  A general class of models is proposed that is able to estimate the whole
predictive distribution of a dependent variable $Y$ given a vector of
explanatory variables $\xb$. 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. Simple 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 like 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.
