Stability and change in longitudinal water-level task performance.

Three longitudinal samples of children (N = 481), 8 to 16 years old, were assessed 3 times at yearly intervals on 8 water-level items. The within-child change in task performance over age is viewed as a stochastic process of the child changing or remaining in 1 of 3 latent (strategy) states: (a) bottom-parallel responders, (b) random responders, or (c) accurate responders. A random-effects binomial mixture distribution is used to model performance at each age. Change over age is gauged by a stochastic transition model. Although there was improvement in task performance over age, the more general finding is that strategy stability, not change, is most typical.