Final answer:
Vincent is conducting a longitudinal research study, observing the same subjects over different points in their lives to examine changes in their eating behavior.
Step-by-step explanation:
Vincent is using a longitudinal research design in his study. Longitudinal research involves gathering data from the same subjects over an extended period of time to observe changes and developments. In contrast, a cross-sectional study would compare different segments of the population at a single point in time, rather than following the same individuals as they age. Therefore, the study Vincent is conducting, where he observes the eating behavior of the same group of children at different ages (five years old, 12, and early 20s), perfectly aligns with the definition of longitudinal research design.