Binary Quantile Regression Research Articles

Bayesian variable selection and estimation in binary quantile regression using global-local shrinkage priors

In this paper, we construct a Bayesian hierarchical model with global-local shrinkage priors for the regression coefficients, which includes the horseshoe prior and normal-gamma prior. This model is used for high-dimensional quantile regression models with dichotomous response data. We have developed an efficient sampling algorithm to generate posterior samplings for making posterior inference. We use a location-scale mixture representation of the asymmetric Laplace distribution. We assess the performance of the proposed methods through Monte Carlo simulations and two real-data applications in terms of parameter estimation and variable selection. Numerical results demonstrate that the proposed methods perform comparably with existing Bayesian methods under a variety of scenarios.

Bayesian Binary Quantile Regression for Modelling Injectable Contraceptive Uptake Among Child Bearing Women in Kenya

Bayesian Binary Quantile Regression for Modelling Injectable Contraceptive Uptake Among Child Bearing Women in Kenya

Bayesian Binary reciprocal LASSO quantile regression (with practical application)

Quantile regression is one of the methods that has taken a wide space in application in the previous two decades because of the attractive features of these methods to researchers, as it is not affected by outliers values, meaning that it is considered one of the robust methods, and it gives more details of the effect of explanatory variables on the dependent variable.In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Current approaches to variable selection in the context of binary classification are sensitive to outliers, heterogeneous values, and other anomalies. The proposed method in this study overcomes these problems in an attractive and direct way.

Всероссийская олимпиада школьников по экономике во время COVID‐19: что мы видим на данных?

This paper evaluates the change in the contribution of factors to the probability of students’ success at the All‐Russian Olympiad in economics during the COVID‐19 pandemic using classical econometric models and binary quantile regression (BQR). No works were found in the Russian literature where BQR would be applied. However, in our opinion, it has great potential both for studying the effects’ heterogeneity and for solving probability prediction problems. Empirical results show that the contribution of school rating to success at the municipal stage decreased in the 2020/21 season compared to the 2019/20 season. High score at the municipal stage (winner status) became a weaker predictor of success at the regional stage in the 2020/21 season compared to the 2019/20 season. The reason for this change may lie in a decrease in the tasks’ complexity (due to a change in their structure), a higher opportunity for cheating (due to weak and non‐mandatory proctoring) or both.

A novel Bayesian method for variable selection and estimation in binary quantile regression

AbstractIn this paper, we develop a Bayesian hierarchical model and associated computation strategy for simultaneously conducting parameter estimation and variable selection in binary quantile regression. We specify customary asymmetric Laplace distribution on the error term and assign quantile‐dependent priors on the regression coefficients and a binary vector to identify the model configuration. Thanks to the normal‐exponential mixture representation of the asymmetric Laplace distribution, we proceed to develop a novel three‐stage computational scheme starting with an expectation–maximization algorithm and then the Gibbs sampler followed by an importance re‐weighting step to draw nearly independent Markov chain Monte Carlo samples from the full posterior distributions of the unknown parameters. Simulation studies are conducted to compare the performance of the proposed Bayesian method with that of several existing ones in the literature. Finally, two real‐data applications are provided for illustrative purposes.

Deep Quantile Regression for Uncertainty Estimation in Unsupervised and Supervised Lesion Detection

Despite impressive state-of-the-art performance on a wide variety of machine learning tasks in multiple applications, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is particularly important in critical applications such as lesion detection and clinical diagnosis, where a realistic assessment of uncertainty is essential in determining surgical margins, disease status and appropriate treatment. In this work, we propose a novel approach that uses quantile regression for quantifying aleatoric uncertainty in both supervised and unsupervised lesion detection problems. The resulting confidence intervals can be used for lesion detection and segmentation. In the unsupervised settings, we combine quantile regression with the Variational AutoEncoder (VAE). The VAE is trained on lesion-free data, so when presented with an image with a lesion, it tends to reconstruct a lesion-free version of the image. To detect the lesion, we then compare the input (lesion) and output (lesion-free) images. Here we address the problem of quantifying uncertainty in the images that are reconstructed by the VAE as the basis for principled outlier or lesion detection. The VAE models the output as a conditionally independent Gaussian characterized by its mean and variance. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. Here we describe an alternative Quantile-Regression VAE (QR-VAE) that avoids this variance shrinkage problem by directly estimating conditional quantiles for the input image. Using the estimated quantiles, we compute the conditional mean and variance for input image from which we then detect outliers by thresholding at a false-discovery-rate corrected p-value. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. We show how BQR can be used to capture uncertainty in lesion boundaries in a manner that characterizes expert disagreement.

Use of Bayesian, Lasso Binary Quantile Regression to Identify Suitable Habitat for Tiger Prey Species in Thap Lan National Park, Eastern Thailand

A Bayesian approach was used to develop binary quantile regression models featuring the lasso penalty. The models afford the advantages of all quantile regression models, such as robustness and detailed insights into covariate effects; they also handle issues associated with overfitting well. Thus, this model was used to investigate habitat suitability for the management of tiger prey species. Field data were collected from 150 sampling sites (2,416 sub-plots) in Thap Lan National Park of the Dong Phayayen-Khao Yai Forest Complex (DPKY) from August 2019 to March 2021. We focused on sambar deer (Rusa unicolor) and gaur (Bos gaurus) because they are the principal prey species of tigers. Vegetation was sampled for biomass and nutrient content to identify suitable habitat. The “bayesQR” package of R was used to identify habitats appropriate for these species. The correlation between forage crop biomass and the normalized difference vegetation index (NDVI) was significantly associated with tiger prey species presence. The habitat can be improved by increasing grass and forb biomasses as the prey species prefer open habitats, such as grassland and open areas of dry evergreen forest. Habitat management has ensured that the grass biomass of open forest is significantly higher than that of dense forest. In addition, the hemicellulose content of open forest was significantly greater than that of dense forest. We found that spatial modeling combined with Bayesian, lasso binary quantile regression could aid wildlife habitat management in a Thai National Park.

Comparative analysis of Bayesian quantile regression models for pedestrian injury severity at signalized intersections

This study intended to (1) investigate the pedestrian injury severity involved in traffic crashes; and (2) address the heterogeneity issue at signalized intersections. To achieve the objectives, Bayesian binary and ordinal quantile regression models were proposed to address the pedestrian injury severity at signalized intersections. The suitability of the proposed method was illustrated with the Hong Kong dataset from 2008 to 2012 and 376 signalized intersections involving 2090 pedestrian-related crashes are selected. It’s found that age, injury location, pedestrian special circumstance, pedestrian contributory and the presence of Tram/LRT stops and right turning pocket are significant variables. The results indicated that both Bayesian binary and ordinal quantile regression models not only provide a more comprehensive and in-depth understanding of the relationship between pedestrian injury severity and the explanatory variables, but also highlight the heterogeneity issue for the data collected at different locations and different times without many assumptions. The goodness-of-fit of the proposed models outperforms existing mean models, while the Bayesian binary quantile model provides a better fit than the Bayesian quantile regression for ordinal model. The results can benefit the pedestrian facilities improvement/management and guide a much safer pedestrian environment.

Binary quantile regression and variable selection: A new approach

ABSTRACTIn this paper, we propose a new estimation method for binary quantile regression and variable selection which can be implemented by an iteratively reweighted least square approach. In contrast to existing approaches, this method is computationally simple, guaranteed to converge to a unique solution and implemented with standard software packages. We demonstrate our methods using Monte-Carlo experiments and then we apply the proposed method to the widely used work trip mode choice dataset. The results indicate that the proposed estimators work well in finite samples.

BayesQR: A Bayesian Approach to Quantile Regression

After its introduction by Koenker and Basset (1978), quantile regression has become an important and popular tool to investigate the conditional response distribution in regression. The R package bayesQR contains a number of routines to estimate quantile regression parameters using a Bayesian approach based on the asymmetric Laplace distribution. The package contains functions for the typical quantile regression with continuous dependent variable, but also supports quantile regression for binary dependent variables. For both types of dependent variables, an approach to variable selection using the adaptive lasso approach is provided. For the binary quantile regression model, the package also contains a routine that calculates the fitted probabilities for each vector of predictors. In addition, functions for summarizing the results, creating traceplots, posterior histograms and drawing quantile plots are included. This paper starts with a brief overview of the theoretical background of the models used in the bayesQR package. The main part of this paper discusses the computational problems that arise in the implementation of the procedure and illustrates the usefulness of the package through selected examples.

Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition

ABSTRACTThe multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary response.

Bayesian variable selection in binary quantile regression

We propose a simple Bayesian variable selection method in binary quantile regression. Our method computes the Bayes factors of all candidate models simultaneously based on a single set of MCMC samples from a model that encompasses all candidate models. The method deals with multicollinearity problems and variable selection under constraints.

Binary quantile regression with local polynomial smoothing

Manski (1975, 1985) proposed the maximum score estimator for the binary choice model under a weak conditional median restriction that converges at the rate of n−1/3 and the standardized version has a nonstandard distribution. By imposing additional smoothness conditions, Horowitz (1992) proposed a smoothed maximum score estimator that often has large finite sample biases and is quite sensitive to the choice of smoothing parameter. In this paper we propose a novel framework that leads to a local polynomial smoothing based estimator. Our estimator possesses finite sample and asymptotic properties typically associated with the local polynomial regression. In addition, our local polynomial regression-based estimator can be extended to the panel data setting. Simulation results suggest that our estimators may offer significant improvement over the smoothed maximum score estimators.

Bankruptcy predictions for U.S. air carrier operations: a study of financial data

We applied the binary quantile regression, a Bayesian quantile regression, and logit models to identify optimal bankruptcy prediction accuracy for U.S. air carriers for the period from 1990 to 2011. We used accuracy ratio and Brier scores as standards of comparison and a Bayesian binary quantile regression with optimal bankruptcy prediction accuracy for both healthy and bankrupt air carriers. Total assets positively and significantly influenced bankruptcy probability for air carriers. Operational variables consisted of quick assets to expenditures for operation, increase in sales, and working capital to assets; however, these variables negatively and significantly influenced air carriers’ bankruptcy probability.

Enhanced decision support in credit scoring using Bayesian binary quantile regression

Fierce competition as well as the recent financial crisis in financial and banking industries made credit scoring gain importance. An accurate estimation of credit risk helps organizations to decide whether or not to grant credit to potential customers. Many classification methods have been suggested to handle this problem in the literature. This paper proposes a model for evaluating credit risk based on binary quantile regression, using Bayesian estimation. This paper points out the distinct advantages of the latter approach: that is (i) the method provides accurate predictions of which customers may default in the future, (ii) the approach provides detailed insight into the effects of the explanatory variables on the probability of default, and (iii) the methodology is ideally suited to build a segmentation scheme of the customers in terms of risk of default and the corresponding uncertainty about the prediction. An often studied dataset from a German bank is used to show the applicability of the method proposed. The results demonstrate that the methodology can be an important tool for credit companies that want to take the credit risk of their customer fully into account.

Bayesian lasso binary quantile regression

In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Existing approaches to variable selection in a binary classification context are sensitive to outliers, heteroskedasticity or other anomalies of the latent response. The method proposed in this study overcomes these problems in an attractive and straightforward way. A Laplace likelihood and Laplace priors for the regression parameters are proposed and estimated with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A conceptional result is that by doing so, the binary regression model is moved from a Gaussian to a full Laplacian framework without sacrificing much computational efficiency. In addition, an efficient Gibbs sampler to estimate the model parameters is proposed that is superior to the Metropolis algorithm that is used in previous studies on Bayesian binary quantile regression. Both the simulation studies and the real data analysis indicate that the proposed method performs well in comparison to the other methods. Moreover, as the base model is binary quantile regression, a much more detailed insight in the effects of the covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is available in the R-package bayesQR.

Differential evolution trained kernel principal component WNN and kernel binary quantile regression: Application to banking

In this paper, two novel kernel based soft computing techniques viz., Differential Evolution trained Kernel Principal Component Wavelet Neural Network (DE-KPCWNN) and DE trained Kernel Binary Quantile Regression (DE-KBQR) are proposed for classification. While, the former can solve multi-class classification problems, the latter can solve binary classification problems only. In the proposed DE-KPCWNN technique, Kernel Principal Component Analysis (KPCA) is applied to input data to get Kernel Principal Components, on which we will employ WNN. Then, DE is used to train the resulting KPCWNN. In DE-KBQR we applied Kernel technique on the input data to get Kernel Matrix, on which we will employ BQR. Then, DE is used to train the resulting KBQR. Several experiments are conducted on four bankruptcy datasets, three benchmark datasets and two Credit scoring datasets to assess the effectiveness of the proposed classification techniques. The results indicate that the proposed Soft Computing hybrids for classification are efficient than the existing classification techniques. Out of the two, DE-KBQR performed relatively better compared to DE-KPCWNN on a majority of binary classification problems. This is the significant outcome of this study.

Matching using semiparametric propensity scores

This paper considers the application of semiparametric methods to estimate propensity scores or probabilities of program participation, which are central to certain program evaluation methods. To evaluate the practical benefits, we first conduct a Monte Carlo study. Second, we use data from the NSW experiment, CPS, and PSID. We compare treatment effect and evaluation bias estimates using propensity scores estimated from parametric logit, semiparametric single index, and semiparametric binary quantile regression models. Our results suggest that it is important to account for very general forms of heterogeneity in (semiparametric) estimation of the propensity score, particularly when the treatment effects vary in an unsystematic manner with the true propensity score.

An evaluation of leading indicators of currency crises

This study tries to construct leading indicators for currency crisis using probit model, logit model and binary quantile regression. The empirical results show that the Inflation rate, Stock price index, Import growth rate, export/GDP, direct investment abroad, GDP growth rate, terms of trade changes, financial derivatives and domestic credit/GDP have significant effects on the occurrence of currency crisis. The Logit model is better than the probit model and binary regression quantiles which is certain, and the Financial derivatives and Direct investment abroad are useful for leading indicators of currency crises. Key words: Currency crises, binary quantile regression, probit model, logit model.

Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

SUMMARYThis paper develops a Bayesian method for quantile regression for dichotomous response data. The frequentist approach to this type of regression has proven problematic in both optimizing the objective function and making inferences on the parameters. By accepting additional distributional assumptions on the error terms, the Bayesian method proposed sets the problem in a parametric framework in which these problems are avoided. To test the applicability of the method, we ran two Monte Carlo experiments and applied it to Horowitz's (1993) often studied work‐trip mode choice dataset. Compared to previous estimates for the latter dataset, the method proposed leads to a different economic interpretation. Copyright © 2010 John Wiley & Sons, Ltd.