Bayesian Penalized Transformation Models Structured Additive Location-Scale Regression for Arbitrary Conditional Distributions
该研究提出一类半参数位置尺度回归模型，直接从数据估计响应变量的条件分布，并通过结构化加性预测器刻画位置和尺度。适合需要灵活建模条件分布且关注不确定性的统计与计量研究者。
Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response’s conditional distribution directly from the data, and model the location and scale through structured additive predictors. 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. PTMs 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 offers straightforward uncertainty quantification for the conditional distribution as well as for the covariate effects. A simulation study demonstrates the effectiveness of the approach and includes comparisons to many alternative methods. Applications to the Fourth Dutch Growth Study and the Framingham Heart Study illustrate the usage and practical utility. A full-featured implementation is available as a Python library. Supplementary material for this article is available online.Keywords: Distributional regression, Conditional distribution function, Transformation model, Bayesian transformation model, Penalized spline, Monotonically increasing penalized spline, Markov chain Monte Carlo