Studying Between-Subject Differences in Trends and Dynamics: Introducing the Random Coefficients Continuous-Time Latent Curve Model with Structured Residuals

The recently proposed continuous-time latent curve model with structured residuals (CT-LCM-SR) addresses several challenges associated with longitudinal data analysis in the behavioral sciences. First, it provides information about process trends and dynamics. Second, using the continuous-time framework, the CT-LCM-SR can handle unequally spaced measurement occasions and describes processes independently of the length of the time intervals used in a given study. Third, it is a hierarchical model. Thus, multiple subjects can be analyzed simultaneously. However, subjects might also differ in dynamics and trends. Therefore, in the present paper, we extend the CT-LCM-SR to capture these differences as well. This newly proposed random coefficients continuous-time latent curve model with structured residuals (RC-CT-LCM-SR) is introduced theoretically and technically. Additionally, we provide an illustrative example with data from the Health and Retirement Study (HRS), and we show how the RC-CT-LCM-SR can be used to study multiple sources of between-subject differences over time.