Progress in Characterizing Strictly Unidimensional IRT Representations
Final rept. Apr-Sep 1990,
ILLINOIS UNIV AT URBANA DEPT OF STATISTICS
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Item response theory, IRT, is a modern attempt to model-and statistically analyze-examinee responses on standardized achievement or aptitude tests. IRT modeling and analysis, which occurs at the level of individual test questions-item-is greatly facilitated by the assumption of unidimensionality, i. e. that the latent trait driving the item responses is a one-dimensional, typically real-valued, random variable. Birnbaum 1968 and Lord 1980 provide complete accounts of traditional unidimensional IRT. In this paper we are concerned with general characterization of the distributions of item response data for which traditional unidimensional IRT representations exist. For our purposes, a test is simply a vector of J items, or equivalently J binary 01 item response variables representing the correctness of responses of a randomly- chosen examinee to the J test items.
- Statistics and Probability