[R-meta] Questions about multilevel meta-analysis structure

[Isaac Calvin Saywell]

Hello all,

I am conducting a multilevel meta-analysis, trying to compare effect sizes across 9 different cognitive domains (using cognitive domain as a categorical moderator). In my dataset some studies provide effect sizes for multiple cognitive domains (dependent effects), some provide only one effect size per cognitive domain, and not all studies contain effect sizes for all cognitive domains of interest. I have four questions:

1. Is my model correctly structured to account for dependency using the inner | outer formula (see MODEL 1 CODE below) or should I just specify random effects at the study and unique effect size level (see MODEL 2 CODE below).

# MODEL 1 CODE

## res <- rma.mv(vi,
                        V,
                        mods = ~ cog_domain,
                        random = list(~ cog_domain | study_id, ~ 1 | effectsize_id),
                        struct = "UN",
                        tdist = TRUE,
                        method = "REML",
                        data = dat)

# MODEL 2 CODE

## res <- rma.mv(vi,
                        V,
                        mods = ~ cog_domain,
                        random = list(~ 1 | study_id, ~ 1 | effectsize_id),# removed inner | outer formula
                        struct = "UN",
                        tdist = TRUE,
                        method = "REML",
                        data = dat)

2. If I do need to specify an inner | outer formula to compare effect sizes across cognitive domains, then is an unstructured variance-covariance matrix ("UN") most appropriate (allowing tau^2 to differ among cognitive domains) or should another structure be specified?

3. To account for effect size dependency is a variance-covariance matrix necessary (this is what my model currently uses) or is it ok to use sampling variance of each in the multilevel model.

4. When subsetting my data by one cognitive domain and investigating this same cognitive domain in a univariate multilevel model the effect estimate tends to be lower compared to when all cognitive domains are included in a single multilevel model as a moderator, is there a reason for this?

Help with any of these questions would be greatly appreciated.

Kind regards,
Isaac

University of Adelaide, Australia
Cognitive Neural Sciences Lab

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