We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution formulating such a model by a transformation function, which in turn is estimated from data. Doing so not only makes the model distribution-free but also allows to limit the number of linear or smooth model terms to a pair of location-scale predictor functions. We derive the likelihood for continuous, discrete, and randomly censored observations, along with corresponding score functions. A plethora of existing algorithms is leveraged for model estimation, including constrained maximum-likelihood, the original GAMLSS algorithm, and transformation trees. Parameter interpretability in the resulting models is closely connected to model selection. We propose the application of a novel best subset selection procedure to achieve especially simple ways of interpretation. All techniques are motivated and illustrated by a collection of applications from different domains, including crossing and partial proportional hazards, complex count regression, non-linear ordinal regression, and growth curves. All analyses are reproducible with the help of the "tram" add-on package to the R system for statistical computing and graphics.

翻译：我们提出了一种广义可加模型的位置、尺度和形状（GAMLSS）的“近亲”，旨在对任意结果进行无分布且简约的回归建模。我们用一个从数据中估计得到的变换函数替代了传统的严格参数分布假设。这样做不仅使模型免于分布假设，还能将线性或光滑模型项的数量限制在一对位置-尺度预测函数上。我们推导了连续、离散和随机删失观测的似然函数及其对应的得分函数。利用一系列现有算法进行模型估计，包括约束最大似然法、原始GAMLSS算法和变换树。所得模型中的参数可解释性与模型选择紧密相关。我们提出应用一种新颖的最佳子集选择程序，以实现特别简单的解释方式。所有技术均通过来自不同领域的应用实例进行论证和说明，包括交叉和部分比例风险、复杂计数回归、非线性有序回归以及生长曲线。所有分析均可借助R统计计算与图形系统的“tram”附加包重现。