[R-meta] quick question about covariances

[James Pustejovsky]

For a reference on the covariance of ROMs with a common control condition,
see:

Lajeunesse, M. J. (2011). On the meta-analysis of response ratios for
studies with correlated and multi-group designs. Ecology, 92, 2049–2055.

I would recommend sticking with vtype = "LS". It strikes me as a bit goofy
to use vtype = "HO" with ROMs because the types of measures for which ROMs
are useful are exactly those where the variance depends on the mean level.
If anything, it seems like it would be better to assume homogeneity of
*dispersion* rather than homogeneity of variance, such that Var(Y) /
[E(Y)]^2 is constant across conditions. In that case, the variance of the
ROM would be

V = Dp * (1 / nc + 1 / ne),

where

Dp = (nc * sdc^2 / mc^2 + ne * sde^2 / me^2) / (nc + ne)

is the pooled variance ratio. If you do this, then the covariance between
two ROMs that share a common control condition would be simply

Cov = Dp / nc.



On Fri, Nov 16, 2018 at 10:30 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> See below for my responses.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
> >project.org] On Behalf Of Andrew Guerin
> >Sent: Friday, 16 November, 2018 17:13
> >To: r-sig-meta-analysis using r-project.org
> >Subject: [R-meta] quick question about covariances
> >
> >Hi, I am running an analysis in which I need to generate a variance-
> >covariance matrix for data with shared controls ('multiple treatments
> >dependence').
> >I have done this before with standardised mean differences, raw mean
> >differences, and lnVR - calculating the covariances using formulas on the
> >metafor website and graciously provided by James Pustejovsky.
> >
> >This time my effect size data are log mean ratios / response ratios, and
> >I was hoping someone could check my logic.
> >
> >Given that the sampling variance for the effect size  - obtained using
> >escalc(measure="ROM", vtype="LS"...) - seems to be based on the formula
> >(from Hedges 1999)
> >
> >v = (sdc ^ 2  / (nc * mc ^ 2)) + (sde ^ 2  / (ne * me ^ 2))
> >
> >sdc, nc , mc  are sd, n and mean for the control treatment
> >sde, ne, me are the same for the experimental samples
> >
> >then does it follow that the covariance for samples which share the same
> >control will simply be
> >
> >Cov = sdc ^ 2  / (nc * mc ^ 2) ?
>
> Correct.
>
> >Out of curiosity, if I were to use vtype="HO" instead, where the formula
> >for the sampling variance is
> >
> >v =  (sdp ^ 2)   *    (1  / (nc * mc ^ 2)) + (1  / (ne * me ^ 2))
> >
> >sdp = pooled standard deviation.
> >
> >Then presumably it is more complicated to calculate the covariance since
> >sdp is already calculated using nc, sdc, ne, and sde, so would be
> >different for every control-treatment pair.
>
> Yes, this would complicate things.
>
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