New Methods for Bayesian Quantile Regression Modeling

本研究项目将为一些分位数回归问题开发灵活的模型和相应的推理和变量选择方法。回归模型探索一些预测变量对响应变量的影响仍然是统计研究中的一项关键活动。通过针对响应变量的不同百分位数，分位数回归为预测因子可能以不同于其中心的方式影响响应分布的尾部的设置提供了传统均值回归的实际重要替代方案。该项目将在复合分位数建模框架内推进统计方法。分位数回归是一个新兴的统计研究领域，具有很大的应用前景。该项目将调查将这些方法应用于经济和社会科学中的几个问题。例如，这些方法将用于研究不同类型的预测因素对高中生不同水平数学成绩的相对重要性。为了方便其他领域的实践者和研究人员使用这些方法，将开发公开可用的软件来实现几个模型。该项目将为研究生创造受教育的机会，并设法增加妇女和代表性不足群体对研究的参与。该研究项目将为复合分位数回归开发一个基于一般模型的框架，以允许根据响应分布的多个百分位数来估计和选择预测器效果。复合分位数回归建模框架涉及分布的结构化混合，这将有助于通过多个响应分位数整合多个预测变量的影响来实现不同的推理目标。复合分位数回归是最近才发展起来的，但尚未在响应分布的概率建模框架下进行研究。该研究项目有一个实质性的分析部分，关于各种分位数回归模型的特性的理论研究，以及一个具有挑战性的计算部分，关于实现计算可处理的模型拟合。在变量选择的背景下，将通过几个模拟研究来研究新方法的实际效用，并与已建立的正则化回归方法进行比较。对于所有模型，该项目将涉及研究相关的理论性质和设计用于推理、模型检查和预测的计算技术。该项目还将探索具有多层数据结构的实际相关设置的分层模型扩展。

This research project will develop flexible models and corresponding methods for inference and variable selection for a number of quantile regression problems. Regression modeling to explore the effect of a number of predictor variables on a response variable remains a key activity in statistical research. By targeting different percentiles of the response variable, quantile regression provides a practically important alternative to traditional mean regression for settings where the predictors may affect the tails of the response distribution in a different fashion than its center. This project will advance statistical methodology within the composite quantile modeling framework. Quantile regression is a burgeoning area of statistical research with great promise for substantive applications. The project will investigate the application of the methods to several problems within the economic and social sciences. The methods will be used, for example, to study the relative importance of different types of predictors on different levels of mathematical achievement for high school students. To facilitate use of the methods by practitioners and researchers from other fields, publicly available software will be developed for implementing several of the models. The project will create educational opportunities for graduate students and seek to increase the participation of women and underrepresented groups in the research.This research project will develop a general model-based framework for composite quantile regression to allow estimation and selection of predictor effects to be informed by multiple percentiles of the response distribution. The composite quantile regression modeling framework involves structured mixtures of distributions that will facilitate different inferential objectives in the integration of effects from several predictor variables through multiple response quantiles. Composite quantile regression is a recent development that has not yet been studied under a probabilistic modeling framework for the response distribution. The research project has a substantial analytic component with regard to the theoretical study of properties for the various quantile regression models as well as a challenging computational component with regard to achieving computationally tractable model fitting. The practical utility of the new methods will be investigated through several simulation studies in the context of variable selection to compare with well-established regularized regression methods. For all the models, the project will involve the study of relevant theoretical properties and design of computational techniques for inference, model checking, and prediction. The project also will explore hierarchical model extensions for practically relevant settings with multilevel data structures.