We discuss inference for additive models with random scaling factors. The additive effects are of the form (1+g)f(z) where f is a nonlinear function of the continuous covariate z modeled by P(enalized)-splines and 1+g is a random scaling factor. Additionally, monotonicity constraints on the...

Gaussian Structured Additive Regression provides a flexible framework for additive decomposition of the expected value with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity, and complex interactions between covariates of different types....

In this paper, we propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed additively of a variety of...

Generalized additive models for location, scale and shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed. This approach allows the actuary to include risk factors not only in the...

In this paper, we propose a unified Bayesian approach for multivariate structured additive distributional regression analysis where inference is applicable to a huge class of multivariate response distributions, comprising continuous, discrete and latent models, and where each parameter of these...

Structured additive regression (STAR) models provide a flexible framework for modeling possible nonlinear effects of covariates: They contain the well established frameworks of generalized linear models (GLM) and generalized additive models (GAM) as special cases but also allow a wider class of...

Models with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between...

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation...