Bayesian Growth Curve Modeling with Measurement Error in Time

Growth curve modeling has been widely used in many disciplines to understand the trajectories of growth. Two popular forms utilized in the real-world analyses are the linear and quadratic growth curve models. These models operate on the assumption that measurements are conducted exactly at pre-set time or intervals. In essence, the reliability of these models is deeply tied to the punctuality and consistency of the data collection process. However, in real-world data collection, this assumption is often violated. Deviations from the ideal measurement schedule often emerge, resulting in measurement error in time and consequent biased responses. Our simulation findings indicate that such error can skew estimations, especially in quadratic GCM. To account for the measurement error in time, we introduce a Bayesian growth curve model to accommodate the error in the individual time values. We demonstrate the performance of the proposed approach through simulation studies. Furthermore, to illustrate its application in practice, we provide a real-data example, underscoring the practical benefits of the proposed model.