Generalized Regression Modeling of Ordinal and Bounded Response Data

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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.