| The latent growth curve model with piecewise functions is a useful analytics tool to investigate the growth trajectory consisted of distinct phases of development in observed variables. An interesting feature of the growth trajectory is the time point that the trajectory changes from one phase to another one. In this thesis, we propose a simple computational pipeline to locate the change point under the linear-linear piecewise model and apply it to the longitudinal study of reading and math ability in early childhood (from kindergarten to eighth grade). In the first step, we conduct the hypothesis testing to filter out the samples that do not exhibit a change point. For samples with significant change point, we use the maximum likelihood estimation(MLE) to determine the location of a change point. However, a small portion of samples contains abnormal observations, which makes the MLE method fail to identify the change point. To overcome this difficulty, we apply a Bayesian approach to locate the change point for these samples. By comparison of the change point distributions in math and reading, as well as students with different overall performance, we conclude that: (a) most students have change points between Spring-first grade and Spring-third grade; (b) students with overall better performance have change point at earlier stage; (c) compared with math, the change point distribution for reading is more concentrated between Spring-first grade and Spring-third grade. |
