Some properties of the correlation matrix of dichotomous guttman items |
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Authors: | Rebecca Zwick |
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Institution: | (1) Educational Testing Service, 08541 Princeton, NJ |
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Abstract: | Both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous Guttman-scalable items can be expressed as simple functions of the number of items if the score distribution is uniform and there is an equal number of items at each difficulty level. Even when these special conditions do not hold, the correlations can often be expressed in a simple form by assuming a particular score distribution.The author thanks Neil Dorans, Bob Mislevy, Ledyard R Tucker, and Howard Wainer for their comments. |
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Keywords: | Guttman scales perfect scales dichotomous items difficulty factors factor analysis component analysis |
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