Multivariate conditional transformation models

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.

Automated summary

Regression models are an important aspect of contemporary regression analysis, but often rely on simplistic assumptions. We propose a general framework for multivariate conditional transformation models that can describe the entire distribution in a tractable and interpretable yet flexible way, allowing for non-linear effects of covariates and likelihood-based inference.