Estimating item and ability parameters in homogeneous tests with the person characteristic function

Abstract

On the basis of monte carlo runs, in which item response data were generated for a variety of test characteristics, procedures for estimating item and ability parameters for homogeneous, unidimensional tests are developed on the assumption that values of the slope parameter a and the guessing parameter c are constant over items. The procedures focus on estimates of the a parameter, regarded as an important statistic for characterizing an ability. This parameter is estimated from person characteristic functions for different levels of the total raw score distribution. The procedures can be applied to datasets with relatively small or very large Ns and with either relatively small or large numbers of items. They are illustrated with data from several cognitive ability tests. Index terms: cognitive ability tests, homogeneous tests, item parameter estimation, item response theory, person characteristic function.