Generalized Additive Models For Location, Scale And Shape Models Research Articles

Prediction of deciduous teeth eruption in Brazilian children: A cross-sectional study nested in a prospective birth cohort (BRISA)

BackgroundDental eruption is part of a set of children´s somatic growth phenomena. The worldwide accepted human dental eruption chronology is still based on a small sample of European children. However, evidence points to some population variations with the eruption at least two months later in low-income countries, and local standards may be useful. So, this study aimed to predict deciduous teeth eruption from 12 months of age in a Brazilian infant population.MethodsWe developed a cross-sectional study nested in four prospective cohorts – the Brazilian Ribeirão Preto and São Luís Cohort Study (BRISA) – in a sample of 3,733 children aged 12 to 36 months old, corrected by gestational age. We made a reference curve with the number of teeth erupted by age using the Generalized Additive Models for location, scale, and shape (GAMLSS) technique. The explanatory variable was the corrected children´s age. The dependent variable was the number of erupted teeth, by gender, evaluated according to some different outcome distributional forms. The generalized Akaike information criterion (GAIC) and the model residuals were used as the model selection criterion.ResultsThe Box-Cox Power Exponential method was the GAMLSS model with better-fit indexes. Our estimation curve was able to predict the number of erupted deciduous teeth by age, similar to the real values, in addition to describing the evolution of children’s development, with comparative patterns. There was no difference in the mean number of erupted teeth between the sexes. According to the reference curve, at 12 months old, 25% of children had four erupted teeth or less, while 75% had seven or fewer and 95% had 11 or fewer. At 24 months old, 5% had less than 12, and 75% had 18 or more. At 36 months old, around 50% of the population had deciduous dentition completed (20 teeth).ConclusionThe adjusted age was an important predictor of the number of erupted deciduous teeth. This outcome can be a variable incorporated into children’s growth and development curves, such as weight and height curves for age to help dentists and physicians in the monitoring the children’s health.

Applicability of the Global Lung Function Initiative prediction equations in Hong Kong Chinese children.

This study aimed to assess the applicability of the Global Lung Function Initiative (GLI) prediction equations for spirometry in Hong Kong childrenand to develop prediction equations based on the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) modeling. Healthy Chinese children and adolescents aged 6-17 years old were recruited from randomly selected schools to undergo spirometry. The measurements were transformed to z-score according to the GLI-2012 equations for South East(SE) Asians and the GLI-2022 global race-neutral equations. Prediction equations for spirometric indices were developed with GAMLSS modeling to identify predictors. A total of 886 children (477 boys) with a mean age of 12.5 years (standard deviation [SD]3.3 years) were included. By the GLI-2012 SE Asian equations, positive mean z-scores were observed in forced expiratory volume in 1 s(FEV1 )(boys: 0.138 ± SD 0.828;girls: 0.206 ± 0.823) and forced vital capacity(FVC) (boys: 0.160 ± 0.930;girls: 0.310 ± 0.895) in both sexes. Negative mean z-scores were observed in FEV1 /FVC ratio (boys: -0.018 ± 0.998; girls: -0.223 ± 0.897). In contrast, negative mean z-scores in FEV1 and FVC, and positive mean z-scores in FEV1 /FVC were observed when adopting the GLI-2022 race-neutral equations. The mean z-scores were all within the range of ±0.5. By GAMLSS models, age and height were significant predictors for all four spirometric indices, while weight was an additional predictor for FVC and FEV1 . Our study provided data supporting the applicability of the GLI prediction equations in Hong Kong Chinese children. The GLI-2012 equations may underestimate FEV1 and FVC, while the GLI-2022 equations may overestimate the parameters, but the differences lie within the physiological limits. By GAMLSS modeling, weight was an additional predictor for FVC and FEV1 .

Flood Frequency Analysis under Nonstationary Modeling in the Gorganrood River Basin, Iran

The nonstationary hydrologic processes due to climate variability and intensification of human activities are challenging and questionable for researchers. This study investigates nonstationary partial duration series (PDS) records for the period 1971–2017 at 14 hydrological stations across the Gorganrood River Basin, Iran. The Gorganrood Basin is very diverse in terms of climate such as humid, semihumid, Mediterranean, semiarid, and arid climates. Change points are analyzed using the Pettitt technique. Trends of PDS are detected using the Mann–Kendall method. The nonstationarity of the PDS series is examined by generalized additive models for location, scale, and shape (GAMLSS). Results indicate that abrupt changes are significant for the PDS series in the Gorganrood River Basin. Change points have a considerable effect on trend detection, and these may be attributed to the fact that an abrupt increase or decrease in mean values affects trend changes. In addition, the GAMLSS results showed that the most suitable performance distribution was LNO distribution and then RGE distribution in the Gorganrood River Basin. On other hand, the GAMLSS model and the Pettitt test have good capability in detecting stationary and nonstationary PDS series.

Childhood to adulthood: Accounting for age dependence in healthy-reference distributions in 129 Xe gas-exchange MRI.

Xenon-129 (129 Xe) gas-exchange MRI is a pulmonary-imaging technique that provides quantitative metrics for lung structure and function and is often compared to pulmonary-function tests. Unlike such tests, it does not normalize to predictive values based on demographic variables such as age. Many sites have alluded to an age dependence in gas-exchange metrics; however, a procedure for normalizing metrics has not yet been introduced. We model healthy reference values for 129 Xe gas-exchange MRI against age using generalized additive models for location, scale, and shape (GAMLSS). GAMLSS takes signal data from an aggregated heathy-reference cohort and fits a distribution with flexible median, variation, skewness, and kurtosis to predict age-dependent centiles. This approach mirrors methods by the Global Lung Function Initiative for modeling pulmonary-function test data and applies it to binning methods widely used by the 129 Xe MRI community to interpret and quantify gas-exchange data. Ventilation, membrane-uptake, red blood cell transfer, and red blood cell:membrane gas-exchange metrics were collected on 30 healthy subjects over an age range of 5 to 68years. A GAMLSS model was fit against age and compared against widely used linear and generalized-linear binning 129 Xe MRI analysis schemes. All 4 gas-exchange metrics had significant skewness, and membrane-uptake had significant kurtosis compared to a normal distribution. Age has significant impact on distribution parameters. GAMLSS-binning produced narrower bins compared to the linear and generalized-linear binning schemes and distributed signal data closer to a normal distribution. The proposed "proof-of-concept" GAMLSS-binning approach can improve diagnostic accuracy of 129 Xe gas-exchange MRI by providing a means of modeling voxel distribution data against age.

Nonstationary analysis of hydrological drought index in a coupled human-water system: Application of the GAMLSS with meteorological and anthropogenic covariates in the Wuding River basin, China

Significant nonstationarity of hydrological sequences, driven by the coupled influence of climate change and anthropogenic activities, has challenged traditional hydrological drought analysis under the stationarity assumption in some regions, and has questioned regional hydrological drought analysis under the changing environment. To evaluate hydrological drought characteristics, the novelty of this paper is the proposition of a GAMLSS (Generalized Additive Models for Location, Scale, and Shape)-based nonstationary standardized runoff index (NSRI), considering climate change and anthropogenic influence, for investigating the hydrological drought regime in the Wuding River basin. To that end, nonstationary test methods were performed on hydrological sequences, and data was segmented into three parts according to the results of the Pettitt test. A nonstationary probability distribution was fitted to runoff data with meteorological covariates (precipitation, temperature) and anthropogenic covariates (water consumption for social development demand, and water consumption triggered by water impounding by check dams). After selecting an optimal combination of covariates, the NSRI was calculated utilizing the GAMLSS model. A newly constructed evaluation threshold was proposed, based on the traditional SRI threshold. The performance of SRI and NSRI were compared at the Dingjiagou station in the Wuding River basin. Results of comparison between index identification and recorded drought events demonstrated that the NSRI better performed in drought event identification. Moreover, the NSRI identified more frequent severe droughts and extreme droughts. Therefore, the proposed NSRI provided a more accurate basis for the identification of drought events, which can offer valuable information for drought planning, preparedness, and mitigation.

Frequency Analysis of Snowmelt Flood Based on GAMLSS Model in Manas River Basin, China

With the acceleration of human economic activities and dramatic changes in climate, the validity of the stationarity assumption of flood time series frequency analysis has been questioned. In this study, a framework for flood frequency analysis is developed on the basis of a tool, namely, the Generalized Additive Models for Location, Scale, and Shape (GAMLSS). We introduced this model to construct a non-stationary model with time and climate factor as covariates for the 50-year snowmelt flood time series in the Kenswat Reservoir control basin of the Manas River. The study shows that there are clear non-stationarities in the flood regime, and the characteristic series of snowmelt flood shows an increasing trend with the passing of time. The parameters of the flood distributions are modelled as functions of climate indices (temperature and rainfall). The physical mechanism was incorporated into the study, and the simulation results are similar to the actual flood conditions, which can better describe the dynamic process of snowmelt flood characteristic series. Compared with the design flood results of Kenswat Reservoir approved by the China Renewable Energy Engineering Institute in December 2008, the design value of the GAMLSS non-stationary model considers that the impact of climate factors create a design risk in dry years by underestimating the risk.

A tutorial on regression-based norming of psychological tests with GAMLSS.

A norm-referenced score expresses the position of an individual test taker in the reference population, thereby enabling a proper interpretation of the test score. Such normed scores are derived from test scores obtained from a sample of the reference population. Typically, multiple reference populations exist for a test, namely when the norm-referenced scores depend on individual characteristic(s), as age (and sex). To derive normed scores, regression-based norming has gained large popularity. The advantages of this method over traditional norming are its flexible nature, yielding potentially more realistic norms, and its efficiency, requiring potentially smaller sample sizes to achieve the same precision. In this tutorial, we introduce the reader to regression-based norming, using the generalized additive models for location, scale, and shape (GAMLSS). This approach has been useful in norm estimation of various psychological tests. We discuss the rationale of regression-based norming, theoretical properties of GAMLSS and their relationships to other regression-based norming models. Based on 6 steps, we describe how to: (a) design a normative study to gather proper normative sample data; (b) select a proper GAMLSS model for an empirical scale; (c) derive the desired normed scores for the scale from the fitted model, including those for a composite scale; and (d) visualize the results to achieve insight into the properties of the scale. Following these steps yields regression-based norms with GAMLSS for a psychological test, as we illustrate with normative data of the intelligence test IDS-2. The complete R code and data set is provided as online supplemental material. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Delineating the relative contribution of climate related variables to chlorophyll-a and phytoplankton biomass in lakes using the ERA5-Land climate reanalysis data

Understanding the climatic drivers of eutrophication is critical for lake management under the prism of the global change. Yet the complex interplay between climatic variables and lake processes makes prediction of phytoplankton biomass a rather difficult task. Quantifying the relative influence of climate-related variables on the regulation of phytoplankton biomass requires modelling approaches that use extensive field measurements paired with accurate meteorological observations. In this study we used climate and lake related variables obtained from the ERA5-Land reanalysis dataset combined with a large dataset of in-situ measurements of chlorophyll-a and phytoplankton biomass from 50 water bodies to develop models of phytoplankton related responses as functions of the climate reanalysis data. We used chlorophyll-a and phytoplankton biomass as response metrics of phytoplankton growth and we employed two different modelling techniques, boosted regression trees (BRT) and generalized additive models for location scale and shape (GAMLSS). According to our results, the fitted models had a relatively high explanatory power and predictive performance. Boosted regression trees had a high pseudo R2 with the type of the lake, the total layer temperature, and the mix-layer depth being the three predictors with the higher relative influence. The best GAMLSS model retained mix-layer depth, mix-layer temperature, total layer temperature, total runoff and 10-m wind speed as significant predictors (p<0.001). Regarding the phytoplankton biomass both modelling approaches had less explanatory power than those for chlorophyll-a. Concerning the predictive performance of the models both the BRT and GAMLSS models for chlorophyll-a outperformed those for phytoplankton biomass. Overall, we consider these findings promising for future limnological studies as they bring forth new perspectives in modelling ecosystem responses to a wide range of climate and lake variables. As a concluding remark, climate reanalysis can be an extremely useful asset for lake research and management.

Nonstationary Ecological Instream Flow and Relevant Causes in the Huai River Basin, China

Based on the daily precipitation data during 1960–2016 at 72 stations and the daily streamflow data during 1956–2016 at 7 hydrological stations in the Huai River Basin (HRB), China, eco-surplus and eco-deficit under influences of abrupt streamflow behaviors were analyzed using Flow Duration Curve (FDC). The relations between indicators of hydrological alteration (IHA) and ecological indicators (Shannon Index, SI) were quantified, investigating impacts of altered hydrological processes on the evaluations of the ecological instream flow. Besides, we also quantified fractional contributions of climatic indices to nonstationary ecological instream flow using the Generalized Additive Models for Location Scale and Shape (GAMLSS) framework. While the possible impact of human activities on ecological instream flow will be revealed based on land use changes data. The results indicated that: (1) FDC is subject to general decrease due to hydrological alterations, and most streamflow components are lower than 25% FDC. We found increased eco-deficit and decreased eco-surplus due to altered hydrological processes. The FDC of the streamflow in the main stream of the HRB is lower than that along the tributaries of the HRB. Eco-surplus (eco-deficit) changes are in good line with precipitation anomaly changes during the Spring, Autumn and Winter periods. However, the hydrological alterations due to hydrological regulations by the reservoirs are the primary cause behind the mismatch between ecological instream flow and precipitation anomalies during summer; (2) Annual and seasonal eco-surplus (eco-deficit) is decreasing (increasing) and that during winter season is an exception. Although higher eco-surplus in winter than in other seasons, the eco-surplus is decreasing persistently and the 21st century witnessed the lowest eco-surplus along the main stream of the HRB. Meanwhile, the Shannon index indicated decreased ecological diversity across the HRB; (3) The ecological instream flow is highly sensitive to The Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO) and Niño 3.4 Sea Surface Temperature Index (Nino3.4). Meanwhile, the ecological instream flow along the mainstream of the HRB is highly sensitive to climate indices. While the ecological instream flow by GAMLSS model has better fitting performance in describing the extreme values and local trends.

Spatiotemporal Distribution of Key Pelagic Microbes in a Seasonal Oxygen-Deficient Coastal Upwelling System of the Eastern South Pacific Ocean

The strong seasonal variability in physical-chemical conditions of the Eastern South Pacific Ocean creates an ideal setting to study spatiotemporal distribution of key marine microbial communities.. We herein report a nearly 4-year-long time series of the variability in amoA gene counts of ammonia oxidizing archaea (AOA) and bacteria (betaproteobacteria, bAOB) by quantitative PCR, GI.1a Thaumarchaeota and MG-II Euryarchaeota by CARD-FISH, and the picoplanktonic community by flow cytometry for this area. During spring-summer, non-photosynthetic picoplankton such as MG-II Euryarchaeota and GI.1a Thaumarchaeota peaked at the surface and deeper waters, respectively. General AOA and bAOB achieved higher abundances at the oxycline mainly in summer (up to 105-104 amoA copies mL-1). Generalized additive models for location, scale, and shape (GAMLSS) indicated that season and depth account for 19-46% of variations in the abundance of the groups studied, particularly GI.1a Thaumarchaeota and AOA. The oxygen and nitrite concentration were statistically meaningful predictors for the studied groups. GAMLSS models indicate that ammonia oxidizing assemblage’s variability is coupled with ammonia, nitrite, and nitrate variations. Our results indicate that microbial abundances fluctuation is associated with upwelling variability and oxygen-deficient water conditions that shape the substrates availability and metabolic response of marine microbes, including keystone ammonia oxidizing assemblages and their ecological interactions. Overall, our results support planktonic nitrification activity and its contribution to nitrous oxide excess production in the time series off Concepción and the ecological dynamics regarding AOA -bAOB in coastal waters.

Rainfall Prediction in the State of Paraíba, Northeastern Brazil Using Generalized Additive Models

The state of Paraíba is part of the semi-arid region of Brazil, where severe droughts have occurred in recent years, resulting in significant socio-economic losses associated with climate variability. Thus, understanding to what extent precipitation can be influenced by sea surface temperature (SST) patterns in the tropical region can help, along with a monitoring system, to set up an early warning system, the first pillar in drought management. In this study, Generalized Additive Models for Location, Scale and Shape (GAMLSS) were used to filter climatic indices with higher predictive efficiency and, as a result, to perform rainfall predictions. The results show the persistent influence of tropical SST patterns in Paraíba rainfall, the tropical Atlantic Ocean impacting the rainfall distribution more effectively than the tropical Pacific Ocean. The GAMLSS model showed predictive capability during summer and southern autumn in Paraíba, highlighting the JFM (January, February and March), FMA (February, March and April), MAM (March, April and May), and AMJ (April, May and June) trimesters as those with the highest predictive potential. The methodology demonstrates the ability to be integrated with regional forecasting models (ensemble). Such information has the potential to inform decisions in multiple sectors, such as agriculture and water resources, aiming at the sustainable management of water resources and resilience to climate risk.

Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model

Under changing environments, the most widely used non-stationary flood frequency analysis (NFFA) method is the generalized additive models for location, scale and shape (GAMLSS) model. However, the model structure of the GAMLSS model is relatively complex due to the large number of statistical parameters, and the relationship between statistical parameters and covariates is assumed to be unchanged in future, which may be unreasonable. In recent years, nonparametric methods have received increasing attention in the field of NFFA. Among them, the linear quantile regression (QR-L) model and the non-linear quantile regression model of cubic B-spline (QR-CB) have been introduced into NFFA studies because they do not need to determine statistical parameters and consider the relationship between statistical parameters and covariates. However, these two quantile regression models have difficulties in estimating non-stationary design flood, since the trend of the established model must be extrapolated infinitely to estimate design flood. Besides, the number of available observations becomes scarcer when estimating design values corresponding to higher return periods, leading to unreasonable and inaccurate design values. In this study, we attempt to propose a cubic B-spline-based GAMLSS model (GAMLSS-CB) for NFFA. In the GAMLSS-CB model, the relationship between statistical parameters and covariates is fitted by the cubic B-spline under the GAMLSS model framework. We also compare the performance of different non-stationary models, namely the QR-L, QR-CB, and GAMLSS-CB models. Finally, based on the optimal non-stationary model, the non-stationary design flood values are estimated using the average design life level method (ADLL). The annual maximum flood series of four stations in the Weihe River basin and the Pearl River basin are taken as examples. The results show that the GAMLSS-CB model displays the best model performance compared with the QR-L and QR-CB models. Moreover, it is feasible to estimate design flood values based on the GAMLSS-CB model using the ADLL method, while the estimation of design flood based on the quantile regression model requires further studies.

Reference equations for spirometry in healthy Asian children aged 5 to 18 years in Taiwan

Background and objectiveThis study aimed to establish reference equations for spirometry in healthy Taiwanese children and assess the applicability of the Global Lung Function Initiative (GLI)-2012 equations to Taiwanese children. MethodsSpirometric data collected from 757 healthy Taiwanese children aged 5 to 18 years in a population-based cohort study. Prediction equations derived using linear regression and the generalized additive models for location, scale and shape (GAMLSS) method, respectively. ResultsThe GLI-2012 South East Asian equations did not provide a close fit with mean ± standard error z-scores of −0.679 ± 0.030 (FVC), −0.186 ± 0.044 (FEV1), −0.875 ± 0.049 (FEV1/FVC ratio) and −2.189 ± 0.063 (FEF25-75) for girls; and 0.238 ± 0.059, −0.061 ± 0.053, −0.513 ± 0.059 and −1.896 ± 0.077 for boys. The proposed GAMLSS models took age, height, and weight into account. GAMLSS models for boys and girls captured the characteristics of spirometric data in the study population closely in contrast to the linear regression models and the GLI-2012 equations. ConclusionThis study provides up-to-date reference values for spirometry using GAMLSS modeling in healthy Taiwanese children aged 5 to 18 years. Our study provides evidence that the GLI-2012 reference equations are not properly matched to spirometric data in a contemporary Taiwanese child population, indicating the urgent need for an update of GLI reference values by inclusion of more data of non-Caucasian decent.

Climate drives the spatial distribution of mycorrhizal host plants in terrestrial ecosystems

Abstract Mycorrhizal associations have massive impacts on ecosystem functioning, but the mode and magnitude heavily depend on the mycorrhizal type involved. Different types of mycorrhizas are recognized to predominate under different environmental conditions. However, the respective importance of climate and soil characteristics in shaping mycorrhizal global distributions are still poorly understood. We provide a quantitative and comprehensive global analysis of the main climatic and edaphic predictors of the distribution of plants featuring different mycorrhizal types. Estimates on per grid‐cell relative above‐ground biomass of plants holding arbuscular mycorrhiza (AM), ectomycorrhiza (EcM) and ericoid mycorrhiza (ErM) association were related to a set of 39 climatic and edaphic variables. We assessed their relationship by applying a Generalized Additive Models for Location, Scale and Shape (GAMLSS). The best GAMLSS models were able to explain 55%, 41% and 46% of the variance in AM, EcM and ErM distribution, respectively. Temperature‐related factors were the main predictors of distribution patterns for the three different mycorrhizal plant types. AM plants are favoured by warm climates, while EcM plants’ dominance (and to some extent ErM plants too) is favoured by colder climates. Synthesis. The observed lack of importance of soil drivers challenges the predominant view that mycorrhizal plants distribution mainly reflects soil type preferences—as related to its nutrient foraging strategies—of the different mycorrhizal types. Instead, our results highlight climate—and particularly temperature—as the main force shaping the distribution of arbuscular mycorrhiza, ectomycorrhiza and ericoid mycorrhiza host plants at the global scale and suggest that climate change can significantly alter the distribution of mycorrhizal host plants, with a subsequent impact on ecosystem functioning.

Modeling spatiotemporal abundance of mobile wildlife in highly variable environments using boosted GAMLSS hurdle models.

Modeling organism distributions from survey data involves numerous statistical challenges, including accounting for zero‐inflation, overdispersion, and selection and incorporation of environmental covariates. In environments with high spatial and temporal variability, addressing these challenges often requires numerous assumptions regarding organism distributions and their relationships to biophysical features. These assumptions may limit the resolution or accuracy of predictions resulting from survey‐based distribution models. We propose an iterative modeling approach that incorporates a negative binomial hurdle, followed by modeling of the relationship of organism distribution and abundance to environmental covariates using generalized additive models (GAM) and generalized additive models for location, scale, and shape (GAMLSS). Our approach accounts for key features of survey data by separating binary (presence‐absence) from count (abundance) data, separately modeling the mean and dispersion of count data, and incorporating selection of appropriate covariates and response functions from a suite of potential covariates while avoiding overfitting. We apply our modeling approach to surveys of sea duck abundance and distribution in Nantucket Sound (Massachusetts, USA), which has been proposed as a location for offshore wind energy development. Our model results highlight the importance of spatiotemporal variation in this system, as well as identifying key habitat features including distance to shore, sediment grain size, and seafloor topographic variation. Our work provides a powerful, flexible, and highly repeatable modeling framework with minimal assumptions that can be broadly applied to the modeling of survey data with high spatiotemporal variability. Applying GAMLSS models to the count portion of survey data allows us to incorporate potential overdispersion, which can dramatically affect model results in highly dynamic systems. Our approach is particularly relevant to systems in which little a priori knowledge is available regarding relationships between organism distributions and biophysical features, since it incorporates simultaneous selection of covariates and their functional relationships with organism responses.

Determination of adjusted reference intervals of urinary biomarkers of oxidative stress in healthy adults using GAMLSS models.

In this study we aimed at identifying main demographic, laboratory and environmental factors influencing the level of urinary biomarkers (DNA-derived 8-oxodG and lipid membrane-derived 8-isoprostane), and deriving their adjusted 95% reference intervals (RI) in a sample of healthy people from the general population. Data from 281 healthy subjects from the Gene Environment Interactions in Respiratory Diseases survey were used in this study. Generalized additive models for location, scale and shape (GAMLSS) were used to find determinants of the biomarkers among gender, age, season and distance from collection (DFC), and to predict their RI. The RI of the biomarkers stratified by season and adjusted for DFC showed a slight statistically significant decrease in the biomarkers at the increasing DFC in two seasons, except the 8-oxodG during the warm season: median levels at the min and max values of DFC were (ng/mgcreat) 7.0–1.1 in the cold and 3.9–3.9 in the warm seasons for 8-oxodG, 0.7–0.2 in the cold and 1.3–0.6 in the warm seasons for 8-isoprostane. Both the biomarkers should be evaluated in association with the DFC and season in large epidemiological studies. The (semi)parametric GAMLSS method is a useful and flexible technique, which makes it possible to estimate adjusted RI.

Non-nested hypothesis testing inference for GAMLSS models

Two or more regression models are said to be non-nested if neither can be obtained from the remaining models when parametric restrictions are imposed. Tests for choosing between linear non-nested regression models are found in literature, such as J and MJ tests. In this paper we propose variants of these two tests for the GAMLSS (Generalized Additive Models for Location, Scale and Shape) class of models. We report Monte Carlo evidence on finite sample behaviour of the proposed tests. Bootstrap-based testing inference is also considered. Overall, bootstrap MJ test had the best performance. An empirical application is presented and discussed.

Optimal Bonus-Malus Systems Using Generalized Additive Models for Location, Scale and Shape

This paper presents the design of optimal Bonus-Malus Systems (BMS) using generalized additive models for location, scale and shape (GAMLSS), extending the work of Tzougas, Frangos and Vrontos (2014). Specifically, for the frequency component we employ a Negative Binomial Type I, a Poisson-Inverse Gaussian, a Sichel and a finite Poisson mixture GAMLSS model, while for the severity component we employ a Pareto and a finite Exponential mixture GAMLSS models. In the path towards actuarial relevance the Bayesian view is taken and the premiums are calculated by updating the posterior mean and posterior probability of the policyholders' classes of risk. Our analysis shows that the employment of more advanced models can provide a measure of uncertainty regarding the credibility updates of claim frequency/severity of each specific risk class and the difference in the premium that they imply can act as a cushion against adverse experience. Finally, these tailor-made premiums are compared to those which correspond to the 'univariate',without regression components, models.

Are generalized additive models for location, scale, and shape an improvement on existing models for estimating skewed and heteroskedastic cost data?

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.

Alternative regression models to assess increase in childhood BMI

BackgroundBody mass index (BMI) data usually have skewed distributions, for which common statistical modeling approaches such as simple linear or logistic regression have limitations.MethodsDifferent regression approaches to predict childhood BMI by goodness-of-fit measures and means of interpretation were compared including generalized linear models (GLMs), quantile regression and Generalized Additive Models for Location, Scale and Shape (GAMLSS). We analyzed data of 4967 children participating in the school entry health examination in Bavaria, Germany, from 2001 to 2002. TV watching, meal frequency, breastfeeding, smoking in pregnancy, maternal obesity, parental social class and weight gain in the first 2 years of life were considered as risk factors for obesity.ResultsGAMLSS showed a much better fit regarding the estimation of risk factors effects on transformed and untransformed BMI data than common GLMs with respect to the generalized Akaike information criterion. In comparison with GAMLSS, quantile regression allowed for additional interpretation of prespecified distribution quantiles, such as quantiles referring to overweight or obesity. The variables TV watching, maternal BMI and weight gain in the first 2 years were directly, and meal frequency was inversely significantly associated with body composition in any model type examined. In contrast, smoking in pregnancy was not directly, and breastfeeding and parental social class were not inversely significantly associated with body composition in GLM models, but in GAMLSS and partly in quantile regression models. Risk factor specific BMI percentile curves could be estimated from GAMLSS and quantile regression models.ConclusionGAMLSS and quantile regression seem to be more appropriate than common GLMs for risk factor modeling of BMI data.