Mixed discrete‐continuous regression—A novel approach based on weight functions

In a wide range of applications, standard regression techniques are hard to apply because the responses may consist of a continuous part but augmented with a discrete number of additional response categories with probability greater than zero. Previous methods often assume that the process of both parts can be treated structurally independent given covariates which facilitates estimation considerably. However, this simplifying assumption is often too restrictive and questionable for the data situation at hand. To address this, we propose a novel approach for modelling mixed discrete‐continuous responses where the probabilities of the boundary cases are based on integrated weighted densities of the continuous part. The weight functions themselves may depend on covariates as well as unknown parameters. We discuss different types of mixed discrete‐continuous distributions and consider inferential methods in a Bayesian and maximum likelihood framework. We evaluate parameter estimation carefully in simulation studies before applying them to the analysis of income distributions using a specific instance of the novel zero‐adjusted‐type model.