[R-meta] Multivariate meta-analysis with unknown covariances?

[schlegei]

for my master thesis, I want to conduct a multivariate meta-analysis 
with the R-package metafor.
Unfortunately, I‘m not sure if it is possible to conduct this analysis 
based on my data set.

To illustrate my problem, a few words about my research question: I 
investigate the efficacy of gestalt therapy (a psychotherapeutic 
approach) for people with a mental disorder according to DSM-IV/ICD-10 
(my focus is on symptom reduction). My literature research resulted in 
12 randomized controlled trials (RCTs).
 From this 12 studies, I extracted 28 outcomes and calculated the effect 
sizes and variances (standardized mean differences). I assume outcomes 
from the same study are dependent. Unfortunately, in no study 
correlations/covariances between the sampling errors of the outcomes are 
reported. So the within study covariance structure is totally missing.
Because I included studies about people with different mental disorders, 
my outcomes are pretty heterogeneous: Only one questionnaire (Beck‘s 
Depression Inventory) was used in 4 studies, apart from that the 
outcomes don‘t overlap between the studies.

Summed up, my data set consists of the following variables:
ES_ID = idenfification number for every effect size (I have 28 effect 
sizes)
study = every study gets one number (I included 12 studies)
outcome = every questionnaire/outcome gets one letter (I included 24 
different outcomes)
yi = effect size
vi = variance of the effect size

Is it possible to conduct a multivariate meta-analysis based on this 
data set?

My supervisor told me, the missing within study covariances can be 
easily estimated with the R-package metafor. Up until now, I do not 
understand how. Following the discussions on stackexchange and this 
mailing list (e.g. 
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2015q2/023727.html), 
it seems to me that estimating the whole covariance structure is not 
that easy and is attended by some disadvantages/assumptions . This also 
coincides with other articles I have read about multivariate 
meta-analysis and in which missing covariances are described as a major 
problem. When I contacted my supervisor, he just told me that the 
literature I read is out-dated and repeated that the problem of missing 
covariances can be solved with metafor (unfortunately, he didn‘t 
recommend up-to-date articles to me).

Right now, I feel a bit locked in a stalemate. Is there a simple, 
up-to-date solution for my problem with the missing covariances that I 
have overseen?
If yes: I would be extremely happy about any tip!
If no: Do you think, it makes sense to conduct a multivariate 
meta-analysis based on my data set or is it more appropriate to choose 
one effect size per study (univariate meta-analysis)? If it is possible 
to conduct a multivariate meta-analysis based on my data: Is there a 
strategy – like making a rough guess of the correlations or using robust 
methods – that you would recommend?

I would be really happy to hear a response,
Isabel Schlegel