Regression models describing the joint distribution of multivariate responses conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models are the rather simplistic assumptions often made, for example, a constant dependence structure not varying with covariates or the restriction to linear dependence between the responses. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood-based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, it scales well-beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the benefits in a trivariate analysis of childhood undernutrition and demonstrate empirically that complex truly multivariate data-generating processes can be inferred from observations.

中文翻译：

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多元条件转换模型

描述以协变量信息为条件的多变量响应联合分布的回归模型已成为当代回归分析的一个重要方面。然而，此类模型的限制是通常做出的相当简单的假设，例如，不随协变量变化的恒定依赖结构或响应之间线性依赖的限制。我们提出了一个多元条件转换模型的通用框架，它克服了这些限制，并以一种易于处理和可解释但灵活的方式描述了整个分布，条件是协变量的非线性效应。该框架可以嵌入到基于似然性的推理中，包括渐近正态性的结果，并允许依赖结构随协变量而变化。此外，它远远超出了双变量响应情况，这是大多数早期调查的主要焦点。我们说明了对儿童营养不良进行三变量分析的好处，并通过经验证明可以从观察中推断出复杂的真正多元数据生成过程。