[R-meta] complex data structure for meta-analysis

[Yogev Kivity]

Dear Prof. Viechtbauer

I am running a meta-analysis using 'metafor'. I would first like to thank
you for the excellent package along with the very detailed and illustrative
tutorials. I came across several questions that I could not find answers
for in 'metafor's documentation, and I was wondering whether it would be ok
to ask you for your opinion.

In short, were are examining psychotherapy data, and how a specific measure
collected at the beginning of treatment (attachment style in relationships)
predicts outcome of therapy as measured at post-treatment. Both measures
are usually dimensional, so we are using Pearson's r which we then convert
to Fisher's z.

The design of the meta-analysis is multilevel and multivariate in that each
study usually includes several different treatment arms, as well as several
subscales of attachment (e.g., level of anxiety in attachment and level of
avoidance in attachment) and several measures of outcome at post-treatment
(e.g., anxiety, depression etc.). This is complicated by the fact that
studies rarely use the same attachment and outcome measures, and for the
most part, we do not have data on the covariance among these measures.

I am assuming that our design is most similar to Konstantopoulos (2011),
but we have an additional level of effect sizes repeated withing groups, so
basically we have multiple effect size per treatment arm, nested within
treatment arm, which in are turn nested within study.

My main questions are:
1. what would be the best approach for modeling all of these levels of
analyses, while taking into account the fact that the effect sizes within
treatment arm are likely no independent. Usually, multivariate is
interpreted to mean multiple outcome measures, but in our case we have
multiple outcome as well as multiple predictors.

2. How should I squared be calculated for such models?

3. is there an extension of funnel plots to multi-level models that could
reliably represent the data? I guess that using the standard funnel plot
ignores the mutilevel structure of the data, is that correct?

Best,
Yogev

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