[R-meta] multilevel meta-analysis using metafor

[Viechtbauer Wolfgang (SP)]

You can specify arbitrary weights in rma.mv() via the 'W' argument (to be precise, one can specify an entire weight matrix, but if one just specifies a vector, then the weight matrix is assumed to be diagonal). 

Alternatively, if I am not mistaken, the robumeta package (https://cran.r-project.org/package=robumeta) provides an implementation of the cluster-robust approach along the lines of Hedges, Tipton, and Johnson (2010). So you might want to use that package.

Best,
Wolfgang

-----Original Message-----
From: brauldeq [mailto:brauldeq at hu-berlin.de] 
Sent: Monday, 11 September, 2017 14:32
To: Viechtbauer Wolfgang (SP)
Cc: r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] multilevel meta-analysis using metafor

I am really sorry for the ongoing confusion on my part. But is there a 
way to use weights corresponding to equation 13 or 17 from Hedges, 
Tipton & Johnson (2010; see 
http://onlinelibrary.wiley.com/doi/10.1002/jrsm.5/abstract) or to assign 
equal weight to correlated within-study effect sizes?
I would like to avoid assigning more total weight to studies with a 
larger number of (dependent) effect sizes than studies with fewer (or 
only one) effect sizes.

Thanks a lot.

Best regards,
Denise

Am 06.09.2017 18:33, schrieb Viechtbauer Wolfgang (SP):
> As I just mentioned in another post, in models with more complex
> random effects structures, there are not just weights, but an entire
> weight matrix. For example, in the model you fitted below, the
> marginal var-cov matrix is block diagonal with vi + sigma^2_sample_nr
> + sigma^2_effect_nr along the diagonal and sigma^2_sample_nr for off
> diagonal elements that correspond to the same level of that factor.
> The weight matrix is then the inverse of that marginal var-cov matrix.
> If the sampling errors had been independent, then this would be the
> 'best' weight matrix (in the sense of giving you the most efficient
> estimates of the fixed effects and giving you appropriate estimates of
> the standard errors) and there would then be no need for any further
> adjustments, manually or statistically.
> 
> In your case, the sampling errors are correlated, but you are fitting
> the model with V=vi, that is, assuming a diagonal V matrix. That will
> lead to less efficient but still unbiased estimates of the fixed
> effects, but invalid estimates of the standard errors, and hence the
> need for using robust(model, cluster=data$sample_nr). But this doesn't
> actually change the weight matrix; it only affects the way the var-cov
> matrix of the fixed effects is computed and hence the computation of
> the standard errors. So, also here there is no need to manually adjust
> any weights.
> 
> And yes, *all else equal*, studies with more effect sizes are weighted
> more than studies with less effect sizes. Let me put this in a
> different way: A study providing more evidence about the phenomenon
> under investigation is getting more weight than a study providing less
> evidence. That seems pretty sensible to me.
> 
> Best,
> Wolfgang