The effects of downstream clustering in longitudinal studies

Many experimental designs in educational and behavioral research involve at least one level of clustering. Clustering affects the precision of estimators and its impact on statistics in cross-sectional studies is well known. Clustering also occurs in longitudinal designs where students that are initially grouped may be regrouped in the following year and regrouped again in subsequent years. The purpose of this article is to explore the clustering effects of multiple waves of grouping on the effect sizes of downstream outcomes; that is, outcomes that are measured after one or more waves of regrouping. We center our framework on the longitudinal cluster randomized trial in which treatments are initially assigned by clusters (such as classrooms) and students are then regrouped into different clusters in subsequent years. This article illustrates how information on the intraclass correlations in longitudinal studies can be used to correct for biases in the effect sizes and variances, and how it can also be used to adjust the significance test for the effects of longitudinal clustering. This article also provides the first empirical evidence of the magnitude of longitudinal clustering effects using data from a state longitudinal data system.