Mathematical Sciences: Modeling and Statistical Analysis of Rank Data and Psychological Test Data

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The first of two distinct parts of this research is the development of statistical models and of procedures for statistical inference for data in the form of rankings or even partial rankings. These models should allow examination of the same kinds of relationships frequently modeled for numerical data; and this research based on orthogonal contrasts may lead to a general framework for the analysis of ranking data. The second part of the research develops further Item Response Theory, appropriate to many standardized multiple item tests used to measure ability and performance. In particular, this research will provide a rigorous mathematical framework for focussing on a multidimensional Item Response Theory, on bias detection procedures, and on more fundamental issues in probabilistic models for response.