Nonlinear Latent Growth Curve Models

The representation and measurement of change is a fundamental concern to practically all scientific disciplines. The researcher interested in demonstrating change in behavior over time must consider longitudinal studies. The models presented in this work, Latent Growth Curve Models, represented a proper technique emerged within Structural Equation Modeling to analyze longitudinal data. They not only describe a single individual developmental trajectory, but also captures individual differences in these trajectories over time have been developed. The simplest latent growth curve model involves one variable measured the same way at two time points. However, two points in time are not ideal for studying development or for using growth curve methodology: two-wave designs are appropriate only if the intervening growth process is considered irrelevant or is known to be linear. With more than two time occasions the validity of the straight-line growth model for the trajectory can be evaluated, and the precision of parameter estimates will tend to increase. For these reasons, this work will cover models for at least three-wave data, and in addition it will focus on nonlinear LCM.