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Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.
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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.
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Aviral, Kumar Tiwari, and Krishnankutty Raveesh. "Determinants of Capital Structure: A Quantile Regression Analysis." Studies in Business and Economics 10, no. 1 (April 1, 2015): 16–34. http://dx.doi.org/10.1515/sbe-2015-0002.
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Abstract In this study, we attempted to analyze the determinants of capital structure for Indian firms using a panel framework and to investigate whether the capital structure models derived from Western settings provide convincing explanations for capital structure decisions of the Indian firms. The investigation is performed using balanced panel data procedures for a sample 298 firms (from the BSE 500 firms based on the availability of data) during 2001-2010. We found that for lowest quantile LnSales and TANGIT are significant with positive sign and NDTS and PROFIT are significant with negative sign. However, in case of 0.25th quantile LnSales and LnTA are significant with positive sign and PROFIT is significant with negative sign. For median quantile PROFIT is found to be significant with negative sign and TANGIT is significant with positive sign. For 0.75th quantile, in model one, LnSales and PROFIT are significant with negative sign and TANGIT and GROWTHTA are significant with positive sign whereas, in model two, results of 0.75th quantile are similar to the median quantile of model two. For the highest quantile, in case of model one, results are similar to the case of 0.75th quantile with exception that now GROWTHTA in model one (and GROWTHSA in model two).
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CAI, YUZHI. "A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS." International Journal of Theoretical and Applied Finance 19, no. 03 (April 21, 2016): 1650016. http://dx.doi.org/10.1142/s0219024916500163.
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Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.
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Chiu, Yohann Moanahere, Fateh Chebana, Belkacem Abdous, Diane Bélanger, and Pierre Gosselin. "Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach." International Journal of Environmental Research and Public Health 18, no. 24 (December 16, 2021): 13277. http://dx.doi.org/10.3390/ijerph182413277.
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Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.
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UTHAMI, IDA AYU PRASETYA, I. KOMANG GDE SUKARSA, and I. PUTU EKA NILA KENCANA. "REGRESI KUANTIL MEDIAN UNTUK MENGATASI HETEROSKEDASTISITAS PADA ANALISIS REGRESI." E-Jurnal Matematika 2, no. 1 (January 30, 2013): 6. http://dx.doi.org/10.24843/mtk.2013.v02.i01.p021.
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In regression analysis, the method used to estimate the parameters is Ordinary Least Squares (OLS). The principle of OLS is to minimize the sum of squares error. If any of the assumptions were not met, the results of the OLS estimates are no longer best, linear, and unbiased estimator (BLUE). One of the assumptions that must be met is the assumption about homoscedasticity, a condition in which the variance of the error is constant (same). Violation of the assumptions about homoscedasticity is referred to heteroscedasticity. When there exists heteroscedasticity, other regression techniques are needed, such as median quantile regression which is done by defining the median as a solution to minimize sum of absolute error. This study intended to estimate the regression parameters of the data were known to have heteroscedasticity. The secondary data were taken from the book Basic Econometrics (Gujarati, 2004) and analyzing method were performed by EViews 6. Parameter estimation of the median quantile regression were done by estimating the regression parameters at each quantile ?th, then an estimator was chosen on the median quantile as regression coefficients estimator. The result showed heteroscedasticity problem has been solved with median quantile regression although error still does not follow normal distribution properties with a value of R2 about 71 percent. Therefore it can be concluded that median quantile regression can overcome heteroscedasticity but the data still abnormalities.
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I. O., Ajao,, Obafemi, O. S., and Osunronbi, F.A. "MEASURING THE IMPACT OF TAU VECTOR ON PARAMETER ESTIMATES IN THE PRESENCE OF HETEROSCEDASTIC DATA IN QUANTILE REGRESSION ANALYSIS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 31, 2023): 3220–29. http://dx.doi.org/10.47191/ijmcr/v11i1.15.
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The ordinary least squares (OLS) regression models only the conditional mean of the response and is computationally less expensive. Quantile regression on the other hand is more expensive and rigorous but capable of handling vectors of quantiles and outliers. Quantile regression does not assume a particular parametric distribution for the response, nor does it assume a constant variance for the response, unlike least squares regression. This paper examines the impact of various quantiles (tau vector) on the parameter estimates in the models generated by the quantile regression analysis. Two data sets, one with normal random error with non-constant variances and the other with a constant variance were simulated. It is observed that with heteroscedastic data the intercept estimate does not change much but the slopes steadily increase in the models as the quantile increase. Considering homoscedastic data, results reveal that most of the slope estimates fall within the OLS confidence interval bounds, only few quartiles are outside the upper bound of the OLS estimates. The hypothesis of quantile estimates equivalence is rejected, which shows that the OLS is not appropriate for heteroscedastic data, but the assumption is not rejected in the case of homoscedastic data at 5% level of significance, which clearly proved that the quantile regression is not necessary in a constant variance data. Using the following accuracy measures, mean absolute percentage error (MAPE), the median absolute deviation (MAD) and the mean squared deviation (MSD), the best model for the heteroscedastic data is obtained at the first quantile level (tau = 0.10).
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Conaway, Mark. "Reference data and quantile regression." Muscle & Nerve 40, no. 5 (October 13, 2009): 751–52. http://dx.doi.org/10.1002/mus.21562.
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Pan, Wen-Tsao, and Yungho Leu. "An Analysis of Bank Service Satisfaction Based on Quantile Regression and Grey Relational Analysis." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/1475148.
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Bank service satisfaction is vital to the success of a bank. In this paper, we propose to use the grey relational analysis to gauge the levels of service satisfaction of the banks. With the grey relational analysis, we compared the effects of different variables on service satisfaction. We gave ranks to the banks according to their levels of service satisfaction. We further used the quantile regression model to find the variables that affected the satisfaction of a customer at a specific quantile of satisfaction level. The result of the quantile regression analysis provided a bank manager with information to formulate policies to further promote satisfaction of the customers at different quantiles of satisfaction level. We also compared the prediction accuracies of the regression models at different quantiles. The experiment result showed that, among the seven quantile regression models, the median regression model has the best performance in terms of RMSE, RTIC, and CE performance measures.
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Sánchez, Luis, Víctor Leiva, Helton Saulo, Carolina Marchant, and José M. Sarabia. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications." Mathematics 9, no. 21 (November 1, 2021): 2768. http://dx.doi.org/10.3390/math9212768.
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Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.
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Olsen, Cody S., Amy E. Clark, Andrea M. Thomas, and Lawrence J. Cook. "Comparing Least-squares and Quantile Regression Approaches to Analyzing Median Hospital Charges." Academic Emergency Medicine 19, no. 7 (July 2012): 866–75. http://dx.doi.org/10.1111/j.1553-2712.2012.01388.x.
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Kong, Efang, and Yingcun Xia. "A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION." Econometric Theory 28, no. 4 (March 14, 2012): 730–68. http://dx.doi.org/10.1017/s0266466611000788.
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Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with probability 1. The resulted estimator of the single-index parametric vector is root-n consistent, asymptotically normal, and based on simulation study, is more efficient than the average derivative method in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). The estimator of the link function converges at the usual rate for nonparametric estimation of a univariate function. As an empirical study, we apply the single-index quantile regression model to Boston housing data. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the housing market.
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Yang, Ming, Sheng Luo, and Stacia DeSantis. "Bayesian quantile regression joint models: Inference and dynamic predictions." Statistical Methods in Medical Research 28, no. 8 (July 2, 2018): 2524–37. http://dx.doi.org/10.1177/0962280218784757.
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In the traditional joint models of a longitudinal and time-to-event outcome, a linear mixed model assuming normal random errors is used to model the longitudinal process. However, in many circumstances, the normality assumption is violated and the linear mixed model is not an appropriate sub-model in the joint models. In addition, as the linear mixed model models the conditional mean of the longitudinal outcome, it is not appropriate if clinical interest lies in making inference or prediction on median, lower, or upper ends of the longitudinal process. To this end, quantile regression provides a flexible, distribution-free way to study covariate effects at different quantiles of the longitudinal outcome and it is robust not only to deviation from normality, but also to outlying observations. In this article, we present and advocate the linear quantile mixed model for the longitudinal process in the joint models framework. Our development is motivated by a large prospective study of Huntington’s disease where primary clinical interest is in utilizing longitudinal motor scores and other early covariates to predict the risk of developing Huntington’s disease. We develop a Bayesian method based on the location–scale representation of the asymmetric Laplace distribution, assess its performance through an extensive simulation study, and demonstrate how this linear quantile mixed model-based joint models approach can be used for making subject-specific dynamic predictions of survival probability.
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CAHYANI, NI WAYAN YUNI, I. GUSTI AYU MADE SRINADI, and MADE SUSILAWATI. "PERBANDINGAN TRANSFORMASI BOX-COX DAN REGRESI KUANTIL MEDIAN DALAM MENGATASI HETEROSKEDASTISITAS." E-Jurnal Matematika 4, no. 1 (January 30, 2015): 8. http://dx.doi.org/10.24843/mtk.2015.v04.i01.p081.
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Ordinary least square (OLS) is a method that can be used to estimate the parameter in linear regression analysis. There are some assumption which should be satisfied on OLS, one of this assumption is homoscedasticity, that is the variance of error is constant. If variance of the error is unequal that so-called heteroscedasticity. The presence heteroscedasticity can cause estimation with OLS becomes inefficient. Therefore, heteroscedasticity shall be overcome. There are some method that can used to overcome heteroscedasticity, two among those are Box-Cox power transformation and median quantile regression. This research compared Box-Cox power transformation and median quantile regression to overcome heteroscedasticity. Applied Box-Cox power transformation on OLS result ????2point are greater, smaller RMSE point and confidencen interval more narrow, therefore can be concluded that applied of Box-Cox power transformation on OLS better of median quantile regression to overcome heteroscedasticity.
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ANKARALI, Handan, Özge YILMAZ, Münevver KIZILAY, İlknur ARSLANOĞLU, and Duygu AYDIN. "The Use of Nonparametric Quantile Regression and Least Median of Squares Regression for Construction of Growth Curves of Weight." Turkiye Klinikleri Journal of Medical Sciences 33, no. 3 (2013): 692–701. http://dx.doi.org/10.5336/medsci.2012-30442.
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Pereira, Sara, Flávio Bastos, Carla Santos, José Maia, Go Tani, Leah E. Robinson, and Peter T. Katzmarzyk. "Variation and Predictors of Gross Motor Coordination Development in Azorean Children: A Quantile Regression Approach." International Journal of Environmental Research and Public Health 19, no. 9 (April 29, 2022): 5417. http://dx.doi.org/10.3390/ijerph19095417.
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We investigated the development of gross motor coordination (GMC) as well as its predictors in school-aged Azorean children. The sample included 181 children (90 girls), followed consecutively for 4 years from 6 to 9 years of age. GMC was assessed with the Körperkoordinationstest für Kinder, and predictors included body mass index, standing long jump, 50-yard dash, and shuttle run. The changes in GMC and the effects of predictors were analyzed with mean-modeling as well as quantile regression. In the latter, we considered the following three quantiles (Q): Q20, Q50, and Q80 as markers of low, median, and high GMC levels, respectively. All analyses were conducted using R software and alpha was set at 5%. The GMC changes were curvilinear in both models, but the quantile approach showed a more encompassing picture of the changes across the three quantiles in both boys and girls with different rates of change. Further, the predictors had different effect sizes across the quantiles in both sexes, but in the mean-model their effects were constant. In conclusion, quantile regression provides more detailed information and permits a more thorough understanding of changes in GMC over time and the influence of putative predictors.
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Mohamad Yunus, Norhanishah, and Norehan Abdullah. "A Quantile Regression Analysis of Absorptive Capacity in the Malaysian Manufacturing Industry." Malaysian Journal of Economic Studies 59, no. 1 (June 14, 2022): 153–70. http://dx.doi.org/10.22452/mjes.vol59no1.8.
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Using a set of absorptive capacity proxies, we present new empirical findings on the role of absorptive capacity in assimilating the technology effects from the presence of multinational corporations (MNCs) in the Malaysian manufacturing industry. We applied a quantile regression estimator to explicitly gauge the level of absorptive capacity among workers by their levels of education at different quantiles of the conditional FDI distribution during the period of 2000–2018. We conclude that the medium-high technology industries benefit more from FDI if the workers’ absorptive capacity level reaches at least the median quantile. Based on the findings of this study, we suggest that educational digitisation efforts in enhancing quality human capital should be intensified, by equipping them with the latest knowledge and skills, which in turn requires cooperation between universities, public technical and vocational education and training (TVET) institutions as well as MNCs.
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T, Nwakuya, M., and Nduka, E. C. "Investigating Performance of Composite Quantile Regression with and without Penalization." Scholars Journal of Physics, Mathematics and Statistics 9, no. 5 (June 22, 2022): 85–91. http://dx.doi.org/10.36347/sjpms.2022.v09i05.002.
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The performance of composite quantile regression with and without penalization was investigated and results compared to Lasso Quantile Regression (LQR), Lasso Regression (LR) and Ridge Regression (RR). The mean square error, Akiake information criteria and mean absolute percentage error were used as the comparative criteria. The comparison was illustrated using real dataset and simulated data sets of sample sizes n=30,100,300,500 and 1000. Five consecutive quantiles; 0.19, 0.39, 0.59, 0.79 and 0.99 were used for the quantile regression methods while the lasso regression and ridge regression were based on the mean effect. Another set of quantiles; 0.25, 0.5, 0.75 and 0.95 were also accessed based on only CQR and CQR_AL. The results shows that the composite quantile regression without penalization (CQR) and composite quantile regression with penalization (CQR_AL) achieved same results with the lowest variance on estimated effects and was best fitted model for very large data sets (n=100, 300, 500 & 1000). For the real life data with sample size of 318, the CQR_AL showed the least MSE=421.7653 and AIC=1930.136, but its prediction accuracy was low at 19.03%. Considering sample size 30, the LQR at the 0.59th quantile had the lowest variance with MSE of 1.3940 and was best fitted with AIC of 340.20, also it was noticed that COR_AL achieved the next lowest value for MSE and AIC. These results led to the conclusion that CQR_AL and CQR can be used alternatively with large data sets. But when the sample size is small the LQR is most suited, but if a combined quantile effect is sort the CQR_AL should be opted for.
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Yang, Yunwen, Anne L. Adolph, Maurice R. Puyau, Firoz A. Vohra, Nancy F. Butte, and Issa F. Zakeri. "Modeling energy expenditure in children and adolescents using quantile regression." Journal of Applied Physiology 115, no. 2 (July 15, 2013): 251–59. http://dx.doi.org/10.1152/japplphysiol.00295.2013.
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Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in energy expenditure (EE). Study objective is to apply quantile regression (QR) to predict EE and determine quantile-dependent variation in covariate effects in nonobese and obese children. First, QR models will be developed to predict minute-by-minute awake EE at different quantile levels based on heart rate (HR) and physical activity (PA) accelerometry counts, and child characteristics of age, sex, weight, and height. Second, the QR models will be used to evaluate the covariate effects of weight, PA, and HR across the conditional EE distribution. QR and ordinary least squares (OLS) regressions are estimated in 109 children, aged 5–18 yr. QR modeling of EE outperformed OLS regression for both nonobese and obese populations. Average prediction errors for QR compared with OLS were not only smaller at the median τ = 0.5 (18.6 vs. 21.4%), but also substantially smaller at the tails of the distribution (10.2 vs. 39.2% at τ = 0.1 and 8.7 vs. 19.8% at τ = 0.9). Covariate effects of weight, PA, and HR on EE for the nonobese and obese children differed across quantiles ( P < 0.05). The associations (linear and quadratic) between PA and HR with EE were stronger for the obese than nonobese population ( P < 0.05). In conclusion, QR provided more accurate predictions of EE compared with conventional OLS regression, especially at the tails of the distribution, and revealed substantially different covariate effects of weight, PA, and HR on EE in nonobese and obese children.
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Tang, Shaowu, Jong-Hyeon Jeong, and Chi Song. "Fractional logistic regression for censored survival data." Journal of Statistical Research 51, no. 2 (February 1, 2018): 101–14. http://dx.doi.org/10.47302/jsr.2017510201.
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In the analysis of time-to-event data, e.g. from cancer studies, the group effect of main interest such as treatment effect of a chemo-therapy often needs to be adjusted by confounding factors (possibly continuous) such as hormonal receptor status, age at diagnosis, and pathological tumor size, when the study outcome is affected by their imbalanced distributions across the comparison groups. The median, or quantile, is a popular summary measure for censored survival data due to its robustness. In this paper, first the logistic regression is extended to fractional responses transformed from censored survival data, which can directly predict conditional survival probabilities beyond a fixed time point given covariates. As a special case, we construct a median test for censored survival data that can be used to assess a group effect adjusting for the potentially multiple confounding factors. A quasi-likelihood-based inference procedure is adopted to construct the test statistic. Simulation studies show empirical type I error probabilities and powers for the adjusted two-sample median test are reasonable. The method is illustrated with a breast cancer data set.
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Teng, Xiaodong, Yanzhi Wang, Aiguo Wang, Bao-Guang Chang, and Kun-Shan Wu. "Environmental, Social, Governance Risk and Corporate Sustainable Growth Nexus: Quantile Regression Approach." International Journal of Environmental Research and Public Health 18, no. 20 (October 15, 2021): 10865. http://dx.doi.org/10.3390/ijerph182010865.
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Despite a huge body of literature revealing that the effect of environmental, social and governance (ESG) scores on a firms’ financial performance and value, it lacks the empirical research on the nexus between corporate sustainable growth and ESG risk in the existing research. The paper aims to examine the nexus between ESG risk and corporate sustainable growth. This study utilizes a quantile regression approach to explore how ESG risk affects corporate sustainable growth (proxied by sustainable growth rate, SGR). The ordinary least squares estimation results confirm that ESG significantly negatively affects corporate sustainable growth. The quantile regression results reveal ESG risk has a significant negative effect on corporate sustainable growth in the upper quantiles of SGR, but not in the lower and median quantiles. The results show that the impact of ESG risk on the corporate sustainable growth is asymmetric and affected by the distribution of SGR. Furthermore, the research results identify that the negative relationship between ESG risk and corporate sustainable growth is particularly apparent for firms in environmentally sensitive industries. This study greatly contributes to existing literature, as with this detailed knowledge, managers can make decisions based on these associations and identify the most lucrative course of action.
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Maswanganyi, Norman, Caston Sigauke, and Edmore Ranganai. "Prediction of Extreme Conditional Quantiles of Electricity Demand: An Application Using South African Data." Energies 14, no. 20 (October 15, 2021): 6704. http://dx.doi.org/10.3390/en14206704.
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It is important to predict extreme electricity demand in power utilities as the uncertainties in the future of electricity demand distribution have to be taken into consideration to achieve the desired goals. The study focused on the prediction of extremely high conditional quantiles (between 0.95 and 0.9999) and extremely low quantiles (between 0.001 and 0.05) of electricity demand using South African data. The paper discusses a comparative analysis of the additive quantile regression model with an extremal mixture model and a nonlinear quantile regression model. The estimated quantiles at each level were then combined using the median approach. The comparisons were carried out using daily peak electricity demand data ranging from January 1997 to May 2014. Proper scoring rules were used to compare the three models, and the model with the smallest score was preferred. The results could be useful to system operators including decision-makers in power utility companies by giving insights and guidance for future electricity demand patterns. The prediction of extremely high quantiles of daily peak electricity demand could help system operators know the possible largest demand that will enable them to supply adequate electricity to consumers and shift demand to off-peak periods. The prediction of extreme conditional quantiles of daily peak electricity demand in the context of South Africa using additive quantile regression, nonlinear quantile regression, and extremal mixture models has not been performed previously to the best of our knowledge.
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Lavín, Felipe Vásquez, Ricardo Flores, and Verónica Ibarnegaray. "A Bayesian quantile binary regression approach to estimate payments for environmental services." Environment and Development Economics 22, no. 2 (November 24, 2016): 156–76. http://dx.doi.org/10.1017/s1355770x16000255.
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AbstractStated preference approaches, such as contingent valuation, focus mainly on the estimation of the mean or median willingness to pay (WTP) for an environmental good. Nevertheless, these two welfare measures may not be appropriate when there are social and political concerns associated with implementing a payment for environmental services (PES) scheme. In this paper the authors used a Bayesian estimation approach to estimate a quantile binary regression and the WTP distribution in the context of a contingent valuation PES application. Our results show that the use of other quantiles framed in the supermajority concept provides a reasonable interpretation of the technical nonmarket valuation studies in the PES area. We found that the values of the mean WTP are 10–37 times higher than the value that would support a supermajority of 70 per cent of the population.
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Mboup, Bassirou, Christophe Le Tourneau, and Aurélien Latouche. "Insights for Quantifying the Long-Term Benefit of Immunotherapy Using Quantile Regression." JCO Precision Oncology, no. 5 (January 2021): 173–76. http://dx.doi.org/10.1200/po.20.00164.
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PURPOSE Immunotherapy has been approved to treat many tumor types. However, one characteristic of this therapeutic class is that survival benefit is due to late immune response, which leads to a delayed treatment effect. Quantifying the benefit, if any, of such treatment, will thus require other metrics than the usual hazard ratio and different approaches have been proposed to quantify the long-term response of immunotherapy. METHOD In this paper, we suggest to use quantile regression for survival data to quantify the long-term benefit of immunotherapy. Our motivation is that this approach is not trial-specific and provides clinically understandable results without specifying arbitrary time points or the necessity to reach median survival, as is the case with other methods. We use reconstructed data from published Kaplan-Meier curves to illustrate our method. RESULTS On average, patients from the immunotherapy group have 60% chance to survive 5.46 months (95% CI, 2.57 to 9.02) more than patients in the chemotherapy group.
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McGreevy, Katharine M., Stuart R. Lipsitz, Jeffrey A. Linder, Eric Rimm, and David G. Hoel. "Using Median Regression to Obtain Adjusted Estimates of Central Tendency for Skewed Laboratory and Epidemiologic Data." Clinical Chemistry 55, no. 1 (January 1, 2009): 165–69. http://dx.doi.org/10.1373/clinchem.2008.106260.
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Abstract Background: Laboratory studies often involve analyses of highly skewed data for which means are not an adequate measure of central tendency because they are sensitive to outliers. Attempts to transform skewed data to symmetry are not always successful, and medians are better measures of central tendency for such skewed distributions. When medians are compared across groups, confounding can be an issue, so there is a need for adjusted medians. Methods: We illustrate the use of quantile regression to obtain adjusted medians. The method is illustrated by use of skewed nutrient data obtained from black and white men attending a prostate cancer screening. For 3 nutrients, saturated fats, caffeine, and vitamin K, we obtained medians adjusted by age, body mass index, and calories for men in each race group. Results: Quantile regression, linear regression, and log-normal regression produced substantially different adjusted estimates of central tendency for saturated fats, caffeine, and vitamin K. Conclusions: Our method was useful for analysis of skewed and other nonnormally distributed continuous outcome data and for calculation of adjusted medians.
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Jiang, Shan, Xiaoyu Ma, Meng Li, Shoumeng Yan, Hantong Zhao, Yingan Pan, Changcong Wang, Yan Yao, Lina Jin, and Bo Li. "Association between dietary mineral nutrient intake, body mass index, and waist circumference in U.S. adults using quantile regression analysis NHANES 2007–2014." PeerJ 8 (May 4, 2020): e9127. http://dx.doi.org/10.7717/peerj.9127.
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Objective Mineral nutrients play an important role in maintaining material and energy metabolism. Reports on mineral nutrient intakes and body mass index (BMI) and waist circumference (WC) are rare in the United States. This study examined the relationship between BMI, WC and dietary mineral intakes. Method We used the data from National Health and Nutrition Examination Survey 2007–2014. Nutrient intakes were adjusted for energy according to the residual adjustment method. We used the quantile regression model to analyze the relationship between BMI, WC under different distributions and the average daily mineral intakes. Result A total of 19,952 people were included in the study, including 9,879 men and 10,073 women (≥20 years old). The median BMI was 27.935 kg/m2 and the median WC was 97.700 cm. The results of quantile regression showed that calcium, magnesium, potassium, copper, zinc and iron intakes were negatively correlated with BMI and WC, after adjusting for age and gender. Sodium and phosphorus intakes were positively correlated with BMI, sodium intakes were positively correlated with WC. This correlation was enhanced with increasing quantiles of risk levels. In high BMI or high WC populations, mineral intakes had a greater impact on BMI and WC. The quantile regression coefficients of selenium intakes were not statistically significant at each quantile. Conclusion Our results suggested that the mineral nutrient intakes were associated with BMI and WC in American adults. However, we also need to further study the longitudinal effects of mineral intakes and obesity.
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Newey, Whitney K., and James L. Powell. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions." Econometric Theory 6, no. 3 (September 1990): 295–317. http://dx.doi.org/10.1017/s0266466600005284.
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We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the regression coefficients is derived. This lower bound corresponds to the covariance matrix of an optimally weighted censored least absolute deviations estimator, where the optimal weight is the conditional density at zero of the disturbance. We also show how an estimator that attains this lower bound can be constructed, via nonparametric estimation of the conditional density at zero of the disturbance. As a special case our results apply to the (uncensored) linear model under a conditional median restriction.
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Hu, Tao, and Baosheng Liang. "A New Class of Estimators Based on a General Relative Loss Function." Mathematics 9, no. 10 (May 18, 2021): 1138. http://dx.doi.org/10.3390/math9101138.
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Motivated by the relative loss estimator of the median, we propose a new class of estimators for linear quantile models using a general relative loss function defined by the Box–Cox transformation function. The proposed method is very flexible. It includes a traditional quantile regression and median regression under the relative loss as special cases. Compared to the traditional linear quantile estimator, the proposed estimator has smaller variance and hence is more efficient in making statistical inferences. We show that, in theory, the proposed estimator is consistent and asymptotically normal under appropriate conditions. Extensive simulation studies were conducted, demonstrating good performance of the proposed method. An application of the proposed method in a prostate cancer study is provided.
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Lakshmanasamy, T. "THE DIFFERENTIAL ECONOMIC BENEFITS OF RURAL ELECTRIFICATION IN INDIA: QUANTILE REGRESSION ESTIMATION." MAN, ENVIRONMENT AND SOCIETY 3, no. 1 (2022): 175–91. http://dx.doi.org/10.47509/mes.2022.v03i01.13.
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Rural electrification not only provides affordable modern energy to rural households at a cheaper price but also improves the quality of life and economic development of the rural sector. The welfare gains of electricity are not the same across households. This paper tries to understand who benefits the most from rural electrification - the poor or the rich rural households. The differential effects of rural electrification on household income and expenditures on health and children’s education are estimated using the 2011-2012 IHDS-II survey data applying the quantile regression method. The estimated results show that household electrification increases both household income and expenditure. The higher-income rural households benefit more than the lower-income households from rural electrification. The upper-income rural households gain more in terms of the education of children relative to poor-income households from rural electrification. Rural electrification benefits are higher for median health expenditure households than either for lower or upper quantile households. The larger benefits from rural electrification accrue to the better-off rural households through higher consumption and use of electricity for many productive uses and electrification benefits accrue from multiple channels.
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Lopez-Martin, Manuel, Antonio Sanchez-Esguevillas, Luis Hernandez-Callejo, Juan Ignacio Arribas, and Belen Carro. "Additive Ensemble Neural Network with Constrained Weighted Quantile Loss for Probabilistic Electric-Load Forecasting." Sensors 21, no. 9 (April 23, 2021): 2979. http://dx.doi.org/10.3390/s21092979.
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This work proposes a quantile regression neural network based on a novel constrained weighted quantile loss (CWQLoss) and its application to probabilistic short and medium-term electric-load forecasting of special interest for smart grids operations. The method allows any point forecast neural network based on a multivariate multi-output regression model to be expanded to become a quantile regression model. CWQLoss extends the pinball loss to more than one quantile by creating a weighted average for all predictions in the forecast window and across all quantiles. The pinball loss for each quantile is evaluated separately. The proposed method imposes additional constraints on the quantile values and their associated weights. It is shown that these restrictions are important to have a stable and efficient model. Quantile weights are learned end-to-end by gradient descent along with the network weights. The proposed model achieves two objectives: (a) produce probabilistic (quantile and interval) forecasts with an associated probability for the predicted target values. (b) generate point forecasts by adopting the forecast for the median (0.5 quantiles). We provide specific metrics for point and probabilistic forecasts to evaluate the results considering both objectives. A comprehensive comparison is performed between a selection of classic and advanced forecasting models with the proposed quantile forecasting model. We consider different scenarios for the duration of the forecast window (1 h, 1-day, 1-week, and 1-month), with the proposed model achieving the best results in almost all scenarios. Additionally, we show that the proposed method obtains the best results when an additive ensemble neural network is used as the base model. The experimental results are drawn from real loads of a medium-sized city in Spain.
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Artemenko, Vladislav, and Volodymyr Petrovych. "REGRESSION MAXIMUM AND ITS USE TO HYDROECOLOGICAL RESEARCH." AUTOMOBILE ROADS AND ROAD CONSTRUCTION, no. 111 (June 30, 2022): 200–205. http://dx.doi.org/10.33744/0365-8171-2022-111-200-205.
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One of the actual problems of hydrochemistry there is influence to solar activity on condition chemical substance in water environment. The goal of the work it is possible estimation relationship some hydrochemical factors and solar activity (Wolf's Numbers W). To this effect the research was given for concentration 〖NH〗_4^+, 〖NO〗_2^- , 〖NO〗_3^- in water large flat river of Ukraine (1991 … 2010 years). The ion concentrations denominated in mg on litre. Were they also analysed given over Wolf's numbers for this period (1991 … 2010 years). Since these dependencies for the best reveals itself at a rate of extreme values that for each value of the Wolf's number selected only maximum to concentrations of the ion. Accordingly building to regressions executed not on all raw data’s but for maximum values concentration only. For this regression execute in two steps: STEP 1: Selected only one (maximum) value concentration of the ion for each unique value of Wolf's number. STEP 2: To prepared by specified way data is used for regression. Experiment has shown that linear regression in this instance to use it is impossible (got the horizontal line). Experiment has also shown adequacy of the use polynomial quantile regression (so it was used this type of regression). It was used median egression (quantile regression for Q=0,5). Median regression demonstrates the observable reduction a concentration of 〖NH〗_4^+, 〖NO〗_2^-,〖 NO〗_3^- when increasing of values Wolf's Numbers. Offered in article “regression for maximus” important for decision of the practical problems of hydroecology. The general trend in behavioyr of Wolf's Numbers can be forecasting on times of the ten years onward. This means as the general trend in behavioyr of 〖NH〗_4^+, 〖NO〗_2^- , 〖NO〗_3^- also can be forecasting on times of ten of years onward (the factor of the purity of natural water). The natural water more pure (the minimum concentration of 〖NH〗_4^+, 〖NO〗_2^- , 〖NO〗_3^-) under high solar activity (high values of Wolf's Numbers).
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Nascimento, Moysés, Paulo Eduardo Teodoro, Isabela de Castro Sant’Anna, Laís Mayara Azevedo Barroso, Ana Carolina Campana Nascimento, Camila Ferreira Azevedo, Larissa Pereira Ribeiro Teodoro, Francisco José Correia Farias, Helaine Claire Almeida, and Luiz Paulo de Carvalho. "Influential Points in Adaptability and Stability Methods Based on Regression Models in Cotton Genotypes." Agronomy 11, no. 11 (October 28, 2021): 2179. http://dx.doi.org/10.3390/agronomy11112179.
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The aim of this work was to answer the following question: can influential points modify the recommendation of genotypes, based on regression methods, in the presence of genotype × environment (G × E)? Therefore, we compared the parameters of the adaptability and stability of three methodologies based on regression in the presence of influential points. Specifically, were evaluated methods based on simple, non-parametric and quantile (τ = 0.50) regressions. The dataset used in this work corresponds to 18 variety trials of cotton cultivars that were conducted in the 2013–2014 and 2014–2015 crop seasons. The evaluated variable was the cotton fiber yield (kg/ha). Once we noticed that the effect of G × E interaction is significant, the statistical procedures adopted for the adaptability and stability analysis of the genotypes. To verify the presence of a possible influential point, we used the leverage values, studentized residuals (SR), DFBETAS and Cook’s distance. As a result, the influential points can modify the recommendation of genotypes, based on regression methods, in the presence of G × E interaction. The non-parametric and quantile (τ = 0.50) regressions, which are based on median estimators, are less sensitive to the presence of influential points avoiding misleading recommendations of genotypes in terms of adaptability.
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Egbunike, Francis Chinedu, Ardi Gunardi, Udunze Ugochukwu, and Atang Hermawan. "Internal Corporate Governance Mechanisms and Corporate Tax Avoidance in Nigeria: A Quantile Regression Approach." Jurnal Ilmiah Akuntansi dan Bisnis 16, no. 1 (January 5, 2021): 20. http://dx.doi.org/10.24843/jiab.2021.v16.i01.p02.
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The main objective of the study was to investigate the effect of corporate governance on tax avoidance of quoted manufacturing firms in Nigeria. The study focused on internal corporate governance mechanisms and specifically examined the effect of board size, board independence, board diligence, CEO duality, and audit committee diligence. The ex post facto research design was adopted. The population comprised of all quoted manufacturing companies on the Nigerian Stock Exchange (NSE). The sample was purposively drawn as all companies in the consumer goods sector of the NSE. The study relied on secondary data obtained from annual reports and accounts of the sampled companies. Both descriptive and inferential statistics were used to analyze the data. The hypotheses were validated using Quantile Regression technique. Results showed that board size, board independence, and board diligence were significant at the median and 75th quantile. CEO duality and audit committee diligence were not significant at the 25th, 50th, and 75th quantile. The study recommended among others moderate board sizes to improve efficiency of decision-making. In addition, the need for more independent directors and meeting frequency should be tailored to suit the needs of the company.
Keywords: corporate governance mechanisms, tax avoidance, quantile regression
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Rahman, Ayesha S., and Ataur Rahman. "Application of Principal Component Analysis and Cluster Analysis in Regional Flood Frequency Analysis: A Case Study in New South Wales, Australia." Water 12, no. 3 (March 12, 2020): 781. http://dx.doi.org/10.3390/w12030781.
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This paper examines the applicability of principal component analysis (PCA) and cluster analysis in regional flood frequency analysis. A total of 88 sites in New South Wales, Australia are adopted. Quantile regression technique (QRT) is integrated with the PCA to estimate the flood quantiles. A total of eight catchment characteristics are selected as predictor variables. A leave-one-out validation is applied to determine the efficiency of the developed statistical models using an ensemble of evaluation diagnostics. It is found that the PCA with QRT model does not perform well, whereas cluster/group formed with smaller sized catchments performs better (with a median relative error values ranging from 22% to 37%) than other clusters/groups. No linkage is found between the degree of heterogeneity in the clusters/groups and precision of flood quantile prediction by the multiple linear regression technique.
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Oware, Kofi Mintah, and T. Mallikarjunappa. "Corporate social responsibility and debt financing of listed firms: a quantile regression approach." Journal of Financial Reporting and Accounting 19, no. 4 (February 9, 2021): 615–39. http://dx.doi.org/10.1108/jfra-07-2020-0202.
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Purpose The purpose of the study is to examine the effect of corporate social responsibility (CSR) on debt financing (natural logarithm of debt and leverage ratios) of listed firms. Design/methodology/approach Using content analysis for data extraction, the study examines listed firms on the Bombay Stock Exchange (BSE) from 2010 to 2019 financial year. It uses a quantile regression and panel fixed effect regression as the model's application. Findings The study shows that CSR expenditure has a positive and strong correlation with debt financing (i.e. natural logarithm of long-term and short-term debts). The first findings show that CSR expenditure has a negative and statistically significant association with total leverage ratio, using conditional mean and median percentile. However, there is a positive and statistically significant association between CSR expenditure and long-term leverage ratio at the 25th and 50th percentile. The second findings show that CSR expenditure has a positive and statistically significant association with long-term debt but an insignificant association with short-term debt and total debt under a conditional mean average. The application of quantile regression addresses the values that fall outside the confidence interval and therefore document a positive and statistically significant association between CSR expenditure and debt financing (short-term debt, long-term debt and total debt) at the 25th, 50th and 75th percentile. Originality/value The introduction of quantile regression gives a novelty in CSR and debt financing study, which to the best of the authors’ knowledge, has not received any attention. Similarly, firms have better information on how to position their CSR expenditure to attract providers of debt financing.
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Porter, W. C., C. L. Heald, D. Cooley, and B. Russell. "Investigating the observed sensitivities of air quality extremes to meteorological drivers via quantile regression." Atmospheric Chemistry and Physics Discussions 15, no. 10 (May 19, 2015): 14075–109. http://dx.doi.org/10.5194/acpd-15-14075-2015.
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Abstract. Air pollution variability is strongly dependent on meteorology. However, quantifying the impacts of changes in regional climatology on pollution extremes can be difficult due to the many non-linear and competing meteorological influences on the production, transport, and removal of pollutant species. Furthermore, observed pollutant levels at many sites show sensitivities at the extremes that differ from those of the overall mean, indicating relationships that would be poorly characterized by simple linear regressions. To address this challenge, we apply quantile regression to observed daily ozone (O3) and fine particulate matter (PM2.5) levels and reanalysis meteorological fields in the United States over the past decade to specifically identify the meteorological sensitivities of higher pollutant levels. From an initial set of over 1700 possible meteorological indicators (including 28 meteorological variables with 63 different temporal options) we generate reduced sets of O3 and PM2.5 indicators for both summer and winter months, analyzing pollutant sensitivities to each for response quantiles ranging from 2–98%. Primary drivers of high-quantile O3 levels include temperature and relative humidity in the summer, while winter O3 levels are most commonly associated with incoming radiation flux. Drivers of summer PM2.5 include temperature, wind speed, and tropospheric stability at many locations, while stability, humidity, and planetary boundary layer height are the key drivers most frequently associated with winter PM2.5. We find key differences in driver sensitivities across regions and quantiles. For example, we find nationally averaged sensitivities of 95th percentile summer O3 to changes in maximum daily temperature of approximately 0.9 ppb °C−1, while the sensitivity of 50th percentile summer O3 (the annual median) is only 0.6 ppb °C−1. This gap points to differing sensitivities within various percentiles of the pollutant distribution, highlighting the need for statistical tools capable of identifying meteorological impacts across the entire response spectrum.
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Porter, W. C., C. L. Heald, D. Cooley, and B. Russell. "Investigating the observed sensitivities of air-quality extremes to meteorological drivers via quantile regression." Atmospheric Chemistry and Physics 15, no. 18 (September 21, 2015): 10349–66. http://dx.doi.org/10.5194/acp-15-10349-2015.
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Abstract. Air pollution variability is strongly dependent on meteorology. However, quantifying the impacts of changes in regional climatology on pollution extremes can be difficult due to the many non-linear and competing meteorological influences on the production, transport, and removal of pollutant species. Furthermore, observed pollutant levels at many sites show sensitivities at the extremes that differ from those of the overall mean, indicating relationships that would be poorly characterized by simple linear regressions. To address this challenge, we apply quantile regression to observed daily ozone (O3) and fine particulate matter (PM2.5) levels and reanalysis meteorological fields in the USA over the past decade to specifically identify the meteorological sensitivities of higher pollutant levels. From an initial set of over 1700 possible meteorological indicators (including 28 meteorological variables with 63 different temporal options), we generate reduced sets of O3 and PM2.5 indicators for both summer and winter months, analyzing pollutant sensitivities to each for response quantiles ranging from 2 to 98 %. Primary covariates connected to high-quantile O3 levels include temperature and relative humidity in the summer, while winter O3 levels are most commonly associated with incoming radiation flux. Covariates associated with summer PM2.5 include temperature, wind speed, and tropospheric stability at many locations, while stability, humidity, and planetary boundary layer height are the key covariates most frequently associated with winter PM2.5. We find key differences in covariate sensitivities across regions and quantiles. For example, we find nationally averaged sensitivities of 95th percentile summer O3 to changes in maximum daily temperature of approximately 0.9 ppb °C−1, while the sensitivity of 50th percentile summer O3 (the annual median) is only 0.6 ppb °C−1. This gap points to differing sensitivities within various percentiles of the pollutant distribution, highlighting the need for statistical tools capable of identifying meteorological impacts across the entire response spectrum.
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Bhattacharya, Shibaprasad, Kanak Kalita, Robert Čep, and Shankar Chakraborty. "A Comparative Analysis on Prediction Performance of Regression Models during Machining of Composite Materials." Materials 14, no. 21 (November 6, 2021): 6689. http://dx.doi.org/10.3390/ma14216689.
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Modeling the interrelationships between the input parameters and outputs (responses) in any machining processes is essential to understand the process behavior and material removal mechanism. The developed models can also act as effective prediction tools in envisaging the tentative values of the responses for given sets of input parameters. In this paper, the application potentialities of nine different regression models, such as linear regression (LR), polynomial regression (PR), support vector regression (SVR), principal component regression (PCR), quantile regression, median regression, ridge regression, lasso regression and elastic net regression are explored in accurately predicting response values during turning and drilling operations of composite materials. Their prediction performance is also contrasted using four statistical metrics, i.e., mean absolute percentage error, root mean squared percentage error, root mean squared logarithmic error and root relative squared error. Based on the lower values of those metrics and Friedman rank and aligned rank tests, SVR emerges out as the best performing model, whereas the prediction performance of median regression is worst. The results of the Wilcoxon test based on the drilling dataset identify the existence of statistically significant differences between the performances of LR and PCR, and PR and median regression models.
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SHARMA, ANDY. "Modelling disparities in health services utilisation for older Blacks: a quantile regression framework." Ageing and Society 35, no. 8 (June 16, 2014): 1657–83. http://dx.doi.org/10.1017/s0144686x14000440.
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ABSTRACTWith the on-going ageing of the United States population, resolving health disparities continues to be a prominent and worthwhile goal, particularly in the areas of promoting minority health and reducing racial/ethnic disparities. This analysis employs the 2004 and 2005 Household Component records from the Medical Expenditures Panel Survey, which correspond to data files H89 and H97, to examine utilisation by race across the entire distribution function; more specifically, applying the behavioural model of health services utilisation and employing a Quantile Regression (QR) framework. This is a noteworthy contribution because the conditional mean may not be the best approximation for a skewed-location distribution. In contrast, QR is robust to outliers and scale effects since the estimation minimises least absolute deviation. The sample consists of 2,525 older adults at least 65 years of age with 303 corresponding to Black and 2,222 corresponding to White. Results suggest older Blacks continue to utilise health services (i.e. office or clinic visits with a physician or medical provider) at lower levels and this is more pronounced at and below the median quantile (i.e. below the 50th cut-off). Usual source of care (USC) continues to play an important role. Beliefs surrounding the need for insurance and medical intervention are also significant and explain some of the racial disparities. Although utilisation disparities persist for older Blacks, collaborative and flexible models of care can reach this group.
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Lee, MinJae, Mohammad H. Rahbar, and Hooshang Talebi. "A nonparametric method for assessment of interactions in a median regression model for analyzing right censored data." Statistical Methods in Medical Research 28, no. 4 (January 9, 2018): 1170–87. http://dx.doi.org/10.1177/0962280217751518.
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We propose a nonparametric test for interactions when we are concerned with investigation of the simultaneous effects of two or more factors in a median regression model with right censored survival data. Our approach is developed to detect interaction in special situations, when the covariates have a finite number of levels with a limited number of observations in each level, and it allows varying levels of variance and censorship at different levels of the covariates. Through simulation studies, we compare the power of detecting an interaction between the study group variable and a covariate using our proposed procedure with that of the Cox Proportional Hazard (PH) model and censored quantile regression model. We also assess the impact of censoring rate and type on the standard error of the estimators of parameters. Finally, we illustrate application of our proposed method to real life data from Prospective Observational Multicenter Major Trauma Transfusion (PROMMTT) study to test an interaction effect between type of injury and study sites using median time for a trauma patient to receive three units of red blood cells. The results from simulation studies indicate that our procedure performs better than both Cox PH model and censored quantile regression model based on statistical power for detecting the interaction, especially when the number of observations is small. It is also relatively less sensitive to censoring rates or even the presence of conditionally independent censoring that is conditional on the levels of covariates.
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Nwakuya, Nwakuya, M. T, and Onyegbuchulam B. O. "Quantile Regression-based Multiple Imputation of Skewed Data with Different Percentages of Missingness." Scholars Journal of Physics, Mathematics and Statistics 9, no. 4 (May 10, 2022): 41–45. http://dx.doi.org/10.36347/sjpms.2022.v09i04.002.
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This study investigates the Quantile Regression-Based Multiple Imputation (QR-based MI) on a simulated right skewed data with 5% and 25% missing data points. Quantile regression analysis on three data sets that comprises of the complete skewed data without missing values, data set with 5% missing values and data set with 25% missing values was performed at 0.25, 0.5, 0.75 and 0.95 quantiles. The data sets with 5% and 25% missing values were imputed using QR-based MI technique, giving rise to two complete data sets. This analysis was performed using both transformed and untransformed version of the three data sets. The transformation was carried out by applying the Yeo-Johnson transformation technique and comparison of results was based on the Mean Square Error (MSE), Akiake Information Criteria (AIC) and Bayesian Information Criteria (BIC). The result from the original complete right skewed data shows that the untransformed data presented better results at 0.25 and 0.50 quantiles compared to the transformed data while results at 0.75 and 0.95 quantiles of the transformed data showed a better result compared to the untransformed. This result is attributed to the fact that the data was right skewed, so that the transformation will benefit the heavy tails on the right while the lighter tail on the left needs not to be transformed hence the 0.25 and 0.50 quantile better result with untransformed data and the 0.75 and 0.95 better result with transformed data. Considering the imputed complete data sets from the 5% and 25% missingness, it was seen that for both data sets at all quantiles considered, the untransformed data produced better results than the transformed data. This led us to conclude that the QR-based MI is not distribution dependent hence it is not sensitive to skewness. Therefore it can be stated based on the results that QR-based MI is robust to skewness, thus can be applied to skewed data sets.
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Qian, Zhonghua, Luyao Wang, Xin Chen, Hui Zhang, and Zimeng Li. "Heteroscedastic Characteristics of Precipitation with Climate Changes in China." Atmosphere 13, no. 12 (December 16, 2022): 2116. http://dx.doi.org/10.3390/atmos13122116.
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With global warming, previous studies have found nonuniformity responses of precipitation because of regional differences. However, climate change affects the mean, extreme, and data structure of precipitation. Quantile regression, which can reflect every part of the trends of data, was used to detect responses of each part of precipitation in China. The V2.0 dataset of daily precipitation grid data (0.5° × 0.5°) from 1961 to 2020 in China was used as practical observation data. Daily precipitation in 2015–2100 from the China Model BCC-CSM2-MR of scenarios SSP2-4.5 and SSP5-8.5 were chosen as future climate changes with moderate and high radiative forcing, respectively. On the basis of the sign consistency of the slope coefficients with quantile regression, the results of quantiles q = 0.3, 0.5, 0.7 and 0.9 were selected to represent low, median, high and flood precipitation, respectively. Precipitation in four seasons was separately analyzed to observe seasonal characteristics in China. For the observation data, precipitation had obviously different responses in the low and high percentiles and was present in mainly spring and summer. In spring, in the middle and lower Yangtze Plains, the low and median precipitation increased, whereas the high and flood precipitation significantly decreased. In summer, Heilongjiang Province and northern Inner Mongolia showed decreasing trends in the low quantile and increasing trends in the high quantile, indicating a completely opposite trend adjustment. These regions deserve more attention. However, obviously different responses in low and high percentiles were not so evident in future climate changes. Self-consistency in model data may weaken the heteroscedastic characteristics of precipitation.
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Shahsavarinia, Kavous, Hassan Soleimanpour, Sepideh Harzand Jadidi, Mohammad Saadati, Aida Javanmardi, and Gilani Neda. "Determinants of Hospital Length of Stay among Burn Patients Using Quantile Regression." Depiction of Health 12, no. 3 (February 13, 2021): 262–72. http://dx.doi.org/10.34172/doh.2021.26.
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Background and Objectives Burns is one of the most common and potentially dangerous public health problems. Burn patients' hospitalization facilitates the provision of medical services. However, prolonging the length of hospital stay can not only impose an economic cost, but also cause various infections in patients. Various factors affect patients’ hospitalization length including patients age and gender, burn cause, anatomic place and its severity. Identifying and considering these factors will reduce burn patient’s hospitalization and its consequences. The aim of this study was to evaluate the factors affecting hospitalization length in burn patients admitted to Sina Hospital as burn referral hospital in Northwest of Iran. Material and Methods In this cross-sectional study, the medical records of burn patients who were admitted to Sina Hospital in Tabriz during 2018, were included. Data collection was performed using a goal-based researcher data collection form. The form included patient’s demographics (age, gende, marital status, education level, occupation, comorbidity) and Status of vital signs at admission including respiratory rate, heart rate, body temperature, Glasgow Coma Scale score (less than 12 moderate injuries, 13 and 14 mild injuries, 15 or more normal) and systolic and diastolic blood pressure, burn place, date, cause, TBSA, burn severity, length of stay and outcome. Data were analyzed using Stata 16 software and through quantile regression modeling. Data normality was evaluated using Kolmogorov-Smirnov test, skewness and kurtosis. Due to the skewness of the hospitalization variable distribution (hospitalization length was a non-negative variable with right skew and skewness coefficient of 4.72 and kurtosis coefficient equal to 6.53), to obtain a complete picture of how the conditioned distribution of the response variable changes from variables Independently, Quantile regression was used for modeling with a significance level of P <0.05. Results The total number of hospitalized burn patients was 1586 of whom 998 (62.3%) were male. The mean age of the patients was 25.5 ± 22.9 years. Most of the patients were in age-group 0-5 years. About 22.3% of patients were in Tachypnea situation and 33.3% had low blood pressure. Based on Glasgow score, 0.3% of patients were with moderate and 2.2% with low injury. Only 15.4% of patients were with more than 20% burn in their body. Burn degree III was the most prevalent injury (35.1%). Upper limbs (62.9%) were the most anatomic sections injured in burn. Totally 94 patients (5.9%) were died due to burn injuries. Burns occurred more often in summer (30.5%) and at home (n=1246, 78.6%). The median length of hospitalization was 8 days (95% CI: 7.34-8.57). Single (P = 0.010) and illiterate patients (P = 0.022) had a longer hospitalization length. The lower the Glasgow coma score at admission, resulted in longer hospital stay (P = 0.034). Patients with burn on face (P = 0.037), head and neck (P <0.001) and back of the trunk (P = 0.031) had longer hospital stay, respectively. The higher the percentage of burns, the longer the hospital stay (P <0.001) and the presence of concurrent trauma also increased the length of hospital stay (P <0.001). Conclusion Glasgow coma score, burns on the face, neck and back were identified as effective clinical signs on hospitalization length of stay amongst burn patients. Considering these factors in the triage of burn patients, providing quality treatment and care services to manage these symptoms can reduce the length of hospital stay and ultimately lead to a reduction in social and economic costs for patients and society. Extended Abstract Background and Objectives Burns is one of the most common and potentially dangerous public health problems. Burn patients' hospitalization facilitates the provision of medical services. However, prolonging the length of hospital stay can not only impose an economic cost, but also cause various infections in patients. Various factors affect patients’ hospitalization length including patients age and gender, burn cause, anatomic place and its severity. Identifying and considering these factors will reduce burn patient’s hospitalization and its consequences. The aim of this study was to evaluate the factors affecting hospitalization length in burn patients admitted to Sina Hospital as burn referral hospital in Northwest of Iran. Material and Methods In this cross-sectional study, the medical records of burn patients who were admitted to Sina Hospital in Tabriz during 2018, were included. Data collection was performed using a goal-based researcher data collection form. The form included patient’s demographics (age, gende, marital status, education level, occupation, comorbidity) and Status of vital signs at admission including respiratory rate, heart rate, body temperature, Glasgow Coma Scale score (less than 12 moderate injuries, 13 and 14 mild injuries, 15 or more normal) and systolic and diastolic blood pressure, burn place, date, cause, TBSA, burn severity, length of stay and outcome. Data were analyzed using Stata 16 software and through quantile regression modeling. Data normality was evaluated using Kolmogorov-Smirnov test, skewness and kurtosis. Due to the skewness of the hospitalization variable distribution (hospitalization length was a non-negative variable with right skew and skewness coefficient of 4.72 and kurtosis coefficient equal to 6.53), to obtain a complete picture of how the conditioned distribution of the response variable changes from variables Independently, Quantile regression was used for modeling with a significance level of P <0.05. Results The total number of hospitalized burn patients was 1586 of whom 998 (62.3%) were male. The mean age of the patients was 25.5 ± 22.9 years. Most of the patients were in age-group 0-5 years. About 22.3% of patients were in Tachypnea situation and 33.3% had low blood pressure.Based on Glasgow score, 0.3% of patients were with moderate and 2.2% with low injury. Only 15.4% of patients were with more than 20% burn in their body. Burn degree III was the most prevalent injury (35.1%). Upper limbs (62.9%) were the most anatomic sections injured in burn. Totally 94 patients (5.9%) were died due to burn injuries.Burns occurred more often in summer (30.5%) and at home (n=1246, 78.6%). The median length of hospitalization was 8 days (95% CI: 7.34-8.57). Single (P = 0.010) and illiterate patients (P = 0.022) had a longer hospitalization length. The lower the Glasgow coma score at admission, resulted in longer hospital stay (P = 0.034). Patients with burn on face (P = 0.037), head and neck (P <0.001) and back of the trunk (P = 0.031) had longer hospital stay, respectively. The higher the percentage of burns, the longer the hospital stay (P <0.001) and the presence of concurrent trauma also increased the length of hospital stay (P <0.001). Conclusion Glasgow coma score, burns on the face, neck and back were identified as effective clinical signs on hospitalization length of stay amongst burn patients. Considering these factors in the triage of burn patients, providing quality treatment and care services to manage these symptoms can reduce the length of hospital stay and ultimately lead to a reduction in social and economic costs for patients and society. Practical implications of research Paying attention to the effective symptoms during the stay of burn patients during triage of these patients and providing quality treatment and care services to manage these symptoms can reduce the length of hospital stay and ultimately lead to a reduction in its social and economic costs. For patients and the community. Ethical considerations This research was carried out after the approval of the Ethics Committee of the Vice Chancellor for Research of Tabriz Azad University of Medical Sciences, as a dissertation for general medicine. Data related to patients with burn injuries admitted to Sina Hospital in 1397 were coded in the form of data registration without name and information. Also, all patient information was kept completely confidential and the information obtained from the study was used for research purposes only. Conflict of interest The authors state that there is no conflict of interest in publishing this article. Acknowledgement The present article is taken from the dissertation of General Doctor of Medicine. The authors consider it necessary to express their gratitude to the Vice Chancellor for Research and Technology of Tabriz Azad University of Medical Sciences and the director of Sina Hospital and the people participating in the research.
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Sousa, Kleber Morais de, and Paulo Aguiar do Monte. "Public expenditure composition and fiscal decentralization in Brazilian local governments: an analysis through unconditional quantile regression with longitudinal data." Revista de Administração Pública 55, no. 6 (December 2021): 1333–54. http://dx.doi.org/10.1590/0034-761220200864.
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Abstract This paper investigates the effect of increasing fiscal decentralization on the composition of public expenditures of Brazilian local governments. The research is innovative, demonstrating that the heterogeneity of expenditure scale influences the correlation between fiscal decentralization and public expenditure of local governments. The sample consisted of unbalanced panel data of 5,565 municipalities for 17 years from 2000 to 2016. The analysis used unconditional quantile regression with panel data. The main findings were: (i) fiscal decentralization affects public expenditure in Brazilian local governments. However, this effect depends on local expenditure scale and fiscal decentralization strategy. For example, the median coefficient was negative in personnel expenditures, and the effect was positive for the third quartile of local governments, when fiscal decentralization was measured by the tax revenue over total revenue. On the other hand, the effects were also positive for median and third quartile regarding intergovernmental transfers per capita like proxy of fiscal decentralization; (ii) the measures (proxies) of fiscal decentralization are correlated with the composition of public expenditure; (iii) in median terms, fiscal decentralization has greater effects on investment expenditures than on current and personnel expenditures; and (iv) in median terms, the tax revenue participation promotes an increase in administrative and planning expenditures instead of expenditures in social functions. Fiscal decentralization measured by intergovernmental transfer per capita has more positive effects on social functions than on legislative and administrative functions.
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Noor, Farhana, Orpita U. Laz, Khaled Haddad, Mohammad A. Alim, and Ataur Rahman. "Comparison between Quantile Regression Technique and Generalised Additive Model for Regional Flood Frequency Analysis: A Case Study for Victoria, Australia." Water 14, no. 22 (November 11, 2022): 3627. http://dx.doi.org/10.3390/w14223627.
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For design flood estimation in ungauged catchments, Regional Flood Frequency Analysis (RFFA) is commonly used. Most of the RFFA methods are primarily based on linear modelling approaches, which do not account for the inherent nonlinearity of rainfall-runoff processes. Using data from 114 catchments in Victoria, Australia, this study employs the Generalised Additive Model (GAM) in RFFA and compares the results with linear method known as Quantile Regression Technique (QRT). The GAM model performance is found to be better for smaller return periods (i.e., 2, 5 and 10 years) with a median relative error ranging 16–41%. For higher return periods (i.e., 20, 50 and 100 years), log-log linear regression model (QRT) outperforms the GAM model with a median relative error ranging 31–59%.
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Khan, Kiren S., Jessica Logan, Laura M. Justice, Ryan P. Bowles, and Shayne B. Piasta. "The Contribution of Vocabulary, Grammar, and Phonological Awareness Across a Continuum of Narrative Ability Levels in Young Children." Journal of Speech, Language, and Hearing Research 64, no. 9 (September 14, 2021): 3489–503. http://dx.doi.org/10.1044/2021_jslhr-20-00403.
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Purpose Narrative skill represents a higher-level linguistic skill that shows incremental development in the preschool years. During these years, there are considerable individual differences in this skill, with some children being highly skilled narrators (i.e., precocious) relative to peers of their age. In this study, we explored the contribution of three lower-level language skills to a range of narrative abilities, from children performing below expected levels for their age to those performing much higher than the expected levels for their age. We speculated that individual differences in lower-level skills would contribute meaningfully to variability in narrative skills. Method Using a sample of 336 children between 3 and 6 years of age ( M = 4.27 years, SD = 0.65), both multiple regression and quantile regression approaches were used to explore how vocabulary, grammar, and phonological awareness account for variance in children's “narrative ability index” (NAI), an index of how children scored on the Narrative Assessment Protocol–Second Edition relative to the expected performance for their age. Results Multiple regression results indicated that lower-level language skills explained a significant amount of variance (approximately 13%) in children's NAI scores. Quantile regression results indicated that phonological awareness and vocabulary accounted for significant variance in children's NAI scores at lower quantiles. At the median quantile, vocabulary and grammar accounted for significant variance in children's NAI scores. For precocious narrators, only vocabulary accounted for a significant amount of variance in children's NAI scores. Conclusion Results indicate that lower-level language skills work in conjunction to support narrative skills at different ability levels, improving understanding of how lower-level language skills contribute across a spectrum of higher-level linguistic abilities.
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Shrivastava, Shreya, Vandana Patil, Madhavi Shelke, Madhura Anvikar, Aditya Mathur, and Ashish Pathak. "Assessment of school readiness of children and factors associated with risk of inadequate school readiness in Ujjain, India: an observational study." BMJ Paediatrics Open 3, no. 1 (August 2019): e000509. http://dx.doi.org/10.1136/bmjpo-2019-000509.
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ObjectiveSchool readiness is a condition or state indicating that the child is ready to learn in a formal educational set-up. The objective of this study was to estimate the prevalence of and factors associated with school readiness in urban schoolchildren in Ujjain, India.MethodsThis cross-sectional study was conducted from February 2016 to March 2017. Two English-medium schools were conveniently selected. All children aged 5–7 years were eligible to participate. A subscale of Differential Ability Scales-Second Edition, namely ‘school readiness scale’, was used to assess school readiness in three major domains—early number concept, matching letter-like forms and phonological processing. Data on factors associated with school readiness were collected through parent interview. Quantile regression analysis was used to explore school readiness scores.ResultsThis study included 203 school-going children (105 boys and 98 girls) having a mean (SD) age of 67.7 (±0.51) months. The phonological processing and matching letter-like forms had 31.5% and 30.5% children, respectively, in lower quantiles (≤25th). The higher quantile (≥75th) scores were achieved for phonological processing and early number concept (47.7% and 44.8% children, respectively). The results of quantile regression showed negative association of school readiness scores with age of children, lower socioeconomic status and hospitalisation status, especially in the lower quantiles (≤25th). The 10th, 50th and 75th quantile scores were positively correlated with the increasing education status of the mother. Birth weight was positively associated with the median and higher quantile scores (≥75th).ConclusionsSchool readiness in a middle-class urban setting in India was negatively associated with lower age of the child, lower socioeconomic status, hospitalisation and positively correlated with increasing birth weight and maternal education. Lower quantile scores were achieved in matching letter-like forms, which measures complex visual–spatial processing, and phonological ability, which correlates with acquired verbal concepts. Focused interventions are needed to improve these skills.
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Xu, Xiaocang, and Linhong Chen. "Projection of Long-Term Care Costs in China, 2020–2050: Based on the Bayesian Quantile Regression Method." Sustainability 11, no. 13 (June 27, 2019): 3530. http://dx.doi.org/10.3390/su11133530.
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The aging population in China highlights the significance of elderly long-term care (LTC) services. The number of people aged 65 and above increased from 96 million in 2003 to 150 million in 2016, some of whom were disabled due to chronic diseases or the natural effects of aging on bodily functions. Therefore, the measurement of future LTC costs is of crucial value. Following the basic framework but using different empirical methods from those presented in previous literature, this paper attempts to use the Bayesian quantile regression (BQR) method, which has many advantages over traditional linear regression. Another innovation consists of setting and measuring the high, middle, and low levels of LTC cost prediction for each disability state among the elderly in 2020–2050. Our projections suggest that by 2020, LTC costs will increase to median values of 39.46, 8.98, and 20.25 billion dollars for mild, moderate, and severe disabilities, respectively; these numbers will reach 141.7, 32.28, and 72.78 billion dollars by 2050. The median level of daily life care for mild, moderate, and severe disabilities will increase to 26.23, 6.36, and 27 billion dollars. Our results showed that future LTC cost increases will be enormous, and therefore, the establishment of a reasonable individual-social-government payment mechanism is necessary for the LTC system. The future design of an LTCI system must take into account a variety of factors, including the future elderly population, different care conditions, the financial burden of the government, etc., in order to maintain the sustainable development of the LTC system.
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Cherdantsev, D. V., A. V. Stroev, E. S. Mangalova, N. V. Kononova, and O. V. Chubarova. "The use of ridge regression for estimating the severity of acute pancreatitis." Bulletin of Siberian Medicine 18, no. 3 (October 27, 2019): 107–15. http://dx.doi.org/10.20538/1682-0363-2019-3-107-115.
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Purpose. Increasing of treatment efficiency for patients with acute pancreatitis by improving objective means of determining the severity of acute pancreatitis.Materials and method. The study was based on a retrospective analysis of 130 cases of acute pancreatitis: 47 cases from «Krasnoyarsk Regional Clinical Hospital» and 83 cases from «Regional Interdistrict Clinical Hospital No 20 named after I.S. Berzon» in the period from 2015 to 2017. The raw data was pre-processed. In particular, different methods (median, linear regression) were used to fill the missing values in the observation matrix. The initial dataset contained features measured in various quantitative and categorical scales. For some features with a pronounced asymmetric distribution, a quantile transformation was applied to initial values. The quantile transformation allows features to be brought to a uniform distribution in order to reduce the risk of excluding significant features. Ridge regression was used in combination with an algorithm for sequential reduction of attribute space.Results. The classifier of three degrees of acute pancreatitis severity was developed. This classifier can help to determine better treatment tactics. During validation, the method of determining the severity of acute pancreatitis classification has proven to be effective. The average accuracy was 92% compared to the experts’ decisions. This procedure for constructing a classifier can be used as part of the basis to the medical decision support system.Conclusion. The results of this study will help to make the choice of a necessary starting therapy, assess the need for surgical intervention and in severe cases, prescribe enhanced antibacterial and detoxification therapy. This will predictably reduce the percentage of septic complications of acute pancreatitis, and consequently will reduce the frequency of fatal outcomes.
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Tobechukwu, Nwakuya Maureen. "Quantile Generalized Additive Model a Robust Alternative to Generalized Additive Model." International Journal of Mathematical Research 10, no. 1 (December 27, 2021): 12–18. http://dx.doi.org/10.18488/journal.24.2021.101.12.18.
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Nonparametric regression is an approach used when the structure of the relationship between the response and the predictor variable is unknown. It tries to estimate the structure of this relationship since there is no predetermined form. The generalized additive model (GAM) and quantile generalized additive (QGAM) model provides an attractive framework for nonparametric regression. The QGAM focuses on the features of the response beyond the central tendency, while the GAM focuses on the mean response. The analysis was done using gam and qgam packages in R, using data set on live-births, fertility-rate and birth-rate, where, live-birth is the response with fertility-rate and birth-rate as the predictors. The spline basis function was used while selecting the smoothing parameter by marginal loss minimization technique. The result shows that the basis dimension used was sufficient. The QGAM results show the effect of the smooth functions on the response variable at 25th, 50th, 75th and 95th quantiles, while the GAM showed only the effect of the predictors on the mean response. The results also reveal that the QGAM have lower Akaike information criterion (AIC) and Generalized cross-validation (GVC) than the GAM, hence producing a better model. It was also observed that the QGAM and the GAM at the 50th quantile had the same R2adj(77%), meaning that both models were able to explain the same percentage of variation in the models, this we attribute to the fact that mean regression and median regression are approximately the same, hence the observation is in agreement with existing literature. The plots reveal that some of the residuals of the GAM were seen to fall outside the confidence band while in QGAM all the residuals fell within the confidence band producing a better smooth.
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Peng, Limin, Joanne Wuu, and Michael Benatar. "Developing reference data for nerve conduction studies: An application of quantile regression." Muscle & Nerve 40, no. 5 (October 13, 2009): 763–71. http://dx.doi.org/10.1002/mus.21489.
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