Completely edited: If a meta-analysis include many studies that reported multiple effect sizes within each study, multi-level meta-analysis is one way to account for this dependency in effect sizes. However, there seems to be two approaches: one that utilize the traditional multilevel models and another that utilize multilevel structural equation modeling (uses metaSEM package; Cheung, 2014)
In regular multi-level modeling, the three levels are:
Level 1- effect size
Level 2- within-study variation
Level 3- between-study variation
However, it’s unclear to me what the three levels are for the multilevel SEM approach. Is it the same? Some papers that used metaSEM and cited Cheung 2014 (e.g., Laboda et al., 2016) describes the three levels as:
Level 1- study participants.
Level 2- effect sizes (within-study variation).
Level 3- study (between-study variation).
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