[R-meta] Difference between univariate and multivariate parameterization

Luke Martinez m@rt|nez|ukerm @end|ng |rom gm@||@com
Wed Aug 18 20:29:41 CEST 2021

Dear Colleagues,

Imagine I have two models.

Model 1:

random = ~1 | study / row_id

Model 2:

random = ~ row_id | study,  struct = "CS"

I understand that the diagonal elements of the variance-covariance matrix
of a study with two effect size estimates for each model will be:

Model 1:

VAR(y_ij) = sigma^2_between  +  sigma^2_within + e_ij

Model 2:

VAR(y_ij) = tau^2 + e_ij

Question: In model 2's variance-covariance matrix, what fills the role of
sigma^2_within (within-study heterogeneity) that exists in model 1's matrix?

Thank you very much for your assistance,
Luke Martinez

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