A simplex process model of the cross-lagged correlation paradigm was applied to 16 tests administered to samples of black and white males and black and white females in Grades 5, 7, 9, and 11.Listening, a measure of aural comprehension, consistently anticipated individual differences on an intellectual composite in all four groups. The other achievement test of the STEP series anticipated individual differences on the so-called aptitude tests of SCAT, which in turn anticipated individual differences on the narrow information scores obtained from the Test of General Information (TGI). This model may be more powerful in revealing lags than the traditional methods of analyzing cross-lagged differences in longitudinal data. The model does not require stationarity and can produce a meaningful outcome in its absence.tions between true scores of X and Y on separate occasions to be equal to each other, it is neces-APPLIED PSYCHOLOGICAL MEASUREMENT