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Generalized additive models for location, scale and shape (GAMLSSs) are a popular semiparametric modelling approach that, in contrast with conventional generalized additive models, regress not only the expected mean but also every distribution parameter (e.g. location, scale and shape) to a set of covariates. Current fitting procedures for GAMLSSs are infeasible for high dimensional data set-ups and require variable selection based on (potentially problematic) information criteria. The present work describes a boosting algorithm for high dimensional GAMLSSs that was developed to overcome these limitations. Specifically, the new algorithm was designed to allow the simultaneous estimation of predictor effects and variable selection. The algorithm proposed was applied to Munich rental guide data, which are used by landlords and tenants as a reference for the average rent of a flat depending on its characteristics and spatial features. The net rent predictions that resulted from the high dimensional GAMLSSs were found to be highly competitive and covariate-specific prediction intervals showed a major improvement over classical generalized additive models.

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.

We tackle two limitations of standard instrumental variable regression in experimental and observational studies: restricted estimation to the conditional mean of the outcome and the assumption of a linear relationship between regressors and outcome. More flexible regression approaches that solve these limitations have already been developed but have not yet been adopted in causality analysis. The paper develops an instrumental variable estimation procedure building on the framework of generalized additive models for location, scale and shape. This enables modelling all distributional parameters of potentially complex response distributions and non-linear relationships between the explanatory variables, instrument and outcome. The approach shows good performance in simulations and is applied to a study that estimates the effect of rural electrification on the employment of females and males in the South African province of KwaZulu-Natal. We find positive marginal effects for the mean for employment of females rates, negative effects for employment of males and a reduced conditional standard deviation for both, indicating homogenization in employment rates due to the electrification programme. Although none of the effects are statistically significant, the application demonstrates the potentials of using generalized additive models for location, scale and shape in instrumental variable regression for both to account for endogeneity and to estimate treatment effects beyond the mean.

Background Clinicians and patients lack an evidence-based framework by which to judge individual-level recovery following total knee arthroplasty (TKA) surgery, thus impeding personalized treatment approaches for this elective surgery. Our study aimed to develop and validate a reference chart for monitoring recovery of knee flexion following TKA surgery. Methods Retrospective analysis of data collected in routine rehabilitation practice for patients following TKA surgery. Reference charts were constructed using Generalized Additive Models for Location Scale and Shape. Various models were compared using the Schwarz Bayesian Criterion, Mean Squared Error in 5-fold cross validation, and centile coverage (i.e. the percent of observed data represented below specified centiles). The performance of the reference chart was then validated against a test set of patients with later surgical dates, by examining the centile coverage and average bias (i.e. difference between observed and predicted values) in the test dataset. Results A total of 1173 observations from 327 patients were used to develop a reference chart for knee flexion over the first 120 days following TKA. The best fitting model utilized a non-linear time trend, with smoothing splines for median and variance parameters. Additionally, optimization of the number of knots in smoothing splines and power transformation of time improved model fit. The reference chart performed adequately in a test set of 171 patients (377 observations), with accurate centile coverage and minimal average bias (< 3 degrees). Conclusion A reference chart developed with clinically collected data offers a new approach to monitoring knee flexion following TKA.

Background/Objectives: Static reference intervals (RIs) fail to capture the dynamic changes in bioanalytes. This study aimed to develop gender-based continuous age- and season-related RIs for neuron-specific enolase (NSE) using real-world data and to compare them with partitioned RIs. Methods: The NSE results from 4097 individuals were included after rigorous screening. Partitioned RIs were determined using the Hoffmann method. Generalized additive models for location, scale and shape (GAMLSS) were selected to develop continuous RIs. Results: The partitioned RIs are as follows: <16.4 µg/L for males aged ≥19 years; <14.47 µg/L for females aged 19–49 years; and <17.25 µg/L for females aged ≥50 years. For continuous RIs, NSE levels in males remain stable with age, while in females, NSE levels evidently increase around the age of 50. Although less impactful than age, seasonal changes still affect NSE levels. Dynamic changes and continuous RIs for NSE are visualized in this study. Conclusions: We developed gender-based continuous age- and season-integrated RIs for NSE in North China, highlighting the variation in NSE levels in females with age and season. Compared to static RIs, continuous RIs are more responsive to NSE, potentially enhancing the precision and individualization of health assessments.

We propose a novel method for neurodevelopmental brain mapping that displays how an individual's values for a quantity of interest compare with age-specific norms. By estimating smoothly age-varying distributions at a set of brain regions of interest, we derive age-dependent region-wise quantile ranks for a given individual, which can be presented in the form of a brain map. Such quantile rank maps could potentially be used for clinical screening. Bootstrap-based confidence intervals are proposed for the quantile rank estimates. We also propose a recalibrated Kolmogorov–Smirnov test for detecting group differences in the age-varying distribution. This test is shown to be more robust to model misspecification than a linear regression-based test. The proposed methods are applied to brain imaging data from the Nathan Kline Institute Rockland Sample and from the Autism Brain Imaging Data Exchange (ABIDE) sample. •We present a method for fitting smooth growth curves to a brain measure of interest.•This allows for mapping an individual's quantile rank at each of a set of regions.•We propose a new test for group differences based on age-varying distributions.•Our methods are illustrated with two magnetic resonance imaging data sets.

On temperate rocky reefs, overexploitation of high‐trophic‐level omnivores can result in the decimation of kelp forest habitats by releasing sea urchin population networks from top‐down control. However, the local dynamics of the resulting trophic cascades are context‐dependent. Here, we investigate the community‐wide patterns associated with both diffuse stressors and localized protection of high‐trophic‐level omnivores in kelp forest ecosystems by comparing communities among marine reserves and fished areas in two contrasting regions in terms of fishing intensity and land‐based stressors, Fiordland and the Marlborough Sounds, New Zealand. We find higher densities of the potential sea urchin predators, red rock lobsters (Jasus edwardsii) and banded wrasse (Notolabrus fucicola), in the Fiordland region, and larger effect sizes of fishing on the exploited fish communities in the Marlborough Sounds. Patterns in sea urchin density were consistent with the idea that high‐trophic‐level species, such as large fish and rock lobsters, regulate sea urchin population density, with lower densities of Evechinus chloroticus observed inside marine reserves, in both regions. Nevertheless, densities of E. chloroticus were generally high (>3 m2) in the Marlborough Sounds, likely above a grazing threshold in both fished and reserve sites. The proportion of habitat where sea urchins were absent was 29% in Marlborough Sounds and 90% in Fiordland. Consequently, we observe 49% barren habitat in Fiordland vs. 70%, and a larger effect of fishing on kelp community structure, in the Marlborough Sounds, where fishing effect sizes and land‐based stressors were more severe. We propose that a combination of diffuse stressors including regional overexploitation of important sea urchin predators, sedimentation, and warming of coastal waters likely contributed to regional differences in the responses of trophic interaction chains to localized reductions in fishing within marine reserves. The present study highlights how physiologically stressed and modified kelp forest ecosystems are more susceptible to detrimental phase shifts at a regional spatial scale.

Generalized additive models for location, scale, and shape (GAMLSS) are a class of semi-parametric models with potential applicability to health care cost data. We compared the bias, accuracy, and coverage of GAMLSS estimators with two distributions [gamma and generalized inverse gaussian (GIG)] using a log link to the generalized linear model (GLM) with log link and gamma family and the log-transformed OLS. The evaluation using simulated gamma data showed that the GAMLSS and GLM gamma model had similar bias, accuracy, and coverage and outperformed the GAMLSS GIG. When applied to simulated GIG data, the GLM gamma was similar or improved in bias, accuracy, and coverage compared to the GAMLSS GIG and gamma; furthermore, the GAMLSS estimators produced wildly inaccurate or overly-precise results in certain circumstances. Applying all models to empirical data on health care costs after a fall-related injury, all estimators produced similar coefficient estimates, but GAMLSS estimators produced spuriously smaller standard errors. Although no single alternative was best for all simulations, the GLM gamma was the most consistent, so we recommend against using GAMLSS estimators using GIG or gamma to test for differences in mean health care costs. Since GAMLSS offers many other flexible distributions, future work should evaluate whether GAMLSS is useful when predicting health care costs.

In this paper, we investigate the problem of how to combine operational losses collected from various banks of different sizes and loss reporting thresholds in order to estimate the distribution of operational loss severities for a bank of a given size. We model the severity of operational losses by using the extreme value theory to account for the reporting bias of the external data, and a regression analysis based on the GAMLSS framework to model the scaling properties of operational losses. In contrast to previous studies on the scaling problem, our analysis gives particular emphasis to the scaling properties of the tail of the loss distribution. Contrary to existing knowledge, we find that the size of a bank is an important determinant of the severity of operational losses and that the tail index of the distribution is negatively correlated with the size of the bank. The results indicate that for very large banks, distribution of the operational loss severity can be extremely heavy tailed (i.e. tail index less than 1), a finding which have significant implications for capital calculation as well as for risk management. Furthermore, we also demonstrate that the capital estimates provided by our model is consistent with the industry standards and the model can be used by individual banks to simulate data to complement their internal data.

Reaction times (RTs) are an essential metric used for understanding the link between brain and behaviour. As research is reaffirming the tight coupling between neuronal and behavioural RTs, thorough statistical modelling of RT data is thus essential to enrich current theories and motivate novel findings. A statistical distribution is proposed herein that is able to model the complete RT’s distribution, including location, scale and shape: the generalised-exponential-Gaussian (GEG) distribution. The GEG distribution enables shifting the attention from traditional means and standard deviations to the entire RT distribution. The mathematical properties of the GEG distribution are presented and investigated via simulations. Additionally, the GEG distribution is featured via four real-life data sets. Finally, we discuss how the proposed distribution can be used for regression analyses via generalised additive models for location, scale and shape (GAMLSS).