Cognitive Diagnosis with Multinomial Response Distributions

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The purpose of this study is to extend the capabilities of cognitively diagnostic adaptive testing to incorporate multiple response outcomes. The cognitively diagnostic adaptive testing methodology of interest employs underlying cognitive models that are finite partially ordered sets (posets). Main research objectives include understanding how to incorporate misconception and erroneous response information into cognitive poset models, establishing techniques for identifying erroneous responses that are both cognitively and statistically interesting, and extending a data-analytic framework for model fitting and analysis of items to the case when items have more than two different class conditional response distributions. Having the means to validate implementation of the methodology through data analysis is critically important, as the underlying cognitive processes are complex and latent. Markov Chain Monte Carlo estimation techniques will be employed. Cognitively diagnostic adaptive testing can form the basis of `intelligent` tutoring systems. Incorporating multinomial responses should allow such systems to utilize response information more fully, provide enhanced cognitive information about students, and perhaps even classify students with fewer number of items. Cognitively diagnostic adaptive testing can be viewed as an important statistical tool for cognitive measurement. Implementation involves building focused cognitive models, which gives insight into the processes of problem-solving. The resulting methods of this research will be applied to actual data from a linguistics domain.