Additive, Dynamic and Multiplicative Regression

Fahrmeir, Ludwig; Gieger, Christian and Klinger, Artur (1995): Additive, Dynamic and Multiplicative Regression. Collaborative Research Center 386, Discussion Paper 1

Abstract

We survey and compare model-based approaches to regression for cross-sectional and longitudinal data which extend the classical parametric linear model for Gaussian responses in several aspects and for a variety of settings. Additive models replace the sum of linear functions of regressors by a sum of smooth functions. In dynamic or state space models, still linear in the regressors, coefficients are allowed to vary smoothly with time according to a Bayesian smoothness prior. We show that this is equivalent to imposing a roughness penalty on time-varying coefficients. Admitting the coefficients to vary with the values of other covariates, one obtains a class of varying-coefficient models (Hastie and Tibshirani, 1993), or in another interpretation, multiplicative models. The roughness penalty approach to non- and semiparametric modelling, together with Bayesian justifications, is used as a unifying and general framework for estimation. The methodological discussion is illustrated by some real data applications.

• Item Type: Paper
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Collaborative Research Center 386; Special Research Fields > Special Research Field 386
• Subjects: 500 Science > 510 Mathematics
• Language: English