Growth rate modeling techniques for longitudinal data

Generally, at least two features are needed to characterize a growth process fully at any time point: the level of growth and the rate of growth. The level of growth represents the current status of a process at a given time point and can be viewed as a static measure of that process. The rate of growth represents how fast the level of the process is changing at that time point and can be viewed as a dynamic measure of the process. The widely used growth curve models usually focus on the analysis of the level of growth. However, techniques for analysis of rates of growth are still relatively rare. Because of the significance of rates of growth in understanding dynamic processes, a stronger and more versatile approach is proposed to model them by constructing growth rate models. The concepts of growth processes and current analytical techniques are first reviewed and both the simple rate of growth and the compound rate of growth are defined. Then, different models are developed to analyze rates of growth. Growth rate models are constructed to analyze simple rates of growth and random coefficient models are developed to analyze compound rates of growth. The proposed models are applied to analyze an empirical data set---the National Longitudinal Study of Youth (NLSY)---consisting of children's mathematics performance data and covariates of gender and behavioral problems (BPI).;Individual differences are found in both simple and compound rates of growth. BPI and gender have different relationship with simple rates of growth at different ages. BPI is also found to be negatively related to compound rates of growth. Finally, a systematic simulation study is conducted to validate the results from the analysis of the NLSY data and to investigate the performance of two main models, the quadratic growth rate model and the random coefficient latent difference score model. The simulation results support the validity of the results from the empirical data analysis. It is further found that the parameter estimates for both models are unbiased and the standard error estimates are consistent.