BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Achim Zeileis Universität InnsbruckAbstract Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade it is now possible to tackle complicated inferential problems, e.g., with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. In order to embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits the general structure of these models and encompasses many di↵erent response distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial, . . . ). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology based on more than 1.2 million observations from more than 50 meteorological stations, as well as a Cox model for continuous time with space-time interactions on a data set with over five thousand "individuals".

Joint modeling of longitudinal autoantibody patterns and progression to type 1 diabetes: results from the TEDDY study

“…All models were estimated within a Bayesian framework using the R-package bamlss [18]. Weakly informative normal priors were used for all coefficients.…”

“…All parts of the model are parameterized as structured additive models. We refer to the original methodological paper [1] and the documentation of the package bamlss [2] for further details. In our estimated models the longitudinal model per autoantibody y for subject i at the observed measurement times t ij was specified as a mixed model allowing smooth, nonlinear, and subject-specific trajectories over time as well as linear and nonlinear effects of the covariates x k …”

A primer on Bayesian distributional regression

“…Since MCMC approaches imply a number of additional challenges for applied researchers (in particular monitoring mixing and convergence of Markov chains), we will also provide step by step guidance on those aspects of the analysis. Model fitting is carried out using the R (R Core Team, 2017) package bamlss (Umlauf et al, 2017). The R code to reproduce all examples is provided in the online materials of this paper.…”

Flexible Bayesian additive joint models with an application to type 1 diabetes research

“…For the posterior mean sampling, we construct approximate full conditionals π (β km |·) based on a second-order Taylor expansion of the log-posterior centered at the last state β [l] km , similar to Fahrmeir et al (2004), Klein, Kneib, Klasen, and Lang (2015), and Klein, Kneib, Lang, and Sohn (2015) and as shown in more detail in Umlauf et al (2017). The proposal density from this approximate full conditional is proportional to a multivariate normal distribution with the precision matrix ( [l] km ) −1 = −H (β [l] km ) and the mean μ [l] …”

“…The presented model is implemented in the R-package bamlss (Umlauf, Klein, & Zeileis, 2017;Umlauf, Klein, Zeileis, & Koehler, 2016). The general model structure and potential extensions are outlined in Section 2.…”