Abstract
In the past decades, the longitudinal approach has been remarkably and increasingly used in the investigations of children's cognitive development. Recently, many researchers have started to realize the importance and necessity of examining measurement invariance for any further longitudinal analysis. However, there are few empirical studies demonstrating how to conduct further analysis when the assumption of measurement invariance of an instrument is violated. The primary purpose of this study is to explore how a newly-developed calibrated projection method can be applied to reduce the impact of lack of parameter invariance in a longitudinal study of preschool children's cognitive development. The sample consisted of 882 children from China who participated in two waves of the cognitive tests when they were 4 and 5 years old. Before this study was conducted, the IRT method was used to examine the measurement invariance of the instrument. The results showed that five items presented difficulty parameter drift and three items presented discrimination/slope parameter drift. In the study, the invariant items were treated as "common items" and calibrated projection linking was used to establish a comparable scale across two time points. Then the linking method was evaluated by three properties: grade-to-grade growth, grade-to-grade variability, and the separation of distributions. The results showed that the grade-to-grade growth across two waves was larger and exhibited a larger effect size; the grade-to-grade variability showed less scale shrinkage, which indicated a smaller measurement error; the separation of distributions showed a larger growth as well.