This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online.

这篇文章的动机是分析农业田间试验的挑战，观察结果在连续尺度或零上为正值。可以使用两部分模型分析此类数据，其中分布是正分布和伯努利分布的混合。然而，传统的两部分模型不包括模型的两部分之间的任何依赖关系。由于当正部分的期望值较低时，零概率预计较高，反之亦然，本文介绍了依赖扩展的两部分模型。此外，这些扩展允许对中位数而不是均值进行建模，这在分布偏斜时具有优势。激励示例是一个不完整的块试验，比较了十种针对杂草的处理方法。Gamma 和对数正态分布用于正响应，尽管可以适应任何支持实数的密度。在交叉验证研究中，将提议的新模型相互比较，并与没有依赖关系的基线模型进行比较。通过模拟研究了模型性能和对先验选择的敏感性。对数正态分布中值的依赖扩展的两部分模型在预测中的均方误差方面表现最佳。本文随附的补充材料出现在网上。通过模拟研究了模型性能和对先验选择的敏感性。对数正态分布中值的依赖扩展的两部分模型在预测中的均方误差方面表现最佳。本文随附的补充材料出现在网上。通过模拟研究了模型性能和对先验选择的敏感性。对数正态分布中值的依赖扩展的两部分模型在预测中的均方误差方面表现最佳。本文随附的补充材料出现在网上。