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Abstract


Likelihood Ratio Approach for Identifying Hierarchical Attribute Structure

When attributes are hierarchically structured, modifying the Q-matrix or prior distribution in the estimation process yields more accurate and precise item and person parameter estimates. Modification of the prior distribution and the Q-matrix depend on the assumed hierarchical structure, as such, identifying the correct hierarchical structure is of the essence. To address the subjectivity in the conventional methods for attribute structure identification (i.e., expert opinions via content analysis and verbal data analyses such as interviews and think-aloud protocols), this study proposes a likelihood-ratio test based exhaustive empirical search for identifying hierarchical structures. It further suggests a likelihood-ratio approach for selection of the most accurate hierarchical structure when multiple candidates are present. Results show that the likelihood ratio test based exhaustive search yields an R-matrix that specifies all the prerequisite relationships among all attributes. Thus, the method is promising and can be used for exploratory purposes in attribute hierarchy identification.



Keywords
CDM, attribute hierarchy, likelihood ratio, hierarchy identification



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