An Examination of the Characteristics of Unidimensional IRT Parameter Estimates Derived From Two-Dimensional Data

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Abstract
The purpose of this investigation was to study the nature of the item and ability estimates obtained when the modified three-parameter logistic model is used with two-dimensional data. To examine the effects of two-dimensional data on unidimensional parameter es timates, the relative potency of the two dimensions was systematically varied by changing the correlations between the two ability dimensions. Data sets based on correlations of .0, .3, .6, .9, and .95 were gener ated for each of four combinations of sample size and test length. Also, for each of these four combinations, five unidimensional data sets were simulated for com parison purposes. Relative to the nature of the unidi mensional estimates, it was found that the â value seemed best considered as the average of the true a values. The b value seemed best thought of as an overestimate of the true b1 values. The θ value seemed best considered as the average of the true ability pa rameters. Although there was a consistent trend for these relationships to strengthen as the ability dimen sions became more highly correlated, there was al ways a substantial disparity between the magnitudes of these values and of those derived from the unidimen sional data. Sample size and test length had very little effect on these relationships.