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. Author manuscript; available in PMC: 2021 Mar 31.
Published in final edited form as: Stat Methods Med Res. 2020 Jul 6;30(2):612–639. doi: 10.1177/0962280220932962

Table 2.

Illustration of the non-decaying (exchangeable) and decaying within-cluster correlation structure implied by the random-effects model in cross-sectional, closed-cohort, and open-cohort designs.

Nested exchangeable structure Exponential decay structure
Cross-sectional (Section 3.4) graphic file with name nihms-1650457-t0001.jpg graphic file with name nihms-1650457-t0002.jpg
Block exchangeable structure Proportional decay structure
Closed-cohort (Section 3.5) graphic file with name nihms-1650457-t0003.jpg graphic file with name nihms-1650457-t0004.jpg
Blended exchangeable structure Blended correlation decay structure
Open-cohort (Section 3.6) graphic file with name nihms-1650457-t0005.jpg graphic file with name nihms-1650457-t0006.jpg

Note: In each correlation matrix, each block represents the correlation structure in a given cluster-period or between two cluster-periods, and the total number of periods is T = 3. The cluster-period sizes are assumed to be equal (Nij = 2). In the open-cohort design, we assume only one individual is followed through all periods, and a new individual will be supplemented in each period. Each correlation matrix is defined for the vector of observations collected across all periods in the same cluster.