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I am preparing a correlational meta-analysis. Some studies in my sample provide multiple effect sizes based on various different measures for the predictor, the criterion variable, or both. To avoid that I over- or underestimate the precision of the final estimate, I wanted to model both within-study variance and between-study variance. Therefore, I entered several effect sizes for study 1 and several effect sizes for further studies.

Here is a sample of my data:

> study<-c(1,1,1,2,3,3)
> number<-c(1:6)
> yi<-c(.12,.18,.05,.14,.19,.24)
> vi<-c(.0005,.0005,.0005,.0012,.0009,.0008)
> example<-data.frame(study, number, yi,vi)
> head(example)
 study number yi vi
1 1 1 0.12 0.0005
2 1 2 0.18 0.0005
3 1 3 0.05 0.0005
4 2 4 0.14 0.0012
5 3 5 0.19 0.0009
6 3 6 0.24 0.0008

I followed recommendations outlined here to fit a three-level meta-analysis: http://www.metafor-project.org/doku.php/analyses:konstantopoulos2011

> res.mv <- rma.mv(yi, vi, random = ~ factor(number) | study, data=example)
> print(res.mv, digits=3)

Multivariate Meta-Analysis Model (k = 6; method: REML)

Variance Components: 

outer factor: study (nlvls = 3)
inner factor: factor(number) (nlvls = 6)

 estim sqrt fixed
tau^2 0.004 0.064 no
rho 0.384 no

Test for Heterogeneity: 
Q(df = 5) = 35.299, p-val < .001

Model Results:

estimate se zval pval ci.lb ci.ub 
 0.156 0.034 4.608 <.001 0.090 0.222 ***

---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

However, I later found out that the model used above assumes that the sampling errors of the effect size estimates are independent, which is obviously not the case here, as multiple estimates are obtained from the same group of people. Is there anything I can do to account for this dependency in the model?