Nadja Klein

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

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.

Correction: Bayesian structured additive distributional regression with an application to regional income inequality in Germany

We propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed additively of a variety of different functional effect types such as nonlinear effects, spatial effects, random coefficients, interaction surfaces or other (possibly nonstandard) basis function representations. To enforce specific properties of the functional effects such as smoothness, informative multivariate Gaussian priors are assigned to the basis function coefficients. Inference can then be based on computationally efficient Markov chain Monte Carlo simulation techniques where a generic procedure makes use of distribution-specific iteratively weighted least squares approximations to the full conditionals. The framework of distributional regression encompasses many special cases relevant for treating nonstandard response structures such as highly skewed nonnegative responses, overdispersed and zero-inflated counts or shares including the possibility for zero- and one-inflation. We discuss distributional regression along a study on determinants of labour incomes for full-time working males in Germany with a particular focus on regional differences after the German reunification. Controlling for age, education, work experience and local disparities, we estimate full conditional income distributions allowing us to study various distributional quantities such as moments, quantiles or inequality measures in a consistent manner in one joint model. Detailed guidance on practical aspects of model choice including the selection of several competing distributions for labour incomes and the consideration of different covariate effects on the income distribution complete the distributional regression analysis. We find that next to a lower expected income, full-time working men in East Germany also face a more unequal income distribution than men in the West, ceteris paribus.

Corridors restore animal-mediated pollination in fragmented tropical forest landscapes.

Tropical biodiversity and associated ecosystem functions have become heavily eroded through habitat loss. Animal-mediated pollination is required in more than 94% of higher tropical plant species and 75% of the worlds leading food crops, but it remains unclear if corridors avert deforestation-driven pollination breakdown in fragmented tropical landscapes. Here, we used manipulative resource experiments and field observations to show that corridors functionally connect neotropical forest fragments for forest-associated hummingbirds and increase pollen transfer. Further, corridors boosted forest-associated pollinator availability in fragments by 14.3 times compared with unconnected equivalents, increasing overall pollination success. Plants in patches without corridors showed pollination rates equal to bagged control flowers, indicating pollination failure in isolated fragments. This indicates, for the first time, that corridors benefit tropical forest ecosystems beyond boosting local species richness, by functionally connecting mutualistic network partners. We conclude that small-scale adjustments to landscape configuration safeguard native pollinators and associated pollination services in tropical forest landscapes.

Simultaneous inference in structured additive conditional copula regression models: a unifying Bayesian approach

While most regression models focus on explaining distributional aspects of one single response variable alone, interest in modern statistical applications has recently shifted towards simultaneously studying multiple response variables as well as their dependence structure. A particularly useful tool for pursuing such an analysis are copula-based regression models since they enable the separation of the marginal response distributions and the dependence structure summarised in a specific copula model. However, so far copula-based regression models have mostly been relying on two-step approaches where the marginal distributions are determined first whereas the copula structure is studied in a second step after plugging in the estimated marginal distributions. Moreover, the parameters of the copula are mostly treated as a constant not related to covariates and most regression specifications for the marginals are restricted to purely linear predictors. We therefore propose simultaneous Bayesian inference for both the marginal distributions and the copula using computationally efficient Markov chain Monte Carlo simulation techniques. In addition, we replace the commonly used linear predictor by a generic structured additive predictor comprising for example nonlinear effects of continuous covariates, spatial effects or random effects and furthermore allow to make the copula parameters covariate-dependent. To facilitate Bayesian inference, we construct proposal densities for a Metropolis–Hastings algorithm relying on quadratic approximations to the full conditionals of regression coefficients avoiding manual tuning. The performance of the resulting Bayesian estimates is evaluated in simulations comparing our approach with penalised likelihood inference, studying the choice of a specific copula model based on the deviance information criterion, and comparing a simultaneous approach with a two-step procedure. Furthermore, the flexibility of Bayesian conditional copula regression models is illustrated in two applications on childhood undernutrition and macroecology.

Boosting joint models for longitudinal and time-to-event data.

Joint models for longitudinal and time-to-event data have gained a lot of attention in the last few years as they are a helpful technique clinical studies where longitudinal outcomes are recorded alongside event times. Those two processes are often linked and the two outcomes should thus be modeled jointly in order to prevent the potential bias introduced by independent modeling. Commonly, joint models are estimated in likelihood-based expectation maximization or Bayesian approaches using frameworks where variable selection is problematic and that do not immediately work for high-dimensional data. In this paper, we propose a boosting algorithm tackling these challenges by being able to simultaneously estimate predictors for joint models and automatically select the most influential variables even in high-dimensional data situations. We analyze the performance of the new algorithm in a simulation study and apply it to the Danish cystic fibrosis registry that collects longitudinal lung function data on patients with cystic fibrosis together with data regarding the onset of pulmonary infections. This is the first approach to combine state-of-the art algorithms from the field of machine-learning with the model class of joint models, providing a fully data-driven mechanism to select variables and predictor effects in a unified framework of boosting joint models.

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

ABSTRACT 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, for example, 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. To embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits 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, as well as a Cox model for continuous time with space-time interactions. Supplementary material for this article is available online.

Quality and resource efficiency in hospital service provision: A geoadditive stochastic frontier analysis of stroke quality of care in Germany

We specify a Bayesian, geoadditive Stochastic Frontier Analysis (SFA) model to assess hospital performance along the dimensions of resources and quality of stroke care in German hospitals. With 1,100 annual observations and data from 2006 to 2013 and risk-adjusted patient volume as output, we introduce a production function that captures quality, resource inputs, hospital inefficiency determinants and spatial patterns of inefficiencies. With high relevance for hospital management and health system regulators, we identify performance improvement mechanisms by considering marginal effects for the average hospital. Specialization and certification can substantially reduce mortality. Regional and hospital-level concentration can improve quality and resource efficiency. Finally, our results demonstrate a trade-off between quality improvement and resource reduction and substantial regional variation in efficiency.

More green space is related to less antidepressant prescription rates in the Netherlands: A Bayesian geoadditive quantile regression approach

Background: Exposure to green space seems to be beneficial for self‐reported mental health. In this study we used an objective health indicator, namely antidepressant prescription rates. Current studies rely exclusively upon mean regression models assuming linear associations. It is, however, plausible that the presence of green space is non‐linearly related with different quantiles of the outcome antidepressant prescription rates. These restrictions may contribute to inconsistent findings. Objective: Our aim was: a) to assess antidepressant prescription rates in relation to green space, and b) to analyze how the relationship varies non‐linearly across different quantiles of antidepressant prescription rates. Methods: We used cross‐sectional data for the year 2014 at a municipality level in the Netherlands. Ecological Bayesian geoadditive quantile regressions were fitted for the 15%, 50%, and 85% quantiles to estimate green space–prescription rate correlations, controlling for physical activity levels, socio‐demographics, urbanicity, etc. Results: The results suggested that green space was overall inversely and non‐linearly associated with antidepressant prescription rates. More important, the associations differed across the quantiles, although the variation was modest. Significant non‐linearities were apparent: The associations were slightly positive in the lower quantile and strongly negative in the upper one. Conclusion: Our findings imply that an increased availability of green space within a municipality may contribute to a reduction in the number of antidepressant prescriptions dispensed. Green space is thus a central health and community asset, whilst a minimum level of 28% needs to be established for health gains. The highest effectiveness occurred at a municipality surface percentage higher than 79%. This inverse dose‐dependent relation has important implications for setting future community‐level health and planning policies. Graphical abstract: Figure. No caption available. HighlightsGreen space was inversely correlated with antidepressant prescription rates.Bayesian geoadditive quantile regression showed non‐linear dose‐response functions.The shape of the associations showed moderate variations across quantiles.For health gains, communities should have at least one quarter green space; the most health gains occur when the proportion exceeds three quarters.

Studying the occurrence and burnt area of wildfires using zero-one-inflated structured additive beta regression

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.

Studying the relationship between a woman's reproductive lifespan and age at menarche using a Bayesian multivariate structured additive distributional regression model

Studies addressing breast cancer risk factors have been looking at trends relative to age at menarche and menopause. These studies point to a downward trend of age at menarche and an upward trend for age at menopause, meaning an increase of a womans reproductive lifespan cycle. In addition to studying the effect of the year of birth on the expectation of age at menarche and a womans reproductive lifespan, it is important to understand how a womans cohort affects the correlation between these two variables. Since the behavior of age at menarche and menopause may vary with the geographic location of a womans residence, the spatial effect of the municipality where a woman resides needs to be considered. Thus, a Bayesian multivariate structured additive distributional regression model is proposed in order to analyze how a womans municipality and year of birth affects a womans age of menarche, her lifespan cycle, and the correlation of the two. The data consists of 212,517 postmenopausal women, born between 1920 and 1965, who attended the breast cancer screening program in the central region of Portugal.