[R-meta] Negative r value for effect sizes within studies

[James Pustejovsky]

To add to Wolfgang's comments, yes it is possible in principle. However, on
a practical level, it seems like it would be a very odd situation where you
would include two outcomes in the same meta-analysis that are *negatively*
correlated with each other. Say that one intervention study reports a
negative effect size estimate for depression and a positive effect size for
positive affect, two outcomes which are negatively correlated. It would not
make much practical sense to average the negative ES for depression and the
positive ES for positive affect together, which suggests that it would be
very odd to include both in a single meta-analysis.

On Fri, Sep 3, 2021 at 12:09 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Stefanou,
>
> Would be unusual, but in principle, yes, it can. However, only certain
> values of r are actually possible. Let's say there is a study with 5
> estimates and you assume r = -0.6. Then the correlation matrix for this
> study would be:
>
> v <- matrix(-.6, 5, 5); diag(v) <- 1
>
> which is not positive definite, which we can see by examining its
> eigenvalues:
>
> round(eigen(v)$values, 4)
>
> (note the last eigenvalue is negative). The largest negative correlation
> possible when p=5 (to get at least a positive semi-definite matrix) is
> -0.25:
>
> v <- matrix(-.25, 5, 5); diag(v) <- 1
> round(eigen(v)$values, 4)
>
> (the last eigenvalue is now essentially 0).
>
> More generally, the lower bound is:
>
> -1/(p-1)
>
> So, you need to determine which study has the largest number of estimates
> and based on that, you know what the lower bound for r is (at least, when
> we assume that the correlation matrix is compound symmetric - as above).
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of Stefanou Revesz
> >Sent: Friday, 03 September, 2021 18:47
> >To: R meta
> >Subject: [R-meta] Negative r value for effect sizes within studies
> >
> >Dear All,
> >
> >This may be too basic to ask. But can the r value chosen to represent
> >the common correlation among effect sizes within studies be a negative
> >one?
> >
> >For example, is there a situation where I would need to use the following?
> >
> >impute_covariance_matrix(..., r = -.6)
> >
> >Thank you,
> >Stefanou
>
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