Fast optimization methods for high-dimensional row-sparse multivariate quantile linear regression

Simultaneous variable selection and parametric estimation for quantile regression

This paper focuses on the Least Square (LS) regression using the mean and Quantile (M) regression analysis using median which is based on “well-Known” parametric estimation methodologies. Data from Oregon and California highway bridges were used for the comparison of the two methods. Relationships were developed to predict the unit cost of FRP repair work and FRP cost was found to have a high degree of correlation with FRP area for both Oregon and California. It was observed that the Cost Estimating Relationships (CERs) obtained by Quantile (M) regression method had the smaller Mean Absolute Deviation (MAD) values and lower Mean Absolute Percentage Error (MAPE) values than Least Square (LS) regression. The stuudy showed that Quantile Regression is much less sensitive to outliers than Least Squares Regression.

Underweight is one of the important anthropometric components of malnutrition among under-five children and is a major public health concern in Bangladesh because it contributes to mortality as well as morbidity. In designing suitable health programs and policies with the goal of attaining UN SDG Goals, it is necessary to identify the critical risk factors of under-five malnutrition. It is evident that the quantile regression produces robust estimates in the presence of outliers. However, in the context of Bangladesh, no study has been conducted considering the sequential quantile regression on this topic. Therefore, the authors aimed to find the determinants of underweight among under-5 children in Bangladesh considering the latest country representative dataset. The paper considers a weighted sample of size 7762 children are used and data were extracted from the latest Bangladesh Demographic and Health Survey (BDHS) 2017-18 data. Multivariable simultaneous quantile regression models were used to fulfill the objectives of this study. Findings depict that undernutrition affects the majority of children in the population as compared to the reference population. The WAZ-score of the child increases by 0.202 points at the 10th quantile of the conditional distribution, and by 0.565 points at the 90th quantile as we move from children of underweight to overweight women. Moreover, the WAZ scores of children from the richest families in the 10th, 50th, and 75th quantiles, respectively, are increased by 0.171, 0.016, and 0.084 points. Quantile regression revealed the results of several socioeconomic and demographic factors acting differently across the WAZ distribution. Therefore, policymakers may consider the identified risk factors to lessen malnutrition among under-5 children in Bangladesh.

Varying coefficient model (VCM) is extensively used in various scientific fields due to its capability of capturing the changing structure of predictors. Classical mean regression analysis is often complicated in the existence of skewed, heterogeneous and heavy-tailed data. For this purpose, this work employs the idea of model averaging and introduces a novel comprehensive approach by incorporating quantile-adaptive weights across different quantile levels to further improve both least square (LS) and quantile regression (QR) methods. The proposed procedure that adaptively takes advantage of the heterogeneous and sparse nature of input data can gain more efficiency and be well adapted to extreme event case and high-dimensional setting. Motivated by its nice properties, we develop several robust methods to reveal the dynamic close-to-truth structure for VCM and consistently uncover the zero and nonzero patterns in high-dimensional scientific discoveries. We provide a new iterative algorithm that is proven to be asymptotic consistent and can attain the optimal nonparametric convergence rate given regular conditions. These introduced procedures are highlighted with extensive simulation examples and several real data analyses to further show their stronger predictive power compared with LS, composite quantile regression (CQR) and QR methods.

Individuals with sickle cell anemia (SCA) exhibit delayed growth trajectories and lower blood pressure (BP) measurements than individuals without SCA. We evaluated factors associated with height, weight, and BP and established reference growth curves and BP tables using data from the Silent Cerebral Infarct Multi-Center Clinical (SIT) Trial (NCT00072761). Quantile regression models were used to determine the percentiles of growth and BP measurements. Multivariable quantile regression was used to test associations of baseline variables with height, weight, and BP measurements. Height and weight measurements were collected from a total of 949 participants with median age of 10.5 years [Interquartile range (IQR) 8.2-12.9] and median follow-up time of 3.2 years (IQR 1.8-4.7, range 0-12.9). Serial BP measurements were collected from a total of 944 and 943 participants, respectively, with median age of 10.6 years (IQR = 8.3-12.9 years), and median follow-up time of 3.3 years (IQR = 1.7-4.8). Multivariable quantile regression analysis revealed that higher hemoglobin measurements at baseline were associated with greater height (P < 0.001), weight (P = 0.000), systolic BP (P < 0.001), and diastolic BP (P = 0.003) measurements. We now provide new reference values for height, weight, and BP measurements that are now readily available for medical management.

Objective: The question of whether breastfeeding has a protective effect against the development of overweight or obesity later in life remains controversial, especially during adolescence. The objective was to assess the relationship between breastfeeding and adolescents' body composition. Methods: The HELENA study is a cross-sectional study involving 3,528 adolescents from 10 European cities. The outcome measures were body weight and height, subscapular skinfolds as well as waist circumferences. Breastfeeding, smoking status, and parental socioeconomic status were assessed by self-administered questionnaires. Dietary intake was recorded using two 24-hour recall surveys. Two adjustment approaches were used: i) covariance analysis adjusted for confounding factors (propensity score adjustment) and ii) multivariate quantile regression. Results: After adjustment, no significant associations were observed between breastfeeding and body composition parameters (BMI Z-score; sum of skinfolds; waist-to-height ratio). An adjusted quantile regression analysis showed a non-significant trend for a protective effect of breastfeeding toward the highest percentiles of adiposity in boys but not in girls. This is of particular interest with respect to the superiority of the waist-to-height ratio over waist circumference and BMI for detecting cardiometabolic risk factors. Conclusion: This first European study, including a large set of factors influencing adolescents' body composition, showed a non-significant trend toward a protective effect of breastfeeding on highest percentiles of adolescent's abdominal adiposity.

Maternal and child mortality remain unacceptably high in the Sustainable Development Goals era. Continuum of care has become a key strategy for improving the health of mothers and newborns. Previous research on the continuum of care in Ethiopia is often limited to maternal health services. Maternal and child health services are inseparably linked, and an integrated approach to care is essential. This study assessed the continuum of maternal, newborn, and child health care and associated factors in Ethiopia. The analysis was based on the 2016 Ethiopian Demographic and Health Survey data. We restricted our analysis to women with their most recent children—alive and living with their mother- aged 12–23 months at the time of the survey (n = 1891). The modified composite coverage index, constructed from twelve maternal and child health services, was calculated as an indicator of the continuum of care. Bivariable and multivariable quantile regression were used to analyse the relationship between the predictors and specific quantiles of the composite coverage index. The effect of each variable was examined at the 10th, 25th, 50th, 75th, and 95th quantiles. The results showed that the average composite coverage index value was 39%. The overall completion rate of the continuum of care was low (2%). Four % of the women did not receive any of the services along the continuum of care. Postnatal care for newborns had the lowest coverage (12%). This study provides evidence that factors such as the educational status of women, region, residence, socio-economic status, perceived distance to a health facility, pregnancy intention, mode of delivery, parity, and early antenatal care initiation influence the continuum of care differently across levels of the composite coverage index. The findings call for integrated and targeted strategies that aim to improve the continuum of care considering the determinants.

Exposure to arsenic even at low levels can lead to adverse health outcomes, however, there is a paucity of research from South Africa in relation to human exposure to arsenic. We investigated long-term exposure of residents in Limpopo province, South Africa, in a cross-sectional study by analysing water, soil and blood arsenic concentrations from two arsenic-exposed (high and medium–low exposure) villages and one non-exposed (control) village. There were statistically significant differences in the distribution of arsenic in water, soil and blood amongst the three sites. The median drinking water arsenic concentration in the high-exposure village was 1.75 µg/L (range = 0.02 to 81.30 µg/L), 0.45 µg/L (range = 0.100 to 6.00 µg/L) in the medium- / low-exposure village and 0.15 µg/L (range = < limit of detection (LOD) to 29.30 µg/L) in the control site. The median soil arsenic concentration in the high-exposure village was 23.91 mg/kg (range = < LOD to 92.10 mg/kg) whilst arsenic concentrations were below the limit of detection in all soil samples collected from the medium-/low-exposure and control villages. In the high-exposure village, the median blood arsenic concentration was 1.6 µg/L (range = 0.7 to 4.2 µg/L); 0.90 µg/L (range = < LOD to 2.5 µg/L) in the medium-/low-exposure village and 0.6 µg/L (range = < LOD to 3.3 µg/L) in the control village. Significant percentages of drinking water, soil and blood samples from the exposed sites were above the internationally recommended guidelines (namely, 10 µg/L, 20 mg/kg and 1 µg/L, respectively). Majority of participants (86%) relied on borehole water for drinking and there was a significant positive correlation between arsenic in blood and borehole water (p-value = 0.031). There was also a statistically significant correlation between arsenic concentrations in participants’ blood and soil samples collected from gardens (p-value = 0.051). Univariate quantile regression found that blood arsenic concentrations increased by 0.034 µg/L (95% CI = 0.02–0.05) for each one unit increase in water arsenic concentrations (p < 0.001). After adjusting for age, water source and homegrown vegetable consumption in multivariate quantile regression, participants from the high-exposure site had significantly higher blood concentrations than those in the control site (coefficient: 1.00; 95% CI = 0.25–1.74; p-value = 0.009) demonstrating that blood arsenic is a good biomarker of arsenic exposure. Our findings also provide new evidence for South Africa on the association between drinking water and arsenic exposure, emphasising the need for the provision of potable water for human consumption in areas with high environmental arsenic concentrations.

This paper presents two probabilistic approaches based on bootstrap method and quantile regression (QR) method to estimate the uncertainty associated with solar photovoltaic (PV) power point forecasts. Solar PV output power forecasts are obtained using a hybrid intelligent model, which is composed of a data filtering technique based on wavelet transform (WT) and a soft computing model (SCM) based on radial basis function neural network (RBFNN) that is optimized by particle swarm optimization (PSO) algorithm. The point forecast capability of the proposed hybrid WT + RBFNN + PSO intelligent model is examined and compared with other hybrid models as well as individual SCM. The performance of the proposed bootstrap method in the form of probabilistic forecasts is compared with the QR method by generating different prediction intervals (PIs). Numerical tests using real data demonstrate that the point forecasts obtained from the proposed hybrid intelligent model can be effectively used to quantify PV power uncertainty. The performance of these two uncertainty quantification methods is assessed through reliability.

Study regionTwo hyper-arid regions (Atbara and Kassala stations) in Sudan. Study focusThe study aims to evaluate the potential of the D-vine Copula-based quantile regression (DVQR) model for estimating daily ETo during 2000–2015 based on various input structures. Further, the DVQR model was compared with Multivariate Linear quantile regression (MLQR), Bayesians Model Averaging quantile regression (BMAQR), Empirical Models (EMMs), and Classical Machine Learning (CML). Besides, the CML models including Random Forest (RF), Support Vector Machine (SVM), Extreme Learning Machine (ELM), Extreme Gradient Boosting (XGBoost), and M5 Model Tree (M5Tree) were employed. New hydrological insights for the regionThe original EMMs showed poor performance, which improved after calibration techniques. The DVQR, MLQR, and BMAQR models showed better performance than the calibrated EMMs. However, the DVQR model exhibited the highest accuracy than the MLQR and BMAQR models over two study sites. The M5Tree, SVM, and XGBoost models perfumed better than ELM and RF models at both study sites. The DVQR and XGBoost models showed equivalent performance (R2, NSE, and WIA > 0.99, MAE, and RMSE < 0.2) to the M5Tree and SVM models, but they had significantly more accuracy than the calibrated EMMs, MLQR, BMAQR, ELM, and RF models in two hyper-arid regions. Overall, the high dimensional DVQR model is recommended as a promising alternative technique for estimating daily ETo in hyper-arid climate conditions around the world.

There is currently much discussion about lasso-type regularized regression which is a useful tool for simultaneous estimation and variable selection. Although the lasso-type regularization has several advantages in regression modelling, owing to its sparsity, it suffers from outliers because of using penalized least-squares methods. To overcome this issue, we propose a robust lasso-type estimation procedure that uses the robust criteria as the loss function, imposing L1-type penalty called the elastic net. We also introduce to use the efficient bootstrap information criteria for choosing optimal regularization parameters and a constant in outlier detection. Simulation studies and real data analysis are given to examine the efficiency of the proposed robust sparse regression modelling. We observe that our modelling strategy performs well in the presence of outliers.

Together with quantile regression methods, such a model would have the potential for clinical utility through automated quantitative comparison of individual cases relative to their age and gender-matched peer group. Our aim was to demonstrate the automated processing of digital clinical head CT data in the development of a clinically useful model of age-related changes of the brain in the first 2 decades of life. A total of 415 (209 female) consecutive, clinical head CTs with radiographically normal findings from patients from birth through 20 years of age were retrospectively selected and subjected to automated segmentation. Brain volume, brain parenchymal fraction, brain radiodensity, and brain radiomass were assessed as a function of patient age. Statistical modeling and quantile regression were performed. Brain volume increased from 400 cm3 at birth to 1350 cm3 at 20 years of age (>3-fold). Males had a slightly steeper growth trajectory than females, with approximately 8% difference in volume between the sexes established in the first few years of life. Brain parenchymal fraction was variable at younger than 2 years of age, stabilizing between 0.85 and 0.92 at 2-3 years of age. Brain mean radiodensity was lower at birth (24 HU) and increased through 3 years of age, after which it stabilized near 30 HU, an approximately 25% increase. The product of brain volume and mean brain radiodensity (radiomass), increased from 700 HU × mL at birth to 3900 HU × mL, a 5.6-fold increase, with approximately 5% difference between males and females at 20 years. Quantile regression enables a given metric to be interpreted relative to an age- and sex-matched peer group. Automated segmentation of clinical head CT images permitted the generation of a reference database for quantitative analysis of pediatric and adolescent brains. Quantile regression facilitates clinical application.

This study aims to construct the model for the length of hospital stay for patients with COVID-19 using quantile regression and Bayesian quantile approaches. The quantile regression models the relationship at any point of the conditional distribution of the dependent variable on several independent variables. The Bayesian quantile regression combines the concept of quantile analysis into the Bayesian approach. In the Bayesian approach, the Asymmetric Laplace Distribution (ALD) distribution is used to form the likelihood function as the basis for formulating the posterior distribution. All 688 patients with COVID-19 treated in M. Djamil Hospital and Universitas Andalas Hospital in Padang City between March-July 2020 were used in this study. This study found that the Bayesian quantile regression method results in a smaller 95% confidence interval and higher value than the quantile regression method. It is concluded that the Bayesian quantile regression method tends to yield a better model than the quantile method. Based on the Bayesian quantile regression method, it investigates that the length of hospital stay for patients with COVID-19 in West Sumatra is significantly influenced by Age, Diagnoses status, and Discharge status.

Objective: To assess various marginal effects of nutrient intakes, health behaviours and nutrition knowledge on the entire distribution of body mass index (BMI) across individuals. Design: Quantitative and distributional study. Setting: Taiwan Methods: This study applies Becker’s (1965) model of health production to construct an individual’s BMI determining function. Quantile regression method is used to analyse the entire distribution of BMI across a nationwide survey sample in Taiwan. Endogeneity associated with choice variables of nutrient intakes, health behaviours and nutrition knowledge in determining BMI is corrected using a two-stage least-squares method. Results: Empirical results indicate that energy, oleic acid and cholesterol increase BMI, while fibre, calcium and sodium reveal a reverse effect. For overweight and obese females, protein lowers BMI. For underweight and slightly to severely obese males, vitamin C reduces BMI. Jogging lowers BMI, but drinking raises non-obese individuals’ BMI. For males whose BMI is in the ideal weight to slightly overweight ranges, nutrition knowledge reduces BMI, but this effect is insignificant for females. Conclusions: Several important conclusions can be drawn. (1) Having a BMI which is too high or too low is a risk factor to health. (2) Quantile regression is a useful empirical method to evaluate crucial factors determining the entire distribution (high, medium and low) of BMI. (3) The econometric problem of endogeneity in regressors has to be considered and corrected when using a quantile regression approach. (4) BMI-relevant health education and policy can be evaluated and derived using quantile regression effects of an individual’s choices of nutrient intakes, health behaviours and nutrition knowledge.

A battery capacity estimation method based on the equivalent circuit model and quantile regression using vehicle real-world operation data