A comparison of methods for determining dimensionality in Rasch measurement

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Abstract
This study compares the Rasch item fit approach for detecting multidimensionality in response data with principal component analysis without rotation using simulated data. The data in this study were simulated to represent varying degrees of multidimensionality and varying proportions of items representing each dimension. Because the requirement of unidimensionality is necessary to preserve the desirable measurement properties of Rasch models, useful ways of testing this requirement must be developed. The results of the analyses indicate that both the principal component approach and the Rasch item fit approach work in a variety of multidimensional data structures. However, each technique is unable to detect multidimensionality in certain combinations of the level of correlation between the two variables and the proportion of items loading on the two factors. In cases where the intention is to create a unidimensional structure, one would expect few items to load on the second factor and the correlation between the factors to be high. The Rasch item fit approach detects dimensionality more accurately in these situations.

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