ABSTRACT
There is a growing interest in models for situations where repeated measurements over time are made on each of a number of subjects and the nature of differences in individual change characteristics needs to be explained. Some models of this type are deterministic in that expected performance of an individual at a specified time point is determined only by time and certain parameters associated with the individual. Models of this type are nonlinear random coefficient models (e.g., Cudeck & du Toit, 2003) or nonlinear latent curve models (e.g., Browne, 1993). No allowance is made for external influences or shocks that impinge on the change process and alter the direction of the individual change trajectory. Other models are stochastic in that the course of individual trajectories is governed by unpredictable external shocks (Browne & Nesselroade, 2005). This chapter will be concerned with models where an individual change trajectory is composed of a deterministic component and a stochastic component. The deterministic component will not vary between individuals and the differences between individual trajectories will be accounted for by the stochastic component. This model is a further development of the fixed learning curve model with time series deviations, which is one of three models presented by Browne and du Toit (1991). Attention is now given to the estimation of measurement error and to the use of the model in explaining the nature of the change process.
