Multiple Quantile Regression Research Articles

TRAVEL AND TOURISM COMPETITIVENESS INDEX 2019 –QUANTILE REGRESSION APPROACH ON 2nd SUB-INDEX

The aim of the paper is to examine how much four pillars of the Travel and Tourism Competitiveness Index (TTCI) sub-index “T&T Policy and Enabling Conditions” contribute to the overall TTCI and ranking among 140 countries. To meet the goal, quantile regression has been used. Several findings were obtained by analysis. The first result shows that pillar Price Competitiveness has almost no effect on the overall TTCI score or TTCI rank in the considered model. Second, the most important pillars are Prioritization of Travel and Tourism and International Openness. Third, a comparison of the results of the multiple quantile regression analysis with the ordinary least squares showed that the results of the above methods differ significantly for Pillar Environmental Sustainability. On the lower quantile levels, this pillar does not significantly affect the ranking while at higher quantile levels it does. On the contrary, it affects the overall TTCI score in the opposite way. Another reason for using quantile regression is justified by the restrictive assumptions of OLS that it does not require. This paper contributes to the existing literature connected with tourism competitiveness. It can help reveal hidden multidimensional relationships between variables considered at different quantile levels, and thus can be a motivation for further improving the methods used to create the index.

Brief Report: Association Between Pain, Pulmonary Function, and Respiratory Symptoms in People With HIV.

People with HIV (PWH) experience chronic pain and respiratory symptoms, which are closely related in the general population. Pain may affect the impaired pulmonary function seen in PWH beyond its association with HIV alone. Our objective was to investigate the relationship of pain severity to pulmonary function, respiratory symptoms, and sleep disturbance in PWH. Study sites included the University of Pittsburgh, University of California San Francisco, and University of Washington. Pain, dyspnea, and sleep were assessed using the Brief Chronic Pain Questionnaire, St. George's Respiratory Questionnaire, and Pittsburgh Sleep Quality Index. Participants performed prebronchodilator and postbronchodilator spirometry and 6-minute walk test. Associations between pain severity, lung function, dyspnea, and sleep were assessed with bivariate and multiple quantile regression analysis adjusted for age, sex, race, body mass index, and smoking status. Of 159 PWH, the median age was 56 years with 30.8% women. Two-thirds experienced pain in the past week, with 40.3% reporting chronic pain. Pain severity was higher with female sex (P = 0.038), non-White race (P = 0.005), current smoking (P = 0.003), and lower CD4+ count (P = 0.035). In adjusted analysis, higher pain severity was correlated with reduced postbronchodilator forced expiratory volume in 1 second %predicted (P = 0.008), reduced postbronchodilator forced vital capacity %predicted (P = 0.019), and chronic obstructive pulmonary disease (P = 0.032). Greater pain severity was strongly associated with a higher St. George's Respiratory Questionnaire score (P < 0.001) and sleep disturbance (P < 0.001). In PWH, pain is common and associated with airflow obstruction, dyspnea, and sleep disturbance. Future studies assessing pain severity and pulmonary function over time could clarify the direction of this association and the impact on quality of life.

Model-based recursive partitioning algorithm to penalized non-crossing multiple quantile regression for the right-censored data

Quantile functions of the response variable provide a tool for practitioners to analyze both the central tendency and statistical dispersion of data. As a counterpart to the regression tree models, quantile regression tree methods (QRT) gained interest in constructing tree models for quantile functions. Previous QRT methods, however, estimate different tree models for each quantile level as they separately estimate QRT models. To The unified non-crossing multiple quantile regression tree (UNQRT) model was proposed to construct a common tree structure by aggregating information across all quantile levels. UNQRT, however, does not benefit from automatic variable selection techniques developed in regression literature. We propose a penalized UNQRT (P-UNQRT) method by incorporating adaptive sup-norm penalty into the original UNQRT model to perform variable selection. Additionally, we extend P-UNQRT to cope with the right-censored data that often arise in healthcare applications. The Kaplan-Meier estimator is used as weights for each observation of the censored data in our proposed model. We demonstrate the benefits of our algorithms through empirical studies and analyze the military training data from Korea Combat Training Center to study the major factors that contribute to successfully completing military operations.

Perceived built environment, health-related quality of life and health care utilization.

Previous research has shown that the built environment plays a crucial role for health-related quality of life (HRQoL) and health care utilization. But, there is limited evidence on the independence of this association from lifestyle and social environment. The objective of this cross-sectional study was to investigate these associations, independent of the social environment, physical activity and body mass index (BMI). We used data from the third follow-up of the Swiss study on Air Pollution and Lung and Heart diseases In Adults (SAPALDIA), a population based cohort with associated biobank. Covariate adjusted multiple quantile and polytomous logistic regressions were performed to test associations of variables describing the perceived built environment with HRQoL and health care utilization. Higher HRQoL and less health care utilization were associated with less reported transportation noise annoyance. Higher HRQoL was also associated with greater satisfaction with the living environment and more perceived access to greenspaces. These results were independent of the social environment (living alone and social engagement) and lifestyle (physical activity level and BMI). This study provides further evidence that the built environment should be designed to integrate living and green spaces but separate living and traffic spaces in order to improve health and wellbeing and potentially save health care costs.

Associations of Preoperative Self-rated Symptoms of Anxiety and Depression on Length of Hospital Stay and Long-term Quality of Life in Patients Undergoing Cardiac Surgery.

Anxiety and depression are often associated with cardiovascular diseases. Nevertheless, few study authors have investigated psychological effects on immediate and long-term cardiac surgery-related outcomes, such as surgical complications, length of hospital stay (LOS), and long-term health-related quality of life (HRQoL). The aims of this study were to (a) investigate the role of preoperative symptoms of anxiety and depression in predicting LOS in a sample of surgical patients and (b) evaluate the impact of preoperative symptoms of anxiety and depression on the patients' HRQoL 3 months after surgery. One hundred fifty-one patients waiting for surgery were included. To evaluate symptoms of anxiety and depression, the Hospital Anxiety and Depression Scale was used. Multiple regression analyses were conducted to evaluate the impact of both clinical and psychological factors on LOS, whereas quantile regression was performed to assess their effect on the patients' HRQoL 3 months after surgery. The multiple regression shows that EuroSCORE, length of endotracheal intubation, and anxiety symptoms predict LOS. The multiple quantile regression analyses also show that both symptoms of anxiety and depression predict a negative HRQoL up to 3 months after surgery. Preoperative symptoms of anxiety predict the patients' LOS, and both symptoms of anxiety and depression predict a scarce HRQoL 3 months after cardiac surgery. These results suggest the need for implementing presurgical in-hospital screening procedures for both symptoms of anxiety and depression. Finally, focused psychological interventions should be implemented for reducing inpatients' hospital LOS and improving their future quality of life.

Model averaging for multiple quantile regression with covariates missing at random

ABSTRACT In this paper, we develop a model averaging estimation procedure for multiple quantile regression where missingness occurs to the covariates. Our concern is on the improvement of prediction accuracy for multiple quantiles of response conditional on observed covariates. A set of candidate models is constructed according to missingness data patterns. In this model set, one model is based on the subjects with complete-case data, and the remaining models are based on the subsets of covariates with observed data. The weights for our model averaging are determined by a leave-one-out cross-validation criterion that is minimized over the complete case datasets. Under certain regularity conditions, we establish the asymptotic optimality for the selected weights in the sense of minimizing the out-of-sample combined quantile prediction error. Simulation studies are presented to demonstrate the advantages of the proposed approach vs. several existing active methods. As an illustration, a dataset from NHANES 2005-2006 is analysed.

Sex-specific differences in spring migration timing of Song Thrush Turdus philomelos at the Baltic coast in relation to temperatures on the wintering grounds

Environmental factors influencing the timing of bird migration frequently affect age and sex groups differently. We applied discriminant functions to determine the sex of adult Song Thrushes ringed during spring migration in 1968–2019 at Hel on the Polish Baltic coast. We aimed to determine any differences between the sexes in the timing of spring migration and changes in protandry, and to identify any relationships between migration timing and temperatures at the wintering grounds. We analysed relationships between the date of migration and the year and monthly mean minimum temperatures in December–February by sex, using multiple quantile regression for q10, q50 and q90 of spring passage. On average males migrated six days before females. Spring protandry increased over 1968–2019 and with warm winters. The sexes responded differently to winter temperatures, likely because of the species’ mating strategy. For males the warmer the winter, especially in February, the earlier spring migration began and the later it ended, prolonging its duration. The influence of February’s temperature on the beginning of males’ migration is likely explained by selective pressure for their early arrival to establish territories. The later end of their arrival with a warm winter might reflect more low-quality males surviving, and migrating later than high-quality males, than with cold winters. For females December and January temperatures had no effect on the beginning and the end of spring migration; but the warmer the February, the earlier migration started and the later it ended. Females probably benefitted from improved conditions in a warm February in two ways: early-arriving females maximized their breeding success with a chance to raise a second brood, and late-arriving females maximized their chances of surviving migration by prolonging fuelling and stopovers, which extended females’ arrivals.

Fifteen-Year Follow-Up of Stapedotomy Patients: Audiological Outcomes and Associated Factors in a Middle Income Country

Objective: To evaluate the short-term (postoperative), medium-term (5 years), and long-term (10 and 15 years) audiometric results of patients who underwent stapedotomy and to determine specific factors associated with better postoperative outcomes. Methods: This study is a retrospective case review of 486 ears with surgically confirmed stapes fixation who underwent microscopic small fenestra stapedotomy. Preoperative, postoperative, and medium- and long-term air conduction (AC), bone conduction (BC), and air-bone gap (ABG) were assessed. Postoperative factors associated with better postoperative outcomes were evaluated. Results: At 10- and 15-year follow-ups, ABG, AC, and BC were significantly deteriorated but clinically preserved in comparison with postoperative results. According to a multiple quantile regression, younger age was associated with better postoperative results at 0.25 kHz (p = 0.003) and 4 kHz (p = 0.028) and a smaller preoperative ABG was associated with better audiometric results at 0.25 kHz (p = 0.048), 0.5 kHz (p = 0.001), and 4 kHz (p = 0.001). In addition, younger age (p = 0.001 for AC and p < 0.001 for BC) and preoperative AC PTA (p < 0.001 for AC) were significantly associated with better postoperative AC and BC PTA. Conclusions: Stapedotomy surgery provides short-, medium-, and long-term hearing benefits in our studied cohort. ABG, AC, and BC thresholds obtained after the surgery are clinically preserved in 5-, 10-, and 15-year follow-ups, with an age-expected BC deterioration. Smaller preoperative ABG and younger age were positive predictors for better postoperative ABG. Future research should address long-term subjective and quality of life outcomes.

The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life

Noise exposure is affecting health-related quality of life (HRQoL). There are many modelling approaches linking specific noise sources with single health-related outcomes. However, an integrated approach is missing taking into account measured levels as well as noise annoyance and sensitivity and assessing their independent association with HRQoL domains. Therefore, we investigated the predictive association of most common transportation noise sources (aircraft, railway and road traffic) as well as transportation noise annoyance and noise sensitivity with HRQoL using data from SAPALDIA (Swiss Cohort Study on Air Pollution and Lung and Heart Diseases in Adults).We assessed 2035 subjects, who participated in the second and third wave of SAPALDIA (3&4) and had complete information on exposure, outcome and covariates. At SAPALDIA3, we calculated annual means (Lden) of source-specific transportation noise exposure at the most exposed facade of participant’s dwelling floor height. Participants reported noise annoyance on the widely used 11-point ICBEN scale and answered to 10 questions assessing individual noise sensitivity. To assess the potentially predictive effect of these noise exposures, HRQoL was assessed about 8 years later (SAPALDIA4) using the SF-36. We performed predictive multiple quantile regression models to elucidate associations of noise parameters measured at SAPALDIA3 with median SF-36 scores at SAPALDIA4.Source-specific transportation noise exposures showed few yet not consistent associations with HRQoL scores. We observed statistically significant negative associations of transportation noise annoyance with HRQoL scores covering mental health components (adjusted difference in SF-36 mental health score between highest vs. lowest annoyance tertile: −2.54 (95%CI: −3.89; −1.20). Noise sensitivity showed strongest and most consistent associations with HRQoL scores covering both general and mental health components (adjusted difference in SF-36 scores between highest vs. lowest sensitivity tertile: Mental health −5.96 (−7.57; −4.36); general health −5.16 (−7.08; −3.24)).Within all noise parameters, we predominantly observed negative associations of noise sensitivity with HRQoL attaining a magnitude of potential clinical relevance. This implies that factors other than transportation noise exposure may be relevant for this exposure-outcome relation. Nonetheless, transportation noise annoyance showed relevant associations with mental health components, indicating a negative association of transportation noise with HRQoL.

Bayesian Multiple Quantile Regression for Linear Models Using a Score Likelihood

We propose the use of a score based working likelihood function for quantile regression which can perform inference for multiple conditional quantiles of an arbitrary number. We show that the proposed likelihood can be used in a Bayesian framework leading to valid frequentist inference, whereas the commonly used asymmetric Laplace working likelihood leads to invalid interval estimations and requires further correction. For computation, we propose a novel adaptive importance sampling algorithm to compute important posterior summaries such as the posterior mean and the covariance matrix. Our proposed approach makes it feasible to perform valid inference for parameters such as the slope differences at different quantile levels, which is either not possible or cumbersome using existing Bayesian approaches. Empirical results demonstrate that the proposed likelihood has good estimation and inferential properties and that the proposed computational algorithm is more efficient than its competitors.

Performance Evaluation of the Multiple Quantile Regression Model for Estimating Spatial Soil Moisture after Filtering Soil Moisture Outliers

The spatial distribution of soil moisture (SM) was estimated by a multiple quantile regression (MQR) model with Terra Moderate Resolution Imaging Spectroradiometer (MODIS) and filtered SM data from 2013 to 2015 in South Korea. For input data, observed precipitation and SM data were collected from the Korea Meteorological Administration and various institutions monitoring SM. To improve the work of a previous study, prior to the estimation of SM, outlier detection using the isolation forest (IF) algorithm was applied to the observed SM data. The original observed SM data resulted in IF_SM data following outlier detection. This study obtained an average data removal rate of 20.1% at 58 stations. For various reasons, such as instrumentation, environment, and random errors, the original observed SM data contained approximately 20% uncertain data. After outlier detection, this study performed a regression analysis by estimating land surface temperature quantiles. The soil characteristics were considered through reclassification into four soil types (clay, loam, silt, and sand), and the five-day antecedent precipitation was considered in order to estimate the regression coefficient of the MQR model. For all soil types, the coefficient of determination (R2) and root mean square error (RMSE) values ranged from 0.25 to 0.77 and 1.86% to 12.21%, respectively. The MQR results showed a much better performance than that of the multiple linear regression (MLR) results, which yielded R2 and RMSE values of 0.20 to 0.66 and 1.08% to 7.23%, respectively. As a further illustration of improvement, the box plots of the MQR SM were closer to those of the observed SM than those of the MLR SM. This result indicates that the cumulative distribution functions (CDF) of MQR SM matched the CDF of the observed SM. Thus, the MQR algorithm with outlier detection can overcome the limitations of the MLR algorithm by reducing both the bias and variance.

Does the Quantile Regression Forest Learn More Information on Chinese Systemic Risk?

This article applies the quantile regression forest (QRF), which is an improved method for predicting future monetary policy and macroeconomic downside risks in China. The information used to forecast is derived from Chinese systemic risk. We construct two Chinese systemic risk information sets, one is the old information set with 12 indexes, the other is our information set with 19 indexes added. We also applied two methods to learn systemic risk information, including multiple regression and principal component analysis (PCA). We show that the multiple quantile regression forest (MQRF) and the principal component quantile regression forest (PCQRF) exhibit a superior out-of-sample forecasting ability when compared to alternative forecasting models, such as the multiple quantile regression (MQR) and the principal component quantile regression (PCQR). Furthermore, our systemic risk information set has good economic implications in predicting China’s monetary policy and macroeconomic downside risks.

An efficient estimation for the parameter in additive partially linear models with missing covariates

In this paper, we study the weighted quantile average estimation technique for the parameter in additive partially linear models with missing covariates, which is proved to be an efficient method. The proposed method is based on optimally combining information over different quantiles via multiple quantile regression. We establish asymptotic normality of the weighted quantile average estimators when the selection probability is known, estimated using the non-parametrical method and parametrical method, respectively. Moreover, we compute optimal weights by minimizing asymptotic variance and then obtain the corresponding optimal weighted quantile average estimators. To examine the finite performance of our proposed method, we use the numerical simulations and apply to model time sober for the patients from a rehabilitation center. Simulation results and data analysis further verify that the proposed method is an efficient and safe alternative to both the WCQR method and WLS method.

An Institution-Based Assessment of Students' Hand Washing Behavior.

Background Hand hygiene is cost-effective and has been recognized as an effective measure in the control of communicable diseases. The main aim of this study is to evaluate the hand washing knowledge, practices, and skills of students in both private and public institutions of higher learning. Methods This was an institution-based cross-sectional study that included a mix of 577 university students from different disciplines (49.6% males and 50.4% females) with a mean age of 21.8 ± 3.5 years. Departments were selected at random, and the quota sampling technique was used to select the study participants. Hand washing knowledge, practices, and skills scores were assessed using a structured questionnaire. The differences in scores were further quantified across different factors using multiple quantile regression analysis. Results The prevalence of hand washing with soap was 10.7%. Also, the majority of the study participants (75.2%) had a poor hand washing practices score. Age ≥29 years was associated with a 6.3% lower median hand washing knowledge score (p=0.039). Also, being in the public institution was significantly associated with 6.3%, 36.0%, and 10.0% lower median hand washing knowledge (p=0.021), practices (p < 0.001), and skills (p=0.025) scores, respectively. In addition, being a medical student (p=0.029) and washing hands ≥ six times a day (p=0.008) were significantly associated with an increase in the median hand washing knowledge score of 6.3% and 18.7%, respectively. Conclusions Educational interventions need to be carried out to create awareness of the importance of hand washing and also to enhance the hand washing knowledge, practices, and skills of university students.

Association of faecal pH with childhood stunting: Results from a cross-sectional study

BackgroundGut microbiota plays an important role in the growth of children. The gut of children with optimum growth is enriched in certain species, especially Bifidobacteria and Clostridia. Bifidobacteria and commensal...

Value-at-Risk dynamics: a copula-VAR approach

In financial research and among risk management practitioners the estimation of a correct measure of the Value-at-Risk still proves interesting. A current approach, the multivariate CAViaR allows to provide an accurate measure of VaR modelling the joint dynamics in the Values-at-Risk by capturing the quantile conditional dependence structure to take into account financial contagion risk. The parameter estimates are based on multiple quantile regressions which assume linear combinations of sample quantiles. In this paper we argue that the analysis of multiple time-series aimed to model the time-varying quantile dependence can require non-linear and flexible estimation procedures. To this end, we examine the conditional quantile behaviour of some assets included in the Eurostoxx50 with respect to the quantile of a portfolio representing the market with a new copula-based quantile Vector AutoRegressive approach, and compare the results with the bivariate CAViaR model. Findings show that the copula approach is highly competitive, providing a time-varying model aimed to give a better specification of the Value-at-Risk, especially in terms of loss functions.

Unified Noncrossing Multiple Quantile Regressions Tree

ABSTRACTIn this article, we consider the estimation problem of a tree model for multiple conditional quantile functions of the response. Using the generalized, unbiased interaction detection and estimation algorithm, the quantile regression tree (QRT) method has been developed to construct a tree model for an individual quantile function. However, QRT produces different tree models across quantile levels because it estimates several QRT models separately. Furthermore, the estimated quantile functions from QRT often cross each other and consequently violate the basic properties of quantiles. This undesirable phenomenon reduces prediction accuracy and makes it difficult to interpret the resulting tree models. To overcome such limitations, we propose the unified noncrossing multiple quantile regressions tree (UNQRT) method, which constructs a common tree structure across all interesting quantile levels for better data visualization and model interpretation. Furthermore, the UNQRT estimates noncrossing multiple quantile functions simultaneously by enforcing noncrossing constraints, resulting in the improvement of prediction accuracy. The numerical results are presented to demonstrate the competitive performance of the proposed UNQRT over QRT. Supplementary materials for this article are available online.

A Median Analysis of Factors Influencing Body Fatness in Urban School-Age Children in Cameroon.

Background Childhood overweight/obesity is a fast growing public health problem in developing countries. The adverse health consequences of obesity have been attributed to higher body fat levels and this has drawn overwhelming attention towards more accurate assessment of body fat. The goal of this study is to evaluate the relationships between selected behavioral factors and percentage body fat (%BF) estimated using bioelectrical impedance analysis in school-age children. Methods A cross-sectional analysis was carried out in randomly selected 6- to 11-year-old children (507 boys and 501 girls). Percentage body fat was assessed using bioelectrical impedance analysis. The behavioral factors were reported by parents using a structured questionnaire. Multiple quantile regression analysis was used to evaluate the relationship between the selected behavioral factors and %BF. Results With quantile regression, the daily consumption of fruits and vegetables, daily breakfast consumption, and high physical activity (>4–7 times/week) were significantly (p < 0.001) associated with a 4.95, 3.29, and 3.66 decrease in median %BF, respectively. Also, consumption of snacks (>3 times a day) (p < 0.001), high sedentary lifestyle (>3–6 hours/day) (p < 0.001), and motorization to school (p < 0.005) significantly increased the median %BF by 3.69, 3.01, and 1.39, respectively. The largest changes in median %BF were observed in girls. Conclusions Efforts are needed using longitudinal studies to clarify the effects of these behavioral factors on %BF in different regions and ethnic groups of Cameroon and also to assess whether any observed differences are of clinical relevance.

Bayesian non-crossing quantile regression for regularly varying distributions

ABSTRACTQuantile regression is a very important statistical tool for predictive modelling and risk assessment. For many applications, conditional quantile at different levels are estimated separately. Consequently the monotonicity of conditional quantiles can be violated when quantile regression curves cross each other. In this paper, we propose a new Bayesian multiple quantile regression based on heavy tailed distribution for non-crossing. We consider a linear quantile regression model for simultaneous Bayesian estimation of multiple quantiles based on a regularly varying assumptions. The numerical and competitive performance of the proposed method is illustrated by simulation.

A study on the attributes involved in the hedonic pricing of Brazilian clothing

ABSTRACTThe objective of this study is to identify the weighted importance of intrinsic and extrinsic attributes. Intrinsic attributes are defined as the specific features of products. Extrinsic attributes refer to other characteristics that are also important for price composition, such as brand, store layout and services, and purchasing experiences. In a survey with 1,923 collected responses, it was possible to identify and quantify intrinsic and extrinsic influencing factors beyond price strategy in the Brazilian fashion market for blue jeans. The statistical analysis was based on the hedonic price method. The idea of expressing the price based on a series of intrinsic and extrinsic variables avoids the problem of using the regression technique. In this research, multiple linear regression and quantile regression were applied. The results show that extrinsic attributes have greater influence than intrinsic features on explaining the final market prices using log-linear and quantile regression statistical methods.