PENALIZED STRUCTURED ADDITIVE REGRESSION FOR SPACE-TIME DATA: A BAYESIAN PERSPECTIVE

By Ludwig Fahrmeir, Thomas Kneib, Stefan Lang. 2004

424 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0805634ecde955aea56124d13c7e24ec45fc8975

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Coverage Properties of Confidence Intervals for Generalized Additive Model Components (2012, methodology): “As an alternative, Fahrmeir et al. (2004) and Fahrmeir & Lang (2001) adopted the fully Bayesian approach, which employs MCMC for practical computations.”
BayesX: Analyzing Bayesian Structural Additive Regression Models (2005, background): “Specific examples for Xj and Kj are given in Fahrmeir and Lang (2001a), Lang and Brezger (2004) and Brezger and Lang (2005).”
Propriety of posteriors in structured additive regression models: Theory and empirical evidence (2009, methodology): “The design matrix of bj can then be constructed from the remaining eigen vectors corresponding to positive eigen values, compare Fahrmeir et al. (2004) for details.”
Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression (2016, methodology): “In the context of Bayesian inference in structured additive regression as it has originally been proposed in Fahrmeir and Lang (2001) or Fahrmeir et al. (2004) for exponential families, prior elicitation is in particular an issue when it comes to choosing hyperpriors for the smoothing variances.”
Low‐Rank Scale‐Invariant Tensor Product Smooths for Generalized Additive Mixed Models (2006, background): “where yi is a univariate response; θ is a vector of fixed parameters; Xi is a row of a fixed effects model matrix; the wjis are covariates, dummy variables or often simply 1 (they are used in ‘variable coefficient models’: Hastie and Tibshirani, 1993); the fjs are smooth functions of covariates xk; ”
Conditional transformation models (2012, methodology): “Taking the tensor product after applying the decomposition yields a decomposition into linear and non-linear main effects of xj and υ as well as linear and non-linear interaction terms (see Fahrmeir, Kneib, and Lang 2004, Kneib, Hothorn, and Tutz 2009, for technical details of this decomposition).”
Soap film smoothing (2008, methodology): “In the next section we provide a characterization of the minimizer of expression (1) which allows it to be computed to arbitrary accuracy by relatively simple numerical methods.”
Generalized Additive Models (2006, unknown): “Another alternative, is to take the fully Bayesian approach to GAMs of Fahrmeir, Lang and co-workers (e.g. Fahrmeir and Lang, 2001; Fahrmeir et al., 2004; Lang and Bresger, 2004).”
Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models (2008, methodology): “This setup penalizes deviations of the fitted smooth function from a (d − 1)th-degree polynomial (Fahrmeir et al., 2004).”
Fast Calibrated Additive Quantile Regression (2017, methodology): “…that are widely used in applied statistics, especially since the advent of efficient and stable methods for smoothing parameter selection and interval estimation in this model class (see, e.g., Wood 2000; Ruppert, Wand, and Carroll 2003; Fahrmeir, Kneib, and Lang 2004; Kim and Gu 2004; Wood 2017).”
Bayesian semi parametric multi-state models (2008, background): “…estimation in semiparametric regression models has been considerably facilitated by the insight that regression models with smoothness priors of the form (2.5) can be represented as mixed models with i.i.d. random effects (compare, for example, Fahrmeir et al. (2004) or Ruppert et al. (2003)).”
Smooth Transition from Fixed Effects to Mixed Effects Models in Multi-level regression Models (2008, methodology): “In applied statistics, semiparametric Bayesian approaches are often used in combination with (penalized) splines, series or MCMC (random field) estimators, see Fahrmeir, Kneib, and Lang (2004), Kneib and Fahrmeir (2006) and Fahrmeir and Lang (2001) among others.”
Bayesian Structured Additive Distributional Regression (2013, methodology): “…additive models for location, scale and shape (GAMLSS, [Rigby and Stasinopoulos, 2005]) in which all parameters of a potentially complex response distribution are related to additive regression predictors in the spirit of GAMs [Ruppert et al., 2003, Wood, 2004, 2008, Fahrmeir et al., 2004, 2013].”
P-spline ANOVA-type interaction models for spatio-temporal smoothing (2011, background): “They extend the geoadditive models proposed by Kammann and Wand (2003) or assume a smooth function to model non-linear time effects (MacNab and Dean, 2001; Fahrmeir et al., 2004; Kneib and Fahrmeir, 2006).”
Generalized additive models for large data sets (2015, background): “…(1) is a GAM (Hastie and Tibshirani, 1986, 1990) which occurs when the Lij are evaluation functionals, but other examples are varying-coefficient models, functional generalized linear models (e.g. Marx and Eilers (1999)) and structured additive regression models (e.g. Fahrmeir et al. (2004)).”
Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting (2012, methodology): “Building on earlier approaches to address the problem of heteroscedasticity in this type of data (Stasinopoulos et al., 2000; Fahrmeir et al., 2004), we showed that the point predictions for the net rent per square metre obtained from GAMLSSs are highly competitive with those obtained from mean…”