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Recent developments in statistical regression methodology shift away from pure mean regression toward distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire conditional distribution directly by applying a transformation function to the response conditionally on a set of covariates toward a simple log-concave reference distribution. Thereby, CTMs allow not only variance, kurtosis or skewness but the complete conditional distribution to depend on the explanatory variables. We propose a Bayesian notion of conditional transformation models (BCTMs) focusing on exactly observed continuous responses, but also incorporating extensions to randomly censored and discrete responses. Rather than relying on Bernstein polynomials that have been considered in likelihood-based CTMs, we implement a spline-based parameterization for monotonic effects that are supplemented with smoothness priors. Furthermore, we are able to benefit from the Bayesian paradigm via easily obtainable credible intervals and other quantities without relying on large sample approximations. A simulation study demonstrates the competitiveness of our approach against its likelihood-based counterpart but also Bayesian additive models of location, scale and shape and Bayesian quantile regression. Two applications illustrate the versatility of BCTMs in problems involving real world data, again including the comparison with various types of competitors. for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and non-linear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented. [ABSTRACT FROM AUTHOR]

First, the bias is higher in scenarios for which HT ht compared to HT ht . [Extracted from the article]

A newly emerging field in statistics is distributional regression, where not only the mean but each parameter of a parametric response distribution can be modelled using a set of predictors. As an extension of generalized additive models, distributional regression utilizes the known link functions (log, logit, etc.), model terms (fixed, random, spatial, smooth, etc.) and available types of distributions but allows us to go well beyond the exponential family and to model potentially all distributional parameters. Due to this increase in model flexibility, the interpretation of covariate effects on the shape of the conditional response distribution, its moments and other features derived from this distribution is more challenging than with traditional mean-based methods. In particular, such quantities of interest often do not directly equate the modelled parameters but are rather a (potentially complex) combination of them. To ease the post-estimation model analysis, we propose a framework and subsequently feature an implementation in R for the visualization of Bayesian and frequentist distributional regression models fitted using the bamlss, gamlss and betareg R packages. [ABSTRACT FROM AUTHOR]

Thomas and Brian first met when Brian was a visiting professor in Munich in 2000 and taught a course on generalized regression that Thomas attended as a student. On November 25, 2021, Brian Douglas Marx died in his home in Baton Rouge, Louisiana. It was in Trento, where Brian and Paul first met. [Extracted from the article]

A test score on a psychological test is usually expressed as a normed score, representing its position relative to test scores in a reference population. These typically depend on predictor(s) such as age. The test score distribution conditional on predictors is estimated using regression, which may need large normative samples to estimate the relationships between the predictor(s) and the distribution characteristics properly. In this study, we examine to what extent this burden can be alleviated by using prior information in the estimation of new norms with Bayesian Gaussian distributional regression. In a simulation study, we investigate to what extent this norm estimation is more efficient and how robust it is to prior model deviations. We varied the prior type, prior misspecification and sample size. In our simulated conditions, using a fixed effects prior resulted in more efficient norm estimation than a weakly informative prior as long as the prior misspecification was not age dependent. With the proposed method and reasonable prior information, the same norm precision can be achieved with a smaller normative sample, at least in empirical problems similar to our simulated conditions. This may help test developers to achieve cost‐efficient high‐quality norms. The method is illustrated using empirical normative data from the IDS‐2 intelligence test. [ABSTRACT FROM AUTHOR]

The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross‐validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial‐, the t‐, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia. [ABSTRACT FROM AUTHOR]

Spatio-temporal models are becoming increasingly popular in recent regression research. However, they usually rely on the assumption of a specific parametric distribution for the response and/or homoscedastic error terms. In this article, we propose to apply semiparametric expectile regression to model spatio-temporal effects beyond the mean. Besides the removal of the assumption of a specific distribution and homoscedasticity, with expectile regression the whole distribution of the response can be estimated. For the use of expectiles, we interpret them as weighted means and estimate them by established tools of (penalized) least squares regression. The spatio-temporal effect is set up as an interaction between time and space either based on trivariate tensor product P-splines or the tensor product of a Gaussian Markov random field and a univariate P-spline. Importantly, the model can easily be split up into main effects and interactions to facilitate interpretation. The method is presented along the analysis of spatio-temporal variation of temperatures in Germany from 1980 to 2014. [ABSTRACT FROM AUTHOR]

Abstract In many empirical situations, modelling simultaneously three or more outcomes as well as their dependence structure can be of considerable relevance. Copulae provide a powerful framework to build multivariate distributions and allow one to view the specification of the marginal responses' equations and their dependence as separate but related issues. We propose a generalizationof the trivariate additive probit model where the link functions can in principle be derived from any parametric distribution and the parameters describing the residual association between the responses can be made dependent on several types of covariate effects (such as linear, nonlinear, random, and spatial effects). All the coefficients of the model are estimated simultaneously within a penalized likelihood framework that uses a trust region algorithm with integrated automatic multiple smoothing parameter selection. The effectiveness of the model is assessed in simulation as well as empirically by modelling jointly three adverse birth binary outcomes in North Carolina. The approach can be easily employed via the gjrm() function in the R package GJRM. Highlights • Development of trivariate binary models with arbitrary link functions. • The correlation parameters are allowed to depend upon covariates. • The models allow spline-type structures to capture nonlinear relationships. • The above developments are available via the gjrm() function from the R package GJRM. [ABSTRACT FROM AUTHOR]

Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely, binary) whereas the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood-based approach for the resulting class of copula regression models and employ it in the context of modeling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested. [ABSTRACT FROM AUTHOR]

Abstract When studying the empirical phenomenon of wildfires, we can distinguish between the occurrence at a specific location and time and the burnt area measured. This study proposes using structured additive regression models based on zero-one-inflated beta distribution for studying wildfire occurrence and burnt area simultaneously. Beta distribution affords a convenient way of studying the percentage of burnt area in cases where such percentages are bounded away from zero and one. Inflation with zeros and ones enables observations without wildfires or with 100% burnt areas to be treated as special cases. Structured additive regression allows one to include a variety of covariates, while simultaneously exploring spatial and temporal correlations. Our inferences are based on an efficient Markov chain Monte Carlo simulation algorithm utilizing iteratively weighted least squares approximations as proposal densities. Application of the proposed methodology to a large wildfire database covering Galicia (Spain) provides essential information for improved wildfire management. Highlights • Zero-One-Inflated structured additive beta regression is proposed to study wildfire occurrence and burnt area simultaneously. • Structured additive regression allows one to include a variety of covariates, while simultaneously exploring spatial and temporal correlations. • The principal advantage of the distributional regression is that allows one to evaluate effects of covariates linked to the response distribution and not just effects on the mean. • Proposed methodology showed provided essential information for improved wildfire management. [ABSTRACT FROM AUTHOR]

In regression analyses of spatially structured data, it is common practice to introduce spatially correlated random effects into the regression model to reduce or even avoid unobserved variable bias in the estimation of other covariate effects. If besides the response the covariates are also spatially correlated, the spatial effects may confound the effect of the covariates or vice versa. In this case, the model fails to identify the true covariate effect due to multicollinearity. For highly collinear continuous covariates, path analysis and structural equation modeling techniques prove to be helpful to disentangle direct covariate effects from indirect covariate effects arising from correlation with other variables. This work discusses the applicability of these techniques in regression setups, where spatial and covariate effects coincide at least partly and classical geoadditive models fail to separate these effects. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Forest inventories are often carried out with a particular design, consisting of a multi-level structure of observation plots spread over a larger domain and a fixed plot design of exact observation locations within these plots. Consequently, the resulting data are collected intensively within plots of equal size but with much less intensity at larger spatial scales. The resulting data are likely to be spatially correlated both within and between plots, with spatial effects extending over two different areas. However, a Gaussian process model with a standard covariance structure is generally unable to capture dependence at both fine and coarse scales of variation as well as for their interaction. In this paper, we develop a computationally feasible multi-level spatial model that accounts for dependence at multiple scales. We use a data-driven approach to determine the weight of each spatial process in the model to partition the variability of the measurements. We use simulated and German small tree inventory data to evaluate the model's performance.Supplementary material to this paper is provided online. [ABSTRACT FROM AUTHOR]

Bayesian methods have become increasingly popular in the past two decades. With the constant rise of computational power, even very complex models can be estimated on virtually any modern computer. Moreover, interest has shifted from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of a response distribution, where covariate effects can have flexible forms, for example, linear, non-linear, spatial or random effects. This tutorial article discusses how to select models in the Bayesian distributional regression setting, how to monitor convergence of the Markov chains and how to use simulation-based inference also for quantities derived from the original model parametrization. We exemplify the workflow using daily weather data on (a) temperatures on Germany's highest mountain and (b) extreme values of precipitation for the whole of Germany. [ABSTRACT FROM AUTHOR]

Wildfires are one of the main environmental problems facing societies today, and in the case of Galicia (north-west Spain), they are the main cause of forest destruction. This paper used binary structured additive regression (STAR) for modelling the occurrence of wildfires in Galicia. Binary STAR models are a recent contribution to the classical logistic regression and binary generalized additive models. Their main advantage lies in their flexibility for modelling non-linear effects, while simultaneously incorporating spatial and temporal variables directly, thereby making it possible to reveal possible relationships among the variables considered. The results showed that the occurrence of wildfires depends on many covariates which display variable behaviour across space and time, and which largely determine the likelihood of ignition of a fire. The joint possibility of working on spatial scales with a resolution of 1 × 1 km cells and mapping predictions in a colour range makes STAR models a useful tool for plotting and predicting wildfire occurrence. Lastly, it will facilitate the development of fire behaviour models, which can be invaluable when it comes to drawing up fire-prevention and firefighting plans. [ABSTRACT FROM AUTHOR]

Multi-state models generalize survival or duration time analysis to the estimation of transition-specific hazard rate functions for multiple transitions. When each of the transition-specific risk functions is parametrized with several distinct covariate effect coefficients, this leads to a model of potentially high dimension. To decrease the parameter space dimensionality and to work out a clear image of the underlying multi-state model structure, one can either aim at setting some coefficients to zero or to make coefficients for the same covariate but two different transitions equal. The first issue can be approached by penalizing the absolute values of the covariate coefficients as in lasso regularization. If, instead, absolute differences between coefficients of the same covariate on different transitions are penalized, this leads to sparse competing risk relations within a multi-state model, that is, equality of covariate effect coefficients. In this paper, a new estimation approach providing sparse multi-state modelling by the aforementioned principles is established, based on the estimation of multi-state models and a simultaneous penalization of the L1 -norm of covariate coefficients and their differences in a structured way. The new multi-state modelling approach is illustrated on peritoneal dialysis study data and implemented in the R package penMSM. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Background: Built environment studies provide broad evidence that urban characteristics influence physical activity (PA). However, findings are still difficult to compare, due to inconsistent measures assessing urban point characteristics and varying definitions of spatial scale. Both were found to influence the strength of the association between the built environment and PA. Methods: We simultaneously evaluated the effect of kernel approaches and network-distances to investigate the association between urban characteristics and physical activity depending on spatial scale and intensity measure. We assessed urban measures of point characteristics such as intersections, public transit stations, and public open spaces in ego-centered network-dependent neighborhoods based on geographical data of one German study region of the IDEFICS study. We calculated point intensities using the simple intensity and kernel approaches based on fixed bandwidths, cross-validated bandwidths including isotropic and anisotropic kernel functions and considering adaptive bandwidths that adjust for residential density. We distinguished six network-distances from 500 m up to 2 km to calculate each intensity measure. A log-gamma regression model was used to investigate the effect of each urban measure on moderate-to-vigorous physical activity (MVPA) of 400 2- to 9.9-year old children who participated in the IDEFICS study. Models were stratified by sex and age groups, i.e. pre-school children (2 to <6 years) and school children (6-9.9 years), and were adjusted for age, body mass index (BMI), education and safety concerns of parents, season and valid weartime of accelerometers. Results: Association between intensity measures and MVPA strongly differed by network-distance, with stronger effects found for larger network-distances. Simple intensity revealed smaller effect estimates and smaller goodnessof- fit compared to kernel approaches. Smallest variation in effect estimates over network-distances was found for kernel intensity measures based on isotropic and anisotropic cross-validated bandwidth selection. Conclusion: We found a strong variation in the association between the built environment and PA of children based on the choice of intensity measure and network-distance. Kernel intensity measures provided stable results over various scales and improved the assessment compared to the simple intensity measure. Considering different spatial scales and kernel intensity methods might reduce methodological limitations in assessing opportunities for PA in the built environment. [ABSTRACT FROM AUTHOR]

Introduction: Existing nomograms predicting lymph node involvement (LNI) in prostate cancer (PCa) are based on conventional lymphadenectomy. The aim of the study was to develop the first nomogram for predicting LNI in PCa patients undergoing sentinel guided pelvic lymph node dissection (sPLND). Materials and Methods: Analysis was performed on 1,296 patients with PCa who underwent radioisotope guided sPLND and retropubic radical prostatectomy (2005-2010). Median prostate specific antigen (PSA): 7.4 ng/ml (IQR 5.3-11.5 ng/ml). Clinical T-categories: T1: 54.8%, T2: 42.4%, T3: 2.8%. Biopsy Gleason sums: ≤6: 55.1%, 7: 39.5%, ≥8: 5.4%. Multivariate logistic regression models tested the association between all of the above predictors and LNI. Regression-based coefficients were used to develop a nomogram for predicting LNI. Accuracy was quantified using the area under the curve (AUC). Results: The median number of LNs removed was 10 (IQR 7-13). Overall, 17.8% of patients (n = 231) had LNI. The nomogram had a high predictive accuracy (AUC of 82%). All the variables were statistically significant multivariate predictors of LNI (p = 0.001). Univariate predictive accuracy for PSA, Gleason sum and clinical stage was 69, 75 and 69%, respectively. Conclusions: The sentinel nomogram can predict LNI at a sPLND very accurately and, for the first time, aid clinicians and patients in making important decisions on the indication of a sPLND. The high rate of LN+ patients underscores the sensitivity of sPLND. © 2015 S. Karger AG, Basel [ABSTRACT FROM AUTHOR]

Quantile regression (QR) has become a widely used tool to study the impact of covariates on quantiles of a response distribution. QR provides a detailed description of the conditional response when considering a dense set of quantiles, without assuming a closed form for its distribution. The Bayesian version of QR, which can be implemented by considering the asymmetric Laplace distribution (ALD) as an auxiliary error distribution, is an attractive alternative to other methods because it returns knowledge on the whole parameter distribution instead of solely point estimations. While for the univariate case there has been a lot of development in the last few years, multivariate responses have only been treated to a little extent in the literature, especially in the Bayesian case. By using a multivariate version of the location scale mixture representation for the ALD, we are able to apply inference techniques developed for multivariate Gaussian models on multivariate quantile regression and make thus the impact of covariates on the quantiles of more than one dependent variable feasible. The model structure also facilitates the determination of conditional correlations between bivariate responses on different quantile levels after adjusting for covariate effects. [ABSTRACT FROM AUTHOR]

Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness. [ABSTRACT FROM AUTHOR]

Frequent problems in applied research preventing the application of the classical Poisson log-linear model for analyzing count data include overdispersion, an excess of zeros compared to the Poisson distribution, correlated responses, as well as complex predictor structures comprising nonlinear effects of continuous covariates, interactions or spatial effects. We propose a general class of Bayesian generalized additive models for zero-inflated and overdispersed count data within the framework of generalized additive models for location, scale, and shape where semiparametric predictors can be specified for several parameters of a count data distribution. As standard options for applied work we consider the zero-inflated Poisson, the negative binomial and the zero-inflated negative binomial distribution. The additive predictor specifications rely on basis function approximations for the different types of effects in combination with Gaussian smoothness priors. We develop Bayesian inference based on Markov chain Monte Carlo simulation techniques where suitable proposal densities are constructed based on iteratively weighted least squares approximations to the full conditionals. To ensure practicability of the inference, we consider theoretical properties like the involved question whether the joint posterior is proper. The proposed approach is evaluated in simulation studies and applied to count data arising from patent citations and claim frequencies in car insurances. For the comparison of models with respect to the distribution, we consider quantile residuals as an effective graphical device and scoring rules that allow us to quantify the predictive ability of the models. The deviance information criterion is used to select appropriate predictor specifications once a response distribution has been chosen. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The article presents comment on the study regarding the use of flexible regression modeling in analyzing original articles and studies. It discusses the development of the stable and versatile statistical method which is also called general smooth models and structured additive distributional regression models. It recognizes the model used, however, the author also recommends theoretical points to the comparison between the methods used by the researchers.

Objectives To stratify the rate and prediction of lymph node involvement in prostate cancer patients undergoing sentinel-lymphadenectomy depending on preoperative tumor characteristics, and to compare the outcome with the European Association of Urology Guideline indication for lymphadenectomy. Methods A total of 1229 patients (median age 66 years) were treated with open sentinel-lymphadenectomy and prostatectomy between 2005 and 2009. Median preoperative prostate-specific antigen was 7.4 ng/mL. The rate of lymph node involvement was analyzed for D' Amico risk groups. Multivariable logistic regression was used to estimate the probability of lymph node involvement. Predictor variables included preoperative prostate-specific antigen, clinical T-category and biopsy Gleason sum. Predictive accuracy has been quantified (area under the curve) and lymph node positive patients were verified under consideration of the recommended European threshold for lymphadenectomy (nomogram-predicted lymph node invasion risk of >7%). Results The median number of lymph nodes removed was 10 (interquartile range 7-13). Overall, 17.1% of patients had lymph node involvement; 3.2% in low-, 14.8% in intermediate- and 37.4% in high-risk disease. The predicted risk for lymph node involvement ranged from 2% (prostate-specific antigen ≤4 ng/mL, T1, Gleason sum ≤6) to 87% (prostate-specific antigen >20 ng/mL, T3, Gleason sum ≥8). The predictive accuracy was 82.1%. According to the European guidelines, 15.9% of all lymph node involved cases would not have been detected. Conclusions The rate of lymph node involvement seems to be higher in the examined sentinel collective than expected according to the European Guideline nomogram. The first sentinel-based lymph node involvement prediction model can assist in deciding on the indication for sentinel-lymphadenectomy. The validation of a corresponding sentinel-based nomogram is still missing. [ABSTRACT FROM AUTHOR]

Recent developments of statistical methods allow for a very flexible modeling of covariates affecting survival times via the hazard rate, including also the inspection of possible time-dependent associations. Despite their immediate appeal in terms of flexibility, these models typically introduce additional difficulties when a subset of covariates and the corresponding modeling alternatives have to be chosen, that is, for building the most suitable model for given data. This is particularly true when potentially time-varying associations are given. We propose to conduct a piecewise exponential representation of the original survival data to link hazard regression with estimation schemes based on of the Poisson likelihood to make recent advances for model building in exponential family regression accessible also in the nonproportional hazard regression context. A two-stage stepwise selection approach, an approach based on doubly penalized likelihood, and a componentwise functional gradient descent approach are adapted to the piecewise exponential regression problem. These three techniques were compared via an intensive simulation study. An application to prognosis after discharge for patients who suffered a myocardial infarction supplements the simulation to demonstrate the pros and cons of the approaches in real data analyses. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Usual exponential family regression models focus on only one designated quantity of the response distribution, namely the mean. While this entails easy interpretation of the estimated regression effects, it may often lead to incomplete analyses when more complex relationships are indeed present and also bears the risk of false conclusions about the significance/importance of covariates. We will therefore give an overview on extended types of regression models that allows us to go beyond mean regression. More specifically, we will consider generalized additive models for location, scale and shape as well as semiparametric quantile and expectile regression. We will review the basic properties of all three approaches and compare them with respect to the flexibility in terms of the supported types of predictor specification, the availability of software and the support for different types of inferential procedures. The considered model classes are illustrated using a data set on rents for flats in the City of Munich. [ABSTRACT FROM AUTHOR]

Quantile regression provides a convenient framework for analyzing the impact of covariates on the complete conditional distribution of a response variable instead of only the mean. While frequentist treatments of quantile regression are typically completely nonparametric, a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields posterior modes equivalent to frequentist estimates. In this paper, we utilize a location-scale mixture of normals representation of the asymmetric Laplace distribution to transfer different flexible modelling concepts from Gaussian mean regression to Bayesian semiparametric quantile regression. In particular, we will consider high-dimensional geoadditive models comprising LASSO regularization priors and mixed models with potentially non-normal random effects distribution modeled via a Dirichlet process mixture. These extensions are illustrated using two large-scale applications on net rents in Munich and longitudinal measurements on obesity among children. The impact of the likelihood misspecification that underlies the Bayesian formulation of quantile regression is studied in terms of simulations. [ABSTRACT FROM AUTHOR]

We investigated the risk factors for childhood malnutrition in India based on the 2005/2006 Demographic and Health Survey by applying a novel estimation technique for additive quantile regression. Ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects, and, as a consequence, focus on average properties of the response. The use of such a regression model for analyzing childhood malnutrition in developing or transition countries implies that the estimated effects describe the average nutritional status. However, it is of even greater interest to analyze quantiles of the response distribution, such as the 5% or 10% quantile, which relate to the risk of extreme malnutrition. Our investigation is based on a semiparametric extension of quantile regression models where different types of nonlinear effects are included in the model equation, leading to additive quantile regression. We addressed the variable selection and model choice problems associated with estimating such an additive quantile regression model using a novel boosting approach. Our proposal allows for data-driven determination of the amount of smoothness required for the nonlinear effects and combines model choice with an automatic variable selection property. In an empirical evaluation, we compared our boosting approach with state-of-the-art methods for additive quantile regression. The results suggest that boosting is an appropriate tool for estimation and variable selection in additive quantile regression models and helps to identify yet unknown risk factors for childhood malnutrition. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In recent years, flexible hazard regression models based on penalized splines have been developed that allow us to extend the classical Cox model via the inclusion of time-varying and nonparametric effects. Despite their immediate appeal in terms of flexibility, these models introduce additional difficulties when a subset of covariates and the corresponding modelling alternatives have to be chosen. We present an analysis of data from a specific patient population with 90-day survival as the response variable. The aim is to determine a sensible prognostic model where some variables have to be included due to subject-matter knowledge while other variables are subject to model selection. Motivated by this application, we propose a two-stage stepwise model building strategy to choose both the relevant covariates and the corresponding modelling alternatives within the choice set of possible covariates simultaneously. For categorical covariates, competing modelling approaches are linear effects and time-varying effects, whereas nonparametric modelling provides a further alternative in case of continuous covariates. In our data analysis, we identified a prognostic model containing both smooth and time-varying effects. [ABSTRACT FROM AUTHOR]

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion, aic, have been used, based either on the marginal or on the conditional distribution. We show that the marginal aic is not an asymptotically unbiased estimator of the Akaike information, and favours smaller models without random effects. For the conditional aic, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that can lead to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional aic, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package (R Development Core Team, 2010) is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia. [ABSTRACT FROM PUBLISHER]

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist perspective. We show that the mixed-model formulation of penalized splines can help obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the proposed methods. The R package ConfBands accompanies the article. [ABSTRACT FROM AUTHOR]

Model choice and variable selection are issues of major concern in practical regression analyses, arising in many biometric applications such as habitat suitability analyses, where the aim is to identify the influence of potentially many environmental conditions on certain species. We describe regression models for breeding bird communities that facilitate both model choice and variable selection, by a boosting algorithm that works within a class of geoadditive regression models comprising spatial effects, nonparametric effects of continuous covariates, interaction surfaces, and varying coefficients. The major modeling components are penalized splines and their bivariate tensor product extensions. All smooth model terms are represented as the sum of a parametric component and a smooth component with one degree of freedom to obtain a fair comparison between the model terms. A generic representation of the geoadditive model allows us to devise a general boosting algorithm that automatically performs model choice and variable selection. [ABSTRACT FROM AUTHOR]

The human sleep process shows dynamic alterations during the night. Methods are needed to examine whether and to what extent such alterations are affected by internal, possibly time-dependent, factors, such as endocrine activity. In an observational study, we examined simultaneously sleep EEG and nocturnal levels of renin, growth hormone (GH), and cortisol (between 2300 and 0700) in 47 healthy volunteers comprising 24 women (41.67 ±2.93 yr of age) and 23 men (37.26 ± 2.85 yr of age). Hormone concentrations were measured every 20 rain. Conventional sleep stage scoring at 30-s intervals was applied. Semipararnetric multinomial logit models are used to study and quantify possible time-dependent hormone effects on sleep stage transition courses. Results show that increased cortisol levels decrease the probability of transition from rapid-eye-movement (REM) sleep to wakefulness (WAKE) and increase the probability of transition from REM to non-REM (NREM) sleep, irrespective of the time in the night. Via the model selection criterion Akalke's information criterion, it was found that all considered hormone effects on transition probabilities with the initial state WAKE change with time. Similarly, transition from alow-wave sleep (SWS) to light sleep (LS) is affected by a "hormone-time" interaction for cortisol and renin, but not GH. For example, there is a considerable increase in the probability of SWS-LS transition toward the end of the night, when cortisol concentrations are very high. In summary, alterations in human sleep possess dynamic forms and are partially influenced by the endeedne activity of certain hormones. Statistical methods, such as semipara- metric multinomial and time-dependant Iogit regression, can offer ambitious ways to investigate and estimate the association intensities between the nonstationary sleep changes and the time-dependent endocrine activities. [ABSTRACT FROM AUTHOR]

Abstract: Structured additive regression comprises many semiparametric regression models such as generalized additive (mixed) models, geoadditive models, and hazard regression models within a unified framework. In a Bayesian formulation, non-parametric functions, spatial effects and further model components are specified in terms of multivariate Gaussian priors for high-dimensional vectors of regression coefficients. For several model terms, such as penalized splines or Markov random fields, these Gaussian prior distributions involve rank-deficient precision matrices, yielding partially improper priors. Moreover, hyperpriors for the variances (corresponding to inverse smoothing parameters) may also be specified as improper, e.g. corresponding to Jeffreys prior or a flat prior for the standard deviation. Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations. We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies. [Copyright &y& Elsevier]

Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example is Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian (using Markov chain Monte Carlo simulation techniques) or empirically Bayesian (based on a mixed model representation). A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual-specific variation has to be accounted for using covariate information and frailty terms. [ABSTRACT FROM AUTHOR]

Mixed model based approaches for semiparametric regression have gained much interest in recent years, both in theory and application. They provide a unified and modular framework for penalized likelihood and closely related empirical Bayes inference. In this article, we develop mixed model methodology for a broad class of Cox-type hazard regression models where the usual linear predictor is generalized to a geoadditive predictor incorporating non-parametric terms for the (log-)baseline hazard rate, time-varying coefficients and non-linear effects of continuous covariates, a spatial component, and additional cluster-specific frailties. Non-linear and time-varying effects are modelled through penalized splines, while spatial components are treated as correlated random effects following either a Markov random field or a stationary Gaussian random field prior. Generalizing existing mixed model methodology, inference is derived using penalized likelihood for regression coefficients and (approximate) marginal likelihood for smoothing parameters. In a simulation we study the performance of the proposed method, in particular comparing it with its fully Bayesian counterpart using Markov chain Monte Carlo methodology, and complement the results by some asymptotic considerations. As an application, we analyse leukaemia survival data from northwest England. [ABSTRACT FROM AUTHOR]

Motivated by a space–time study on forest health with damage state of trees as the response, we propose a general class of structured additive regression models for categorical responses, allowing for a flexible semiparametric predictor. Nonlinear effects of continuous covariates, time trends, and interactions between continuous covariates are modeled by penalized splines. Spatial effects can be estimated based on Markov random fields, Gaussian random fields, or two-dimensional penalized splines. We present our approach from a Bayesian perspective, with inference based on a categorical linear mixed model representation. The resulting empirical Bayes method is closely related to penalized likelihood estimation in a frequentist setting. Variance components, corresponding to inverse smoothing parameters, are estimated using (approximate) restricted maximum likelihood. In simulation studies we investigate the performance of different choices for the spatial effect, compare the empirical Bayes approach to competing methodology, and study the bias of mixed model estimates. As an application we analyze data from the forest health survey. [ABSTRACT FROM AUTHOR]

Background: Due to contradictory results in current research, whether age at menopause is increasing or decreasing in Western countries remains an open question, yet worth studying as later ages at menopause are likely to be related to an increased risk of breast cancer. Using data from breast cancer screening programs to study the temporal trend of age at menopause is difficult since especially younger women in the same generational cohort have often not yet reached menopause. Deleting these younger women in a breast cancer risk analyses may bias the results. The aim of this study is therefore to recover missing menopause ages as a covariate by comparing methods for handling missing data. Additionally, the study makes a contribution to understanding the evolution of age at menopause for several generations born in Portugal between 1920 and 1970.Methods: Data from a breast cancer screening program in Portugal including 278,282 women aged 45-69 and collected between 1990 and 2010 are used to compare two approaches of imputing age at menopause: (i) a multiple imputation methodology based on a truncated distribution but ignoring the mechanism of missingness; (ii) a copula-based multiple imputation method that simultaneously handles the age at menopause and the missing mechanism. The linear predictors considered in both cases have a semiparametric additive structure accommodating linear and non-linear effects defined via splines or Markov random fields smoothers in the case of spatial variables.Results: Both imputation methods unveiled an increasing trend of age at menopause when viewed as a function of the birth year for the youngest generation. This trend is hidden if we model only women with an observed age at menopause.Conclusion: When studying age at menopause, missing ages must be recovered with an adequate procedure for incomplete data. Imputing these missing ages avoids excluding the younger generation cohort of the screening program in breast cancer risk analyses and hence reduces the bias stemming from this exclusion. In addition, imputing the not yet observed ages of menopause for mostly younger women is also crucial when studying the time trend of age at menopause otherwise the analysis will be biased. [ABSTRACT FROM AUTHOR]

Understanding the interconnected nature of rising carbon emissions and income inequality is crucial to achieve social and ecological sustainability. We contribute to the literature with a systematic analysis of the conditional interdependence by means of a distributional copula model. The model estimates the nonlinear dependence between a country's GINI coefficient and CO2 emissions across and within country income groups. This enables us to uncover complex interdependencies that standard linear regression techniques might hide. Using an unbalanced panel data set of 109 countries from 1960 to 2019, composed of different data sets, we show that dependence is related to the prevailing consumption level, energy sources, the structure of the economy and the political system with heterogeneous effects across country income groups. To estimate the potentials for a sustainable future, we define thresholds of potential social and environmental sustainability. We find that richer countries are furthest away from this, but have the highest potential for realizing the defined sustainable space. This further highlights the importance of the service sector and combined policies targeting social and environmental sustainability. [ABSTRACT FROM AUTHOR]

This paper introduces distributional regression also known as generalized additive models for location, scale and shape (GAMLSS) as a modeling framework for analyzing treatment effects beyond the mean. In contrast to mean regression models, GAMLSS relate each distributional parameter to covariates. Therefore, they can be used to model the treatment effect not only on the mean but on the whole conditional distribution. Since they encompass a wide range of different distributions, GAMLSS provide a flexible framework for modeling non-normal outcomes in which additionally nonlinear and spatial effects can easily be incorporated. We elaborate on the combination of GAMLSS with program evaluation methods including randomized controlled trials, panel data techniques, difference in differences, instrumental variables, and regression discontinuity design. We provide practical guidance on the usage of GAMLSS by reanalyzing data from the Mexican Progresa program. Contrary to expectations, no significant effects of a cash transfer on the conditional consumption inequality level between treatment and control group are found. [ABSTRACT FROM AUTHOR]

In a wide range of applications, standard regression techniques are hard to apply because the responses may consist of a continuous part but augmented with a discrete number of additional response categories with probability greater than zero. Previous methods often assume that the process of both parts can be treated structurally independent given covariates which facilitates estimation considerably. However, this simplifying assumption is often too restrictive and questionable for the data situation at hand. To address this, we propose a novel approach for modelling mixed discrete-continuous responses where the probabilities of the boundary cases are based on integrated weighted densities of the continuous part. The weight functions themselves may depend on covariates as well as unknown parameters. We discuss different types of mixed discrete-continuous distributions and consider inferential methods in a Bayesian and maximum likelihood framework. We evaluate parameter estimation carefully in simulation studies before applying them to the analysis of income distributions using a specific instance of the novel zero-adjusted-type model. [ABSTRACT FROM AUTHOR]

Real estate valuation is typically based on hedonic regression models where the expected price of a property is explained in dependence of its attributes. However, investors in the housing market are equally interested in the distribution of real estate market values (including price variation), that is, determining the impact of attributes of a property on the entire conditional distribution. We therefore consider Bayesian structured additive distributional and quantile regression models for real estate valuation. In the first approach, each parameter of a potentially complex parametric response distribution is related to a structured additive predictor. In contrast, the second approach proceeds differently and models arbitrary quantiles of the response distribution directly and nonparametrically. Both models presented are based on a multilevel version of structured additive regression thereby utilizing the typical hierarchical structure of real estate data. We demonstrate the proposed methodology within a detailed case study based on more than 3 000 owner-occupied single family homes in Austria, discuss interpretation of the resulting effect estimates, and compare models based on their predictive ability. [ABSTRACT FROM AUTHOR]

In most previous applications of brand choice models, possible time-varying effects in consumer behavior are ignored by merely imposing constant parameters. However, it is very likely that trends or short-term variations in consumers’ intrinsic brand utilities or sensitivities to marketing instruments occur. For example, preferences for specific brands or price elasticities in product categories such as coffee or chocolate may vary in the run-up to festive occasions like Easter or Christmas. In this paper, we employ flexible multinomial logit models for estimating time-varying effects in brand choice behavior. Time-varying brand intercepts and time-varying effects of covariates are modeled using penalized splines, a flexible, yet parsimonious, nonparametric smoothing technique. The estimation is data driven; the flexible functions, as well as the corresponding degrees of smoothness, are determined simultaneously in a unified approach. Our model further allows for alternative-specific time-varying effects of covariates and can mimic state-space approaches with random walk parameter dynamics. In an empirical application for ground coffee, we compare the performance of the proposed approach to a number of benchmark models regarding in-sample fit, information criteria, and in particular out-of-sample fit. Interestingly, the most complex P-spline model with time-varying brand intercepts and brand-specific time-varying covariate effects outperforms all other specifications both in- and out-of-sample. We further present results from a sensitivity analysis on how the number of knots and other P-spline settings affect the model performance, and we provide guidelines for the model building process about the many options for model specification using P-splines. Finally, the resulting parameter paths provide valuable insights for marketing managers. [ABSTRACT FROM AUTHOR]