数轮廓最大似然”技术来实现的。实施的技术允许处理过度分散以及两级数据场景。