• The Korean Journal of Applied Statistics
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• v.29 no.5
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• pp.773-786
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• 2016

Multiple quantile regression that simultaneously estimate several conditional quantiles of response given covariates can provide a comprehensive information about the relationship between the response and covariates. Some quantile estimates can cross if conditional quantiles are separately estimated; however, this violates the definition of the quantile. To tackle this issue, multiple quantile regression with non-crossing constraints have been developed. In this paper, we carry out a comparison study on several popular methods for non-crossing multiple linear quantile regression to provide practical guidance on its application.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1319-1325
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• 2010

Quantile regression provides a more complete statistical analysis of the stochastic relationships among random variables. Sometimes quantile functions estimated at different orders can cross each other. We propose a new non-crossing quantile regression method applying support vector median regression to restricted regression quantile, restricted support vector quantile regression. The proposed method provides a satisfying solution to estimating non-crossing quantile functions when multiple quantiles for high dimensional data are needed. We also present the model selection method that employs cross validation techniques for choosing the parameters which aect the performance of the proposed method. One real example and a simulated example are provided to show the usefulness of the proposed method.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.293-301
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• 2012

Quantile regression proposed by Koenker and Bassett (1978) is a statistical technique that estimates conditional quantiles. The advantage of using quantile regression is the robustness in response to large outliers compared to ordinary least squares(OLS) regression. A regression tree approach has been applied to OLS problems to fit flexible models. Loh (2002) proposed the GUIDE algorithm that has a negligible selection bias and relatively low computational cost. Quantile regression can be regarded as an analogue of OLS, therefore it can also be applied to GUIDE regression tree method. Chaudhuri and Loh (2002) proposed a nonparametric quantile regression method that blends key features of piecewise polynomial quantile regression and tree-structured regression based on adaptive recursive partitioning. Lee and Lee (2006) investigated wage determinants in the Korean labor market using the Korean Labor and Income Panel Study(KLIPS). Following Lee and Lee, we fit three kinds of quantile regression tree models to KLIPS data with respect to the quantiles, 0.05, 0.2, 0.5, 0.8, and 0.95. Among the three models, multiple linear piecewise quantile regression model forms the shortest tree structure, while the piecewise constant quantile regression model has a deeper tree structure with more terminal nodes in general. Age, gender, marriage status, and education seem to be the determinants of the wage level throughout the quantiles; in addition, education experience appears as the important determinant of the wage level in the highly paid group.

• The Korean Journal of Applied Statistics
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• v.26 no.6
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• pp.915-922
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• 2013

Quantile regression can estimate multiple conditional quantile functions of the response, and as a result, it provide comprehensive information of the relationship between the response and the predictors. However, when estimating several conditional quantile functions separately, two or more estimated quantile functions may cross or overlap and consequently violate the basic properties of quantiles. In this paper, we propose a new stepwise method to estimate multiple non-crossing quantile functions using constraints on the kernel coefficients. A simulation study are presented to demonstrate satisfactory performance of the proposed method.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.31-38
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• 2002

In the case of multiple survival times which might be censored at each covariate vector, we study the regression quantile estimations in this paper. The estimations are based on the empirical distribution functions of the censored times and the sample quantiles of the observed survival times at each covariate vector and the weighted least square method is applied for the estimation of the regression quantile. The estimators are shown to be asymptotically normally distributed under some regularity conditions.

• The Korean Journal of Applied Statistics
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• v.33 no.6
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• pp.753-762
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• 2020

With an increasing interest in integrating artificial intelligence (AI) into interview processes, the Republic of Korea (ROK) army is trying to lead and analyze AI-powered interview platform. This study is to analyze the AI interview data using a unified non-crossing multiple quantile tree (UNQRT) model. Compared to the UNQRT, the existing models, such as quantile regression and quantile regression tree model (QRT), are inadequate for the analysis of AI interview data. Specially, the linearity assumption of the quantile regression is overly strong for the aforementioned application. While the QRT model seems to be applicable by relaxing the linearity assumption, it suffers from crossing problems among estimated quantile functions and leads to an uninterpretable model. The UNQRT circumvents the crossing problem of quantile functions by simultaneously estimating multiple quantile functions with a non-crossing constraint and is robust from extreme quantiles. Furthermore, the single tree construction from the UNQRT leads to an interpretable model compared to the QRT model. In this study, by using the UNQRT, we explored the relationship between the results of the Army AI interview system and the existing personnel data to derive meaningful results.

• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.341-350
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• 2012

Composite quantile regression model is considered for iid error case. Since the regression coefficients are the same across different quantiles, composite quantile regression can be used to combine the strength across multiple quantile regression models. For the composite quantile regression, bootstrap method is examined for statistical inference including the selection of the number of quantiles and confidence intervals for the regression coefficients. Feasibility of the bootstrap method is demonstrated through a simulation study.

• Journal of Preventive Medicine and Public Health
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• v.54 no.2
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• pp.145-152
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• 2021

Objectives: This study aimed to identify regional differences in the high-risk drinking rate among yearly alcohol users in Korea and to identify relevant regional factors for each quintile using quantile regression. Methods: Data from 227 counties surveyed by the 2017 Korean Community Health Survey (KCHS) were analyzed. The analysis dataset included secondary data extracted from the Korean Statistical Information Service and data from the KCHS. To identify regional factors related to the high-risk drinking rate among yearly alcohol users, quantile regression was conducted by dividing the data into 10%, 30%, 50%, 70%, and 90% quantiles, and multiple linear regression was also performed. Results: The current smoking rate, perceived stress rate, crude divorce rate, and financial independence rate, as well as one's social network, were related to the high-risk drinking rate among yearly alcohol users. The quantile regression revealed that the perceived stress rate was related to all quantiles except for the 90% quantile, and the financial independence rate was related to the 50% to 90% quantiles. The crude divorce rate was related to the high-risk drinking rate among yearly alcohol users in all quantiles. Conclusions: The findings of this study suggest that local health programs for high-risk drinking are needed in areas with high local stress and high crude divorce rates.

• Journal of dental hygiene science
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• v.19 no.4
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• pp.271-278
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• 2019

Background: This study aimed to examine the factors that influence clinical performance of dental hygiene students to provide useful data for developing strategies to improve clinical competence. Methods: The effects of variables on clinical competence by quantile level were analyzed using quantile regression analysis in 247 dental hygiene students. Quantile regression and multiple regression analyses were conducted using the Stata 11.0 program to analyze predictors of clinical competence. Results: The clinical competence score of dental hygiene students was 42.69±5.90, the satisfaction of clinical practice was 49.90±7.44, the clinical practice stress was 50.62±7.37, and the professional self-concept was 31.68±4.41. Empathy was the highest at 50.87±4.93. Multiple regression analysis showed that school year, stress from clinical training, satisfaction with clinical training, professional self-concept, and empathy had significant impact on clinical competence. Quantile regression analysis showed that the effects varied depending on the clinical competence level. School year and professional self-concept had a significant positive effect, regardless of the clinical competence level, while empathy had a significant positive effect at the top 10% (Q90) of the clinical competence level. Satisfaction with clinical practice affected clinical competence at Q25, Q50, and Q90. Stress from clinical practice had significant effects at Q25, Q50, and Q90 (p<0.05). Conclusion: According to the study results, different factors affected clinical competence according to the quantile of clinical competence. This study provides valuable implications for designing clinical competence enhancement programs and strategies. In addition, objective indicators for considering factors that may affect the clinical competence, such as academic competence and satisfaction of practice hospitals, are expected to require detailed analysis and measures.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.533-545
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• 2017

Quantile regression models provide a variety of useful statistical information by estimating the conditional quantile function of the response variable. However, the traditional linear quantile regression model can lead to the distorted and incorrect results when analysing real data having a nonlinear relationship between the explanatory variables and the response variables. Furthermore, as the complexity of the data increases, it is required to analyse multiple response variables simultaneously with more sophisticated interpretations. For such reasons, we propose a multivariate quantile regression tree model. In this paper, a new split variable selection algorithm is suggested for a multivariate regression tree model. This algorithm can select the split variable more accurately than the previous method without significant selection bias. We investigate the performance of our proposed method with both simulation and real data studies.