Designing Longitudinal Studies of Negative Exponential Growth According to the Reliabilities of Growth Parameter Estimators

Researchers in the social and behavioral sciences frequently depend on linear models when designingand analyzing longitudinal studies. However, when attempting to precisely understand the underlyinggrowth process, nonlinear growth models are typically more useful. The present work focuses on a relatively simple nonlinear growth model, the negative exponential growth model. In particular, a new parameterization of this growth model is proposed to facilitate meaningful interpretation of its parameters. Further, one of the primary goals of the present work is to develop a method that allows researchers to design longitudinal studies according to the population reliabilities of the nonlinear least square estimators of the negative exponential growth parameters. The method that is recommended makes use of Monte Carlo simulation to approximate the population reliabilities in arelatively accurate manner. An illustration of this method is presented and discussed to promotethe design of efficient longitudinal studies of nonlinear growth in the behavioral sciences.