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用于位置、尺度与形状（GAMLSS）的嫡系方法，旨在对任意结果变量实现无分布且简约的回归建模。我们通过可估计的变换函数替代此类模型中严格的参数分布设定，这不仅使模型摆脱分布假设约束，同时将线性或平滑模型项的数量限制在一对位置-尺度预测函数内。我们推导了连续型、离散型及随机删失观测的似然函数及其对应的得分函数。模型估计利用了现有的大量算法，包括约束极大似然法、原始GAMLSS算法以及变换树。所得模型中的参数可解释性与模型选择密切相关。我们提出应用一种新颖的最佳子集选择程序，以实现特别简洁的解释方式。所有技术均通过来自不同领域的应用案例进行动机阐述与实例验证，包括交叉与部分比例风险、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。