Multilevel structured additive regression

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. Carlo simulation techniques. We provide an in depth description of several highly efficient sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations within a couple of minutes (often even seconds). We demonstrate the practicability of the approach in a complex application on childhood undernutrition with large sample size and three hierarchy levels. Terms of use: Documents in

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

“…Gaussian random e↵ects and⌘ jk (x;˜ jk ) represents a full predictor of nested covariates, e.g., including a discrete regional spatial e↵ect. This way, potential costly operations in updating Algorithm A2a and A2b can be avoided since the number of observations in⌘ jk (x;˜ jk ) is equal to the number of coe cients in jk , which is usually much smaller than the actual number of observations n. Moreover, the full conditionals (see also Section 4.2) for˜ jk are Gaussian regardless of the response distribution and leads to highly e cient estimation algorithms, see Lang, Umlauf, Wechselberger, Harttgen, and Kneib (2014).…”

“…This is much smaller than the total number of observations of the data set and duplicated rows in the corresponding design matrix can be avoided within the model fitting algorithms. Therefore, we implemented updating functions U jk (·) that support shrinkage of the design matrices based on unique covariate observations, using the highly-e cient algorithm of Lang et al (2014). This essentially employs a reduced form of the diagonal weight matrix W kk in the IWLS algorithm and computes the reduced partial residual vector from z k ⌘ usage within bamlss see also the documentation of estimation engines bfit() and GMCMC() and the corresponding updating functions bfit_iwls() and GMCMC_iwls().…”

Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data

“…Recently, Lang et al [2013] proposed a multilevel version of structured additive regression models where it is assumed that the regression coefficients β j of a term f j in (3) may themselves obey a regression model with structured additive predictor, i.e.…”

“…Inference can then be based on optimizing a generalized cross validation criterion [Wood, 2004], a mixed model representation [Ruppert et al, 2003, Fahrmeir et al, 2004, Wood, 2008 or Markov chain Monte Carlo (MCMC) simulations [Brezger and Lang, 2006, Jullion and Lambert, 2007, Lang et al, 2013. The framework of generalized additive models for location, scale and shape (GAMLSS) introduced by Rigby and Stasinopoulos [2005] allows to extend generalized additive models to more complex response distributions where not only the expectation but multiple parameters are related to additive predictors via suitable link functions.…”

“…• We provide a numerically efficient implementation comprising also an extension to multilevel structure that is particularly useful in spatial regression specifications or for models including random effects, see Lang et al [2013]. This implementation is part of the free software package BayesX [Belitz et al, 2012].…”