An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data

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 estimates, 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 generated 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 comparison purposes. Relative to the nature of the unidimensional estimates, it was found that the [circumflex a] value seemed best considered as the average of the true a values. The [circumflex b] value seemed best thought of as an overestimate of the true b[subscript 1] values. The [circumflex theta] value seemed best considered as the average of the true ability parameters. Although there was a consistent trend for these relationships to strengthen as the ability dimensions became more highly correlated, there was always a substantial disparity between the magnitudes of these values and of those derived from the unidimensional data. Sample size and test length had very little effect on these relationships.