Item response theory preequating depends upon item parameter estimate invariance. The impact of differences in true ability on the invariance properties of item parameter estimates was studied with simulated data. Using real SAT-mathematical data that had produced unsatisfactory preequating results to suggest hypotheses, three explanatory models were investigated: 1) differences in mean true ability, 2) a certain type of multidimensionality, and 3) a combination of differences in mean true ability and multidimensionality. This latter model produced results consistent with the real data. (90pp.)
