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.

中文翻译：

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混合离散连续回归-基于权函数的新方法

在广泛的应用中，很难使用标准回归技术，因为响应可能由连续部分组成，但是以离散的附加响应类别（概率大于零）增加。先前的方法通常假定可以在给定协变量的情况下将两个部分的过程在结构上独立对待，这大大促进了估计。但是，对于当前的数据情况，这种简化的假设通常过于局限和可疑。为了解决这个问题，我们提出了一种新颖的方法来对离散连续响应进行混合建模，其中边界情况的概率基于连续部分的加权加权密度。权函数本身可能取决于协变量以及未知参数。我们讨论了不同类型的混合离散连续分布，并在贝叶斯和最大似然框架中考虑了推论方法。我们在模拟研究中仔细评估参数估计，然后使用新颖的零调整类型模型的特定实例将其应用于收入分配分析。