Penalized transformation models (PTMs) are a novel form of location-scale regression. In PTMs, the shape of the response's conditional distribution is estimated directly from the data, and structured additive predictors are placed on its location and scale. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. The transformation function is equipped with a smoothness prior that regularizes how much the estimated distribution diverges from the reference distribution. These models can be seen as a bridge between conditional transformation models and generalized additive models for location, scale and shape. Markov chain Monte Carlo inference for PTMs can be conducted with the No-U-Turn sampler and offers straightforward uncertainty quantification for the conditional distribution as well as for the covariate effects. A simulation study demonstrates the effectiveness of the approach. We apply the model to data from the Fourth Dutch Growth Study and the Framingham Heart Study. A full-featured implementation is available as a Python library.

翻译：惩罚变换模型（PTMs）是一种新型的位置-尺度回归方法。在PTMs中，响应变量条件分布的形状直接从数据中估计，并在其位置和尺度参数上设置结构化加性预测因子。该模型的核心是一个单调递增的变换函数，用于将响应分布与参考分布相关联。该变换函数配备了一种平滑先验，用于正则化估计分布偏离参考分布的程度。此类模型可视为条件变换模型与位置、尺度和形状广义加性模型之间的桥梁。利用无U型转弯采样器可对PTMs进行马尔可夫链蒙特卡洛推断，从而直接对条件分布及协变量效应进行不确定性量化。模拟研究验证了该方法的有效性。我们将模型应用于第四次荷兰生长研究和弗雷明汉心脏研究的数据。其完整功能实现已作为Python库提供。