When ability or psychological traits are measured repeatedly over time, the item-level data can be analyzed by combining a linear growth curve model for the latent trait with an item response model for the relationship between items and traits. The linear growth model includes a random intercept, to allow for variability in the traits at the initial time point, and a random slope, to allow for variability in the rate of change. Such models usually assume that the responses to different items and at different occasions are conditionally independent, given the latent traits. Here we relax this local independence assumption by allowing the response to an item to depend directly on the previous response to the same item. We discuss a method for handling what's known as the "initial conditions problem" in the econometric literature. The power of the test for local dependence is investigated and the model is applied to longitudinal data on Korean students' self esteem.

Sophia Rabe-Hesketh博士，加州大学伯克利分校教育学院教授。1988年于伦敦大学国王学院获得物理学学士学位，1992年于伦敦大学国王学院获得理论物理（统计图像分析）博士学位。研究领域是：统计与心理测量学。个人网址：http://gse.berkeley.edu/people/sophia-rabe-hesketh