Delineating the average rate of change in longitudinal models

The average rate of change is a concept that has been misunderstood in the literature. This article attempts to clarify the concept and show unequivocally the mathematical definition and meaning of the average rate of change in longitudinal models. The slope from the straight-line change model has at times been interpreted as if it were always the average rate of change. It is shown, however, that this is generally not the case and holds true in only a limited number of situations. General equations are presented for two measures of discrepancy when the slope from the straight-line change model is used to estimate the average rate of change. The importance of fitting an appropriate individual change model is discussed, as are the benefits provided by models nonlinear in their parameters for longitudinal data. An empirical data set is used to illustrate the analytic developments.