Chapter 9: Individual Growth Curve Models for Longitudinal data

This chapter introduces individual growth curve modeling within a multilevel framework and provides an overview of three of the simplest and most commonly used individual growth models: the linear growth model, the piecewise linear growth model, and the polynomial growth model. We include an applied example using NLSY97 data (U.S. Bureau of Labor Statistics, 2019) on frequency of alcohol consumption from ages 18 to 25 to illustrate the development and interpretation of individual growth models within a multilevel modeling framework.

Research questions about growth (or decline)¹ implicitly involve the measurement of systematic change over time. How does the outcome variable of interest change across time? Does it systematically increase or systematically decrease across time? Is the rate of growth steady or does the growth rate change over time? Do people grow in the same way or is there variability between people in their rates of change? What predicts inter-individual differences in rates of change? Individual growth curve models allow us to answer such questions. Conceptually, individual growth models allow for a separate growth trajectory for each person in the sample, thereby acknowledging that participants start at different levels and change at different rates.