Item Response Models for Partially Ordered Data

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The project will develop advanced analytic tools for analyzing multiple partially orderedresponses. While partially ordered set (poset) data are prevalent in many branches of the social and behavioral sciences, their presence has been under-reported and their importance underrecognized. A simple example is response categories Agree, Neutral, Disagree, and Don't Know, of which the first three can be ordered and the last forms a category of its own. The project will build upon previous work in poset and extend the methods to multiple poset responses. The methods will be extensions of models based on the item response theory (IRT). Specifically, the project will adapt the graded, nominal, and sequential response IRT models - tools that are able to handle multiple responses and mixed-response types - for partially ordered responses. Simulation studies will be used to establish the validity of the methodology.Very few analytic methods exist for analyzing data in which some of the information is ordered and some is not. Because of the lack of analytic tools, this broad class of data types is often unnecessarily being "forced" into other data types - e.g., through summarization or artificially collapsing response categories - so they can be analyzed by existing ordinal or nominal data methods. Subtle and potentially important information is often lost through such data reduction. While this problem was recognized more than two decades ago as having a negative impact on the development of theory for psychological and educational measurement, little progress has actually been made since then. This research will directly address this gap in measurement. Because item response theory (IRT) has been widely used and adopted in various fields - education, social and psychological sciences, health measurement, and business marketing research - the development of methods for analyzing this data type in IRT has the potential to provide more precise measurement tools for researchers and practitioners in a broad range of areas of study.