Generalized Additive Models For Location, Scale And Shape Research Articles

Centile Reference Curves of the SLOfit Physical Fitness Tests for School-Aged Children and Adolescents.

Blagus, R, Jurak, G, Starc, G, and Leskošek, B. Centile reference curves of the SLOfit physical fitness tests for school-aged children and adolescents. J Strength Cond Res 37(2): 328-336, 2023-The study provides sex- and age-specific centile norms of Slovenian children and youth. Physical fitness was assessed using the SLOfit test battery on population data, including 185,222 children, aged 6-19 years, measured in April and May 2018. Centile curves for both sexes and 12 test items were constructed using the generalized additive models for location, scale, and shape (GAMLSS). Boys generally achieved higher scores in most of the physical fitness tests, except in stand and reach, but this was not consistent throughout childhood and adolescence, nor did it pertain to the entire range of performance. Girls outperformed boys in the arm-plate tapping test throughout childhood; the poorest performing girls outperformed the poorest performing boys in the 600-m run, 60-m dash, backward obstacle course, and standing broad jump. The shapes and trends of physical fitness curves adequately reflect the effects of growth and development on boys' and girls' physical performance. Comparing the existing reference fitness curves showed that Slovenian children and adolescents display higher fitness levels than their peers from other countries. This study provides the most up-to-date sex- and age-specific reference fitness centile curves of Slovenian children, which can be used as benchmark values for health and fitness monitoring and surveillance systems.

Decreasing flood hazard evaluated in Turkey using nonstationary models

AbstractAn assessment of changing flood hazard in the river basins of Turkey is currently lacking. This study evaluates the drivers of flood flows using distributional regression models. The generalized additive models for location, scale, and shape (GAMLSS), a flexible framework well‐suited to probabilistic nonstationary modeling, is applied to annual instantaneous maximum flows (AIMF) from 12 gauging stations located in the upper, middle and lower parts of the Euphrates basin, the most important river basin in the Middle East. First, the Pettitt test was used to detect abrupt changes in the AIMF data series, and the Mann–Kendall test to evaluate temporal trends. Significant change points for two stations and significant decreasing temporal changes for seven stations were observed. Three strictly positive, continuous distributions (namely, Gamma, Lognormal, and Weibull) were then fitted to the AIMF data series and the distribution parameters were specified as functions of both time and physically based covariates (precipitation, temperature, and climate oscillation indices). Among the candidate distributions, the Lognormal was found to be the most appropriate for describing flood flows across the basin. Annual precipitation, seasonal temperature and annual oscillation indices were the most relevant covariates. Among the climate indices, the East Atlantic Oscillation was most relevant in the lower part of the basin, the Southern and North Atlantic Oscillations in the middle, and the East Atlantic‐West Russia pattern in the upper part. The models were then employed to estimate and compare historical stationary flood quantiles with nonstationary quantiles (identified with physically based covariates) under various return periods (10, 20, 50, 100, and 200 years). Results indicate that flood processes can be better described by employing distributional regression models with physical covariates and this study can serve as a reference for regional water resources management in the basin and possibly for other river basins.

Performance of four regression frameworks with varying precision profiles in simulated reference material commutability assessment.

One approach to assessing reference material (RM) commutability and agreement with clinical samples (CS) is to use ordinary least squares or Deming regression with prediction intervals. This approach assumes constant variance that may not be fulfilled by the measurement procedures. Flexible regression frameworks which relax this assumption, such as quantile regression or generalized additive models for location, scale, and shape (GAMLSS), have recently been implemented, which can model the changing variance with measurand concentration. We simulated four imprecision profiles, ranging from simple constant variance to complex mixtures of constant and proportional variance, and examined the effects on commutability assessment outcomes with above four regression frameworks and varying the number of CS, data transformations and RM location relative to CS concentration. Regression framework performance was determined by the proportion of false rejections of commutability from prediction intervals or centiles across relative RM concentrations and was compared with the expected nominal probability coverage. In simple variance profiles (constant or proportional variance), Deming regression, without or with logarithmic transformation respectively, is the most efficient approach. In mixed variance profiles, GAMLSS with smoothing techniques are more appropriate, with consideration given to increasing the number of CS and the relative location of RM. In the case where analytical coefficients of variation profiles are U-shaped, even the more flexible regression frameworks may not be entirely suitable. In commutability assessments, variance profiles of measurement procedures and location of RM in respect to clinical sample concentration significantly influence the false rejection rate of commutability.

A GAMLSS approach to predicting growth of Nopalea cochenillifera Giant Sweet clone submitted to water and saline stress

Water and saline stresses are the main factors affecting agricultural production in semiarid regions. The tolerance of forage cactus to water and salt deficit makes it a promising solution, in particular Nopalea cochenillifera. The growth curves for species facing these conditions can provide useful information supporting the cultivation and management of natural populations and carry significant biological importance as growth rate assessment contributes to maintaining species viability. The objective of this study was to estimate the plant height and linear dimensions (length, width, and thickness) of N. cochenillifera Giant Sweet clone growing under water and saline stress. The experiment design was completely randomized, comprising a 4 × 4 factorial, with four water and four salinity levels; there were four replications. In order to estimate plant height in N. cochenillifera Giant Sweet clone as a function of the accumulated thermal sum, generalized additive models for location, scale, and shape (GAMLSS) were used to determine water level, saline level, length, width, and thickness. We constructed models using four distributions: the Weibull, Gumbel, Logistic, and Box-Cox power exponential distributions. The models were evaluated using global deviation and the generalized Akaike criterion. The Box–Cox power exponential proved to be the most effective in estimating N. cochenillifera height. This model enabled information relevant to practical environmental management to be obtained, as it precisely defined the optimum salt application and the required amount of replacement water, together with the cladode width for each plant growth stage using the accumulated thermal sum.

Generalised exponential-Gaussian distribution: a method for neural reaction time analysis

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).

Hydrological response in a highly urbanized watershed in China

Abstract Urbanization has a strong signal on the hydrologic cycle, leading to reduced infiltration and faster and larger runoff. However, the detailed analysis of the contribution of urbanization to different quantiles of discharge is still lacking; particularly, less is known in watersheds that have been experiencing such large and rapid urbanization as those in China. Here, we focus on the Wenyu watershed, a rapidly urbanizing basin located in the Beijing metropolitan area. Using a statistical attribution framework, we examine the hydrological response to the increasing urbanization across a wide range of discharge quantiles, from low to high flows; moreover, we perform analyses at the seasonal scale to capture differences in the physical processes at play during the year. Results indicate that the selected GAMLSS (generalized additive models for location, scale, and shape) models can capture well the variability in streamflow in this highly urbanized basin, with the average Spearman correlation coefficients between observations and the median of the fitted models of 0.84, 0.79, and 0.81 in spring, summer, and winter, respectively. Overall, urbanization played a different role in the different seasons and discharge quantiles. More specifically, we find its strongest impact to be in winter and spring, and for low and median quantiles. The role of precipitation is the strongest in summer, and it increases as we move toward the upper tail of the discharge distribution, especially above the 55th percentile, for which precipitation is selected as the only important predictor. Recycled water, on the other hand, tends to play a more dominant role in winter and spring. HIGHLIGHTS Urbanization has a strong signal on the hydrologic cycle; however, less is known in watersheds that have been experiencing such large and rapid urbanization. In this research, we focus on a fast urbanizing basin, and the hydrological responses to the increasing urbanization have been examined. The quantification of the impacts of drivers for different discharge quantiles and seasons has been examined. Urbanization plays a decreasing role towards the upper tail of the distribution.

Establishment of Reference Interval and Aging Model of Homocysteine Using Real-World Data.

ObjectiveThe level of Homocysteine (Hcy) in males is generally higher than that of females, but the same reference interval (RI) is often used in clinical practice. This study aims to establish a sex-specific RI of Hcy using five data mining algorithms and compare these results. Furthermore, age-related continuous RI was established in order to show the relationship between Hcy concentration distribution and age.MethodsA total of 20,801 individuals were included in the study and Tukey method was used to identify outliers in subgroups by sex and age. Multiple linear regression and standard deviation ratio (SDR) was used to determine whether the RI for Hcy needs to be divided by sex and age. Five algorithms including Hoffmann, Bhattacharya, expectation maximization (EM), kosmic and refineR were utilized to establish the RI of Hcy. Generalized Additive Models for Location Scale and Shape (GAMLSS) algorithm was used to determine the aging model of Hcy and calculate the age-related continuous RI.ResultsRI of Hcy needed to be partitioned by sex (SDR = 0.735 > 0.375). RIs established by Hoffmann, Bhattacharya, EM (for females) and kosmic are all within the 95% CI of reference limits established by refine R. The Sex-specific aging model of Hcy showed that the upper limits of the RI of Hcy declined with age beginning at age of 18 and began to rise approximately after age of 40 for females and increased with age for males.ConclusionThe RI of Hcy needs to be partitioned by sex. The RIs established by the five data mining algorithms showed good consistency. The dynamic sex and age-specific model of Hcy showed the pattern of Hcy concentration with age and provide more personalized tools for clinical decisions.

A New Birthweight Reference by Gestational Age: A Population Study Based on the Generalized Additive Model for Location, Scale, and Shape Method

BackgroundIt is important to choose a suitable birthweight reference to assess newborns, especially those that are small for gestational age (SGA). Currently, there is no regional standard reference for the north of China or for Shandong province.MethodsA total of 130,911 data records of singleton, live neonates born at 24–42 weeks of gestation were collected from 2016 to 2018 in Shandong province. A new birthweight-for-gestational age percentile reference was constructed based on the Generalized Additive Model for Location, Scale and Shape (GAMLSS) package in R version 3.5. The established gestational age weight curve was compared separately with the Fenton curve, INTERGROWTH−21st curve, and the Chinese Neonatal Network Standard curve of 2015.ResultsWe established the reference values of birthweight by gestational age at the 3rd, 10th, 25th, 50th, 75th, 90th, and 97th percentiles. Newborns had much heavier birthweights than those in the INTERGROWTH-21st and Fenton curves at most gestational ages. Although the newborns' birthweight references were closer to the Chinese Neonatal Network Standard except a few for gestational age, this study and INTERGROWTH-21st had similar birthweight curve shapes.ConclusionsThere are obvious differences among the criteria for newborn birthweights. Therefore, it is more accurate to assess newborns using the local birthweight reference.

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.

Evaluation and projection of the annual maximum streamflow in response to anthropogenic and climatic effects under nonstationary conditions in the Hanjiang River Basin, China

Abstract The flood regimes have been changing due to the climate change and human activities. Evaluating the flood risk under nonstationarity is critical to water resource management authorities in disaster reduction. In this study, the annual maximum streamflow (AMS) was used to analyze the nonstationarity in flood frequency in the Hanjiang River (HJR) Basin. A Generalized Additive Model for Location, Scale and Shape (GAMLSS) is employed to characterize nonstationarity in the AMS with time, as well as climatic and anthropogenic factors. Additionally, changes of the AMS in response to future climate change and human activity are also investigated. Results indicate that flood behavior can be better described by the nonstationary model with physically based covariates than that with time and the stationary model, implying that flood regimes of the HJR Basin are mainly influenced by anthropogenic and climatic factors including reservoir, precipitation and temperature. The precipitation and temperature projected by the Statistical Downscaling Model (SDSM) under two climate scenarios (RCP2.6 and RCP4.5) in the HJR Basin are characterized by an increasing trend over the period of 2006–2100. Furthermore, an increasing trend was found in the AMS during 2051–2100, indicating that flood risk is likely to increase in the future in the HJR Basin due to the climate change alone without further changes in hydrological engineering and flood management. The results quantified the flood frequency under nonstationarity conditions with physically based covariates and provided information to the decision-makers to address the potential risks posed to the HJR Basin.

Factors associated with postpartum psychiatric disorders using routine administrative data

BackgroundAlmost twenty percent of women worldwide experience mental health disorders following childbirth. Despite their importance and consequences, postpartum psychiatric disorders are still under-investigated. In Brazil, studies are restricted to state capitals and are not representative of the country as a whole. Understanding the factors associated with postpartum psychiatric disorders can provide insights for adequate maternal mental health screening. This study was conducted with the objective of evaluating factors associated with postpartum psychiatric disorders in Brazil.
 MethodsWe used Authorization of Outpatient Procedure data for women who used community mental health services in Brazil between 2008 and 2012. The dependent variable was the diagnosis of mental disorders and behavioural factors associated with the puerperium (ICD-10 code F53). Age categorized in quartiles and Psychosocial Care Centre (CAPS) coverage were covariates considered for the analysis. To partially neutralize the bias from repeated observations, we used the Proximity Index (PP), created through of geographic information for each visit to the level of the patient’s neighbourhood. We used Generalized Additive Models for Location, Scale, and Shape (GAMLSS) with double Poisson distribution.
 FindingsWe identified 6,802 records of mental and behavioural disorders associated with the puerperium diagnoses. Among them, 47.6% of the outpatient records were for diagnosis of ICD F53.1, and 32.09% for ICD-10 F53.0, which correspond to severe and mild mental disorders associated with the puerperium, respectively. Diagnosis for ICD-10 F53.0 was higher between the ages of 26 and 30 (10%), while diagnosis for ICD F53.1 was higher between the ages of 31 and 35 (12.7%). For each increment in the maternal age unit and CAPS coverage percentage, there is an increase of 1.01 (p<0.001) in the occurrence of postpartum psychiatric disorders.
 ConclusionsOur results showed that increases in maternal age and municipal CAPS coverage heightened the risk of postpartum psychiatric disorders. With regards to severity, we found that diagnosis for ICD F53.0 (mild mental and behavioural disorders associated with the puerperium) was higher among women aged between 26 and 30, while diagnosis for ICD F53.1(severe mental and behavioural disorders associated with the puerperium) was higher among women aged between 31 and 35. Our findings support the need to improve knowledge of maternal mental health and to integrate routine screening into postnatal care settings, for the early identification of women who are at risk, and to apply timely preventive and therapeutic approaches.
 For collaborations please contact: Email: flaviajosy1@gmail.com

Statistical model applied in the qualitative and quantitative analysis of the relationships between environmental variables and cyanotoxin concentrations in tropical reservoirs.

This article presents the use of generalized additive model for location scale and shape (GAMLSS) in the qualitative and quantitative analysis of the relationships between environmental parameters and cyanotoxins in the tropical reservoirs of Colombia. The physicochemical parameters were evaluated on each of the cyanotoxins detected with levels high by ultra-high-performance liquid chromatography coupled to triple quadrupole mass spectrometry. The models showed a relation between cyanotoxins and the nutrients as soluble total Kjeldahl nitrogen (NTK), soluble phosphorus (soluble P), total phosphorus (total P), and nitrates (NO3-), among other nutrients that are necessary for the growth of organisms that produce toxins. This model confirms that the NTK and soluble P variables favor an increase in the concentration of MC-LR and MC-YR cyanotoxins in the Abreo Malpaso reservoir. The variables NO3- and dissolved O2 contribute to a higher concentration of MC-LR, MC-YR, and MC-ADRR cyanotoxins in the Peñol reservoir. Finally, the variable total P favors the increase in the concentration of MC-LR cyanotoxin and the variable dissolved O2 favors the increase in the concentration of cyanotoxin [D-Asp3, (E)-Dhb7] -MC-RR in the Playas reservoir.

Reference values for performance test outcomes relevant to English female soccer players

The purpose of this study was to present reference standards for physical performance test outcomes relevant to elite female soccer players. We analysed mixed-longitudinal data (n = 1715 observations) from a sample of 479 elite youth and senior players as part of the English Football Association’s national development programme (age range: 12.7 to 36.0 years). Semi-parametric generalized additive models for location, scale and shape (GAMLSS) estimated age-related reference centiles for 5-m sprinting, 30-m sprinting, countermovement jump (CMJ) height, and Yo-Yo Intermittent Recovery Test Level 1 (Yo-Yo IR1) performance. The estimated reference centiles indicated that the median of the distribution of physical performance test scores varied non-linearly with advancing chronological age, improving until around 25 years for each performance variable. These are the first reference ranges for performance test outcomes in elite English female soccer players. These data can assist practitioners when interpreting physical test performance outcomes to track an individual’s progress over time and support decision making regarding player recruitment and development.

Adaptive step-length selection in gradient boosting for Gaussian location and scale models

Tuning of model-based boosting algorithms relies mainly on the number of iterations, while the step-length is fixed at a predefined value. For complex models with several predictors such as Generalized additive models for location, scale and shape (GAMLSS), imbalanced updates of predictors, where some distribution parameters are updated more frequently than others, can be a problem that prevents some submodels to be appropriately fitted within a limited number of boosting iterations. We propose an approach using adaptive step-length (ASL) determination within a non-cyclical boosting algorithm for Gaussian location and scale models, as an important special case of the wider class of GAMLSS, to prevent such imbalance. Moreover, we discuss properties of the ASL and derive a semi-analytical form of the ASL that avoids manual selection of the search interval and numerical optimization to find the optimal step-length, and consequently improves computational efficiency. We show competitive behavior of the proposed approaches compared to penalized maximum likelihood and boosting with a fixed step-length for Gaussian location and scale models in two simulations and two applications, in particular for cases of large variance and/or more variables than observations. In addition, the underlying concept of the ASL is also applicable to the whole GAMLSS framework and to other models with more than one predictor like zero-inflated count models, and brings up insights into the choice of the reasonable defaults for the step-length in the simpler special case of (Gaussian) additive models.

Timing leaf senescence: A generalized additive models for location, scale and shape approach

Accurate estimations of phenophases in deciduous trees are important to understand forest ecosystems and their feedback on the climate. In particular, the timing of leaf senescence is of fundamental importance to trees’ nutrient stoichiometry and drought tolerance and therefore to trees’ vigor and fecundity. Nevertheless, there is no integrated view on the significance, and direction, of seasonal trends in leaf senescence, especially for years characterized by extreme weather events. Difficulties in the acquisition and analyses of hierarchical data can account for this. We collected four years of chlorophyll content index (CCI) measurements in thirty-eight individuals of four deciduous tree species (Betula pendula, Fagus sylvatica, Populus tremula and Quercus robur) in Belgium, Norway and Spain, and analyzed these data using generalized additive models for location, scale and shape (GAMLSS). As a result, (I) the phenological strategy and seasonal trend of leaf senescence in these tree species could be clarified for exceptionally dry and warm years, and (II) the daily average (air) temperature, global radiation, and vapor pressure deficit could be established as main drivers behind the variation in the timing of the senescence transition date. Our results show that the onset of the re-organization phase in the leaf senescence, which we approximated and defined as local minima in the second derivative of a CCI graph, was in all species mainly negatively affected by the average temperature, global radiation and vapor pressure deficit. All together the variables explained 89 to 98% of the variability in the leaf senescence timing. An additional finding is that the generalized beta type 2 and generalized gamma distributions are well suited to model the chlorophyll content index, while the senescence transition date can be modeled using the normal-exponential-student-t, generalized gamma and zero-inflated Box-Cox Cole and Green distributions for beech, oak and birch, and poplar, respectively.

A New Derivation of the Reference Equations of Spirometric Values in the Thai Population Using the GAMLSS Method

Objective: The Global Lung Initiative (GLI)-2012 equation has now been used as the reference for the interpretation of the spirometry worldwide. The equations have been derived using modern statistical methods called Generalized Additive Models for Location, Scale and Shape (GAMLSS) and Spline. A part of the spirometric data from which the equations were derived is the data collected from the Thai population. The present study aimed to create the reference equations using only the data from the Thai population retrieved from the previous cross-sectional study and compared them to the GLI-2012’s. Materials and Methods: The previous data of each spirometric parameters including FVC, FEV₁, FEV₁/FVC, and FEF25-75% in 1,616 male and 2,280 female subjects were retrieved for the statistical modeling by GAMLSS and Spline packages in R Statistics. Lambda-Mu-Sigma (LMS) models were used to establish the best fitted models defined by the smallest Schwarz’s Bayesian Criterion (SBC). The authors also used a set of spirometric data of healthy elderly subjects to validate the equations and compare with the GLI-2012. Results: The GAMLSS-Thai equations were then derived to establish the predicted (Mu) and the lower limit of normal (LLN) values for each parameter. For 140 male and 651 female subjects aged 60 to 80 years, the predicted performance of GAMLSS-Thai is better than GLI-2012 equations as shown by various statistical tools including z-score, mean absolute percentage error (MAPE), and root mean square deviation (RMSD) in all spirometric parameters. Conclusion: The GAMLSS-Thai equation can be alternatively used as reference spirometric values in subjects aged 10 to 80 years in Thai population. It is more appropriate for subjects aged 60 to 80 years than the GLI-2012 equation. Keywords: Spirometry; Reference; Thailand; Population; GAMLSS

Risk factors relate to the variability of health outcomes as well as the mean: A GAMLSS tutorial.

Risk factors or interventions may affect the variability as well as the mean of health outcomes. Understanding this can aid aetiological understanding and public health translation, in that interventions which shift the outcome mean and reduce variability are typically preferable to those which affect only the mean. However, most commonly used statistical tools do not test for differences in variability. Tools that do have few epidemiological applications to date, and fewer applications still have attempted to explain their resulting findings. We thus provide a tutorial for investigating this using GAMLSS (Generalised Additive Models for Location, Scale and Shape). The 1970 British birth cohort study was used, with body mass index (BMI; N = 6007) and mental wellbeing (Warwick-Edinburgh Mental Wellbeing Scale; N = 7104) measured in midlife (42-46 years) as outcomes. We used GAMLSS to investigate how multiple risk factors (sex, childhood social class, and midlife physical inactivity) related to differences in health outcome mean and variability. Risk factors were related to sizable differences in outcome variability-for example males had marginally higher mean BMI yet 28% lower variability; lower social class and physical inactivity were each associated with higher mean and higher variability (6.1% and 13.5% higher variability, respectively). For mental wellbeing, gender was not associated with the mean while males had lower variability (-3.9%); lower social class and physical inactivity were each associated with lower mean yet higher variability (7.2% and 10.9% higher variability, respectively). The results highlight how GAMLSS can be used to investigate how risk factors or interventions may influence the variability in health outcomes. This underutilised approach to the analysis of continuously distributed outcomes may have broader utility in epidemiologic, medical, and psychological sciences. A tutorial and replication syntax is provided online to facilitate this (https://osf.io/5tvz6/). DB is supported by the Economic and Social Research Council (grant number ES/M001660/1), The Academy of Medical Sciences / Wellcome Trust ("Springboard Health of the Public in 2040" award: HOP001/1025); DB and LW are supported by the Medical Research Council (MR/V002147/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Quantification of behavioural variation among sheep grazing on pasture using accelerometer sensors

Context Monitoring the behaviour of animals can provide early warning signs of disease or indicate loss of appetite. Also, an understanding of the variation in behaviours among animals and their distributions is essential for meaningful statistical inference. Therefore, quantifying the variation of behaviours is of both biological and statistical interest. Aim The objectives of this study were to determine the distributions and quantify the variation among animals with respect to the times spent grazing, ruminating, idling, walking, and licking. Methods The activities of 147 (male = 67, female = 80) Merino lambs at 10–11 months of age on a commercial farm in Edenhope, Victoria, Australia were recorded for 26 days, using ActiGraph accelerometer sensors attached to the left side of the sheep’s muzzle. The male and female sheep were kept in separate paddocks. A Support Vector Machine algorithm was used to differentiate sheep behaviour into six categories: grazing, ruminating, idling, walking, licking, and other activities. The distributions of behaviours were analysed using energy statistics-based tests and Generalised Additive Models for Location, Scale, and Shape (GAMLSS). Different distributions were compared using Akaike Information Criterion (AIC) values. Key results Among the distributions that were considered, we found that times spent ruminating in both male and female sheep populations as well as idling in male sheep were best described by the skew exponential type 2 distribution. Grazing, walking and licking behaviours were best described by the Box–Cox t distribution. The distribution of time spent grazing was symmetrical and unimodal in males, and adequately modelled by a normal distribution, but the distribution in females had a prominent left skew. Also, we found that females typically grazed for a longer time than males. However, males spent more time ruminating than grazing. Conclusions The time spent by the animal in each activity varied during the day. Within each population, the variation among animals in the time spent grazing was best described by a Box–Cox t distribution. Implications This study has enhanced our understanding of grazing behaviour and will facilitate more appropriate analyses of the causes of variation among animals in grazing behaviour.

COUNT DATA MODELING USING GAMLSS APPROACH AND ITS APPLICATION IN DENGUE HEMORRHAGIC FEVER CASES IN EAST KALIMANTAN PROVINCE, INDONESIA

Generalized Additive Models for Location, Scale, and Shape (GAMLSS) is a robust approach used to model various types and characteristics of data. Therefore, this research aims to model the count data using the GAMLSS approach through Poisson Regression (PR), Poisson Inverse Gaussian Regression (PIGR), and Negative Binomial Regression (NBR). PIGR and NBR are the best models compared to PR based on their application to modeling the number of dengue hemorrhagic fever (DHF) cases in East Kalimantan Province, Indonesia, in 2019. Furthermore, both models produced varying results on the factors with a significant effect on DHF. Only one factor of the PIGR model, namely altitude, significantly affected these cases. Meanwhile, the NBR model produced three factors that affected the number of dengue cases: altitude, population density, and health workers.

Pricing electricity day-ahead cap futures with multifactor skew-t densities

Short-term risk management is becoming increasingly significant in power trading as the intermittent renewable generators introduce more weather risk into the price formation dynamics. There is a vacuum in hedging instruments at the day-ahead stage to protect retailers in particular from such volatility and price spikes. Motivated by this requirement, this paper analyses a flexible hedging product, day-ahead cap futures. For pricing this product, we parametrically predict the probability distribution of day-ahead prices using the multifactor Generalized Additive Model for Location, Scale and Shape (GAMLSS) based upon the skew-t distribution with weather forecasts and calendar information as explanatory variables. In particular, we reveal that this higher-order moment model is superior to several lower-order models such as the normal distribution in all the following three aspects: fairness as pricing method, underwriting risk of the risk-taker and the variance reduction effect of the risk hedger.