Generalized Regression Modeling of Ordinal and Bounded Response Data

这项研究旨在发展新的统计方法、推理和理论，用于有序和有界数据的回归建模。最近的工作表明，统一最常用的序数模型并将其扩展到更广泛的模型类别的可能性很大。一个统一的方法将导致全面和灵活的有序回归建模。此外，这一研究方向是为时间和空间相关的有序数据开发改进的方法。有界响应数据在许多应用程序中很常见。本项目的第二部分将扩展一般回归方法和有界响应数据的推断方法。参数和半参数方法将被用来模拟有界响应之间的相关性。现代计算算法，如马尔可夫链蒙特卡罗，为开发相关有序和有界响应数据的软件提供了手段。序数建模在社会科学和医学研究中具有广泛的适用性。此外，序数建模最近已成为环境毒理学和土木工程应用中风险评估的重要工具，在这些应用中，需要对不同严重程度的事件的概率进行建模。有界响应数据在基础设施研究中很常见，这些研究使用有界条件得分，例如0-100分。数据可以随时间(例如，路段的历史)和空间(例如，相邻路段相关)而被关联。正在开发的方法将改进建模和不确定性评估，并将在许多领域得到应用，如环境风险评估、基础设施管理、交通风险建模以及抑郁症和其他社会功能障碍的治疗评估。

Abstract0073044This research aims to develop new statistical methods, inferenceand theory for regression modeling of ordinal and boundeddata. Recent work indicates a strong possiblility of unifying the most commonly used ordinal models and extending them to a broader class of models. A unified approach will lead to comprehensiveand flexible ordinal regression modeling. Further this line ofresearch is directed at developing improved methods fortemporally and spatially correlated ordinal data. Bounded response data are common in many applications. The second part of this project will extend general regression methods and inference methods for bounded response data. Parametric and semi-parametric methodswill be developed to model correlations among bounded responses.Modern computing algorithms such as Markov Chain Monte Carloprovide the means for developing software for correlated ordinaland bounded response data. Ordinal modeling has widespread applicability in the social sciences and medical studies. Moreover ordinal modeling has recently emerged as an important tool for risk assessment in environmental toxicology and in civil engineering applications where the probabilities of events of different severity need to be modeled. Bounded response data are common in infrastructure studies, which use bounded condition scores, e.g., 0-100 scale. The data may be correlated over time (e.g., the history of a road section) and space (e.g., neighboring road sections are correlated). The methods being developed will improve modeling and uncertainty assessments and will have applications in many fields such as environmental risk assessment, infrastructure management, transportation risk modeling and the assessment of treatments for depression and other socialfunctioning disorders.