A0378
Title: Density-on-scalar regression for bivariate distributions in Bayes spaces
Authors: Ivana Pavlu - Palacky University Olomouc (Czech Republic) [presenting]
Almond Stoecker - Ecole polytechnique federale de Lausanne (Switzerland)
Adela Czolkova - Palacky University Olomouc (Czech Republic)
Karel Hron - Palacky University Olomouc (Czech Republic)
Sonja Greven - Humboldt University of Berlin (Germany)
Abstract: Additive regression models allow the explanation of the dependence of a response variable on a set of covariates through a parameterized yet flexible regression model. Recent advances allow functional and, more recently also, distributional responses. This contribution presents additive density-on-scalar regression for bivariate distributional responses, either continuous (probability density functions) or discrete (probability distribution/compositional tables). The regression model, embedded in the Bayes space theory, enables a sound analysis of the relationship between the response and covariates, respecting the relative properties of the distributional response. One of the challenges here is to find a good means of interpretation of estimated effects. To achieve this, the model allows the decomposition of bivariate density-on-scalar effects by 1. Orthogonal decomposition of additive effects into linear, non-linear and covariate-interaction parts, and 2. Orthogonal decomposition of the bivariate distribution into an interactive part and two (geometric) margins. Due to this second decomposition, model selection -performed through gradient boosting - allows assessment of the importance of different covariates and independence between the two response variables in their mean distribution and/or covariate effects. The proposed model framework is used for the analysis of salary and workload distributions of cohabiting couples based on the German Socio-Economic Panel study.
