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Some asymptotic results on generalized penalized spline smoothing
 B
"... The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for nonnormal responses. The results are extended in two ways. First, assuming the spline coefficients to be a ..."
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Cited by 24 (7 self)
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The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for nonnormal responses. The results are extended in two ways. First, assuming the spline coefficients to be a priori normally distributed links the smoothing framework to generalized linear mixed models (GLMM). We consider the asymptotic rates such that Laplace approximation is justified and the resulting fits in the mixed model correspond to penalized spline estimates. Secondly, we make use of a fully Bayesian viewpoint by imposing a priori distribution on all parameters and coefficients. We argue that with the postulated rates at which the spline basis dimension increases with the sample size the posterior distribution of the spline coefficients is approximately normal. The validity of this result is investigated in finite samples by comparing Markov Chain Monte Carlo (MCMC) results with their asymptotic approximation in a simulation study. 1 1
Semiparametric Regression During 2003–2007
, 2008
"... Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a ..."
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Cited by 17 (5 self)
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Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
A Bayesian semiparametric latent variable model for binary, ordinal and continuous response. Dissertation
, 2005
"... In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonpara ..."
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Cited by 11 (2 self)
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In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply our approach to a large German social science survey which motivated our methodological development.
Spikeandslab priors for function selection in structured additive regression models
 Journal of the American Statistical Association
"... Structured additive regression provides a general framework for complex Gaussian and nonGaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large fl ..."
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Cited by 5 (1 self)
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Structured additive regression provides a general framework for complex Gaussian and nonGaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spikeandslab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with timevarying effects for rightcensored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix. Keywords: parameter expansion, penalized splines, stochastic search variable selection, generalized additive mixed models, spatial regression 1.
Bayesian semiparametric regression based on MCMC techniques: A tutorial
, 2005
"... This tutorial demonstrates the usage of BayesX for analysing Bayesian semiparametric regression models based on MCMC techniques. As an example we consider data on undernutrition of children in Zambia. The tutorial is designed to be selfcontained and describes all features of BayesX in detail, that ..."
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Cited by 4 (0 self)
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This tutorial demonstrates the usage of BayesX for analysing Bayesian semiparametric regression models based on MCMC techniques. As an example we consider data on undernutrition of children in Zambia. The tutorial is designed to be selfcontained and describes all features of BayesX in detail, that will be needed throughout the tutorial. Therefore it may also serve as a first introduction into the general usage of BayesX.
Geoadditive Latent Variable Modelling of Count Data on Multiple Sexual Partnering in Nigeria
"... that multiple sexual partnering increases the risk of contracting HIV and other sexually transmitted diseases. Therefore, partner reduction is one of the prevention strategies to accomplish the Millenium development goal of halting and reversing the spread of HIV/AIDS. In order to explore possible a ..."
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Cited by 2 (2 self)
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that multiple sexual partnering increases the risk of contracting HIV and other sexually transmitted diseases. Therefore, partner reduction is one of the prevention strategies to accomplish the Millenium development goal of halting and reversing the spread of HIV/AIDS. In order to explore possible association between sexual partnering and some risk factors, this paper utilizes a novel Bayesian geoadditive latent variable model for count outcomes. This allows us to simultaneously analyze linear and nonlinear effects of covariates as well as spatial variations of one or more latent variables, such as attitude towards multiple partnering, which in turn directly influences the multivariate observable outcomes or indicators. Influence of demographic factors such as age, gender, locality, state of residence, educational attainment, etc., and knowledge about HIV/AIDS on attitude towards multiple partnering is also investigated. Results can provide insights to policy makers with the aim of reducing the spread of HIV and AIDS among the Nigerian populace through partner reduction. 1 Key words: factor loading; geographical variations; latent variable model; MCMC; Nigeria; semiparametric Poisson model; 1.
201019 Modeling House Prices using Multilevel Structured Additive Regression
"... This paper analyzes house price data belonging to three hierarchical levels of spatial units. House selling prices with associated individual attributes (the elementary level1) are grouped within municipalities (level2), which form districts (level3), which are themselves nested in counties (leve ..."
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Cited by 2 (2 self)
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This paper analyzes house price data belonging to three hierarchical levels of spatial units. House selling prices with associated individual attributes (the elementary level1) are grouped within municipalities (level2), which form districts (level3), which are themselves nested in counties (level4). Additionally to individual attributes, explanatory covariates with possibly nonlinear effects are available on two of these spatial resolutions. We apply a multilevel version of structured additive regression (STAR) models to regress house prices on individual attributes and locational neighborhood characteristics in a four level hierarchical model. In multilevel STAR models the regression coefficients of a particular nonlinear term may themselves obey a regression model with structured additive predictor. The framework thus allows to incorporate nonlinear covariate effects and time trends, smooth spatial effects and complex interactions at every level of the hierarchy of the multilevel model. Moreover we are able to decompose the spatial heterogeneity effect and investigate its magnitude at different spatial resolutions allowing for improved predictive quality even in the case of unobserved spatial units. Statistical inference is fully Bayesian and based on highly efficient Markov chain Monte Carlo simulation techniques that take advantage of the hierarchical structure in the data.
2003: Nonparametric Bayesian hazard rate models based on penalized splines. SFB 386 Discussion paper 361
"... Extensions of the traditional Cox proportional hazard model, concerning the following features are often desirable in applications: Simultaneous nonparametric estimation of baseline hazard and usual fixed covariate effects, modelling and detection of time–varying covariate effects and nonlinear func ..."
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Cited by 2 (0 self)
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Extensions of the traditional Cox proportional hazard model, concerning the following features are often desirable in applications: Simultaneous nonparametric estimation of baseline hazard and usual fixed covariate effects, modelling and detection of time–varying covariate effects and nonlinear functional forms of metrical covariates, and inclusion of frailty components. In this paper, we develop Bayesian multiplicative hazard rate models for survival and event history data that can deal with these issues in a flexible and unified framework. Some simpler models, such as piecewise exponential models with a smoothed baseline hazard, are covered as special cases. Embedded in the counting process approach, nonparametric estimation of unknown nonlinear functional effects of time or covariates is based on Bayesian penalized splines. Inference is fully Bayesian and uses recent MCMC sampling schemes. Smoothing parameters are an integral part of the model and are estimated automatically. We investigate performance of our approach through simulation studies, and illustrate it with a real data application. 1
Parametrization and Penalties in Spline Models with an Application to Survival Analysis
"... In this paper we show how a simple parametrization, built from the definition of cubic splines, can aid in the implementation and interpretation of penalized spline models, whatever configuration of knots we choose to use. We call this parametrization valuefirst derivative parametrization. We perfo ..."
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Cited by 1 (0 self)
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In this paper we show how a simple parametrization, built from the definition of cubic splines, can aid in the implementation and interpretation of penalized spline models, whatever configuration of knots we choose to use. We call this parametrization valuefirst derivative parametrization. We perform Bayesian inference by exploring the natural link between quadratic penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some penalty functionals. Alternatives include empirical Bayes methods involving model selection type criteria. The proposed methodology is illustrated by an application to survival analysis where the usual Cox model is extended to allow for timevarying regression coefficients.
Projektpartner A geoadditive Bayesian Latent Variable Model for Poisson indicators
, 2006
"... We introduce a new latent variable model with count variable indicators, where usual linear parametric effects of covariates, nonparametric effects of continuous covariates and spatial effects on the continuous latent variables are modelled through a geoadditive predictor. Bayesian modelling of nonp ..."
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Cited by 1 (1 self)
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We introduce a new latent variable model with count variable indicators, where usual linear parametric effects of covariates, nonparametric effects of continuous covariates and spatial effects on the continuous latent variables are modelled through a geoadditive predictor. Bayesian modelling of nonparametric functions and spatial effects is based on penalized spline and Markov random field priors. Full Bayesian inference is performed via an auxiliary variable Gibbs sampling technique, using a recent suggestion of FrühwirthSchnatter and Wagner (2006). As an advantage, our Poisson indicator latent variable model can be combined with semiparametric latent variable models for mixed binary, ordinal and continuous indicator variables within an unified and coherent framework for modelling and inference. A simulation study investigates performance, and an application to post war human security in Cambodia illustrates the approach.