Truly Multivariate Structured Additive Distributional Regression

by   Lucas Kock, et al.

Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary distribution is modelled through covariates. While such models have been developed for univariate and bivariate responses, the truly multivariate case remains extremely challenging for both computational and theoretical reasons. Alternative approaches to GAMLSS may allow for higher dimensional response vectors to be modelled jointly but often assume a fixed dependence structure not depending on covariates or are limited with respect to modelling flexibility or computational aspects. We contribute to this gap in the literature and propose a truly multivariate distributional model, which allows one to benefit from the flexibility of GAMLSS even when the response has dimension larger than two or three. Building on copula regression, we model the dependence structure of the response through a Gaussian copula, while the marginal distributions can vary across components. Our model is highly parameterized but estimation becomes feasible with Bayesian inference employing shrinkage priors. We demonstrate the competitiveness of our approach in a simulation study and illustrate how it complements existing models along the examples of childhood malnutrition and a yet unexplored data set on traffic detection in Berlin.


page 18

page 19


Boosting Multivariate Structured Additive Distributional Regression Models

We develop a model-based boosting approach for multivariate distribution...

Multivariate Conditional Transformation Models

Regression models describing the joint distribution of multivariate resp...

Tractable Bayes of Skew-Elliptical Link Models for Correlated Binary Data

Correlated binary response data with covariates are ubiquitous in longit...

Beyond unidimensional poverty analysis using distributional copula models for mixed ordered-continuous outcomes

Poverty is a multidimensional concept often comprising a monetary outcom...

Fast Bayesian Inference in Nonparametric Double Additive Location-Scale Models With Right- and Interval-Censored Data

Penalized B-splines are routinely used in additive models to describe sm...

conformalInference.multi and conformalInference.fd: Twin Packages for Conformal Prediction

Building on top of a regression model, Conformal Prediction methods prod...

Please sign up or login with your details

Forgot password? Click here to reset