Analysis of Three Approaches to Testing the Dimensionality of Binary Ability Items and Suggestions for Application.
Technical rept. no. 2, Jan 86-May 87,
ILLINOIS UNIV AT URBANA DEPT OF PSYCHOLOGY
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A Monte Carlo investigation of three approaches to the detection of multidimensionality in binary ability times is reported. One approach is based on the property of local independence in a unidimensional scale, a second on the expected configuration of second factor loadings of a perfect Guttman scale, and the third on the shape of the curve of successive Eigenvalues. One hundred samples of both individuals and items from a population model were obtained for 3 levels of sample size, 5 numbers of items, 3 distributions of item difficulties, an 3 levels of factor obliqueness for one through five factors. Indices derived from the principle of local independence are generally most accurate, but they also require a computer program that is not generally available. The program is, however, relatively simple. Under many combinations of parameters indices based on the pattern of second factor loadings are highly accurate and can be computed at ones desk. Indices based on the shape of the curve of successive Eigenvalues, on the other hand, are least accurate. Any variation of th root staring criterion of dimensionality appears to be highly fallible. Within the limits of this investigation indices based on the property of local independence increase monotonically in accuracy as sample size and number of multiple factors increases from two to five, as distributions of item difficulties vary from narrow to wide, and as the obliqueness of multiple factors increases from low to high.
- Statistics and Probability