Varying‐Thresholds Models: a Flexible Approach to Parametric and Nonparametric Regression
提出一类能估计因变量完整预测分布的模型，利用解释变量区分低值和高值的能力随阈值变化，线性版本推广了经典线性回归和序数回归，非参数版本基于随机森林，适用于预测和可视化变量效应。
Abstract A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable given a vector of explanatory variables . The models exploit that the strength of explanatory variables to distinguish between low and high values of the dependent variable may vary across the thresholds that are used to define low and high. Linear versions of the models are generalizations of classical linear regression models but also of widely used ordinal regression models. They allow to visualize the effect of explanatory variables in the form of parameter functions. More general models are based on efficient nonparametric approaches such as random forests, which are more flexible and are strong prediction tools. A general estimation method is given that can use all the estimation tools that have been proposed for binary regression, including selection methods like the lasso or elastic net. For linearly structured models, maximum likelihood estimates are derived. The usefulness of the models is illustrated by simulations and several real data set.