Growth rate models: emphasizing growth rate analysis through growth curve modeling

To emphasize growth rate analysis, we develop a general method to reparametrize growth curve models to analyze rates of growth for a variety of growth trajectories, such as quadratic and exponential growth. The resulting growth rate models are shown to be related to rotations of growth curves. Estimated conveniently through growth curve modeling techniques, growth rate models have advantages above and beyond traditional growth curve models. The proposed growth rate models are used to analyze longitudinal data from the National Longitudinal Study of Youth (NLSY) on children's mathematics performance scores including covariates of gender and behavioral problems (BPI). Individual differences are found in rates of growth from ages 6 to 11. Associations with BPI, gender, and their interaction to rates of growth are found to vary with age. Implications of the models and the findings are discussed.