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：我们提出了一种针对位置、尺度与形状的广义可加模型（GAMLSS）的近亲方法，旨在实现任意结果变量的分布自由与简约回归建模。该方法用从数据中估计的变换函数取代了此类模型中严格的参数分布设定。这样做不仅使模型摆脱了对特定分布的依赖，还能将线性或平滑模型项的数量限制为一对位置-尺度预测函数。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相应的得分函数。模型估计利用了多种现有算法，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。所有技术方法均通过来自不同领域的应用案例进行了动机分析和示范，包括穿越比例风险与部分比例风险、复杂计数回归、非线性有序回归及生长曲线。所有分析均可借助R统计计算与图形系统的"tram"附加包进行复现。