[R-meta] Random effects structure

[James Pustejovsky]

Hi Cesar,

Just to follow up on Wolfgang's comments (which I concur with, surprising
nobody). Based on the example data structure that you sent, it looks like
there might be a further source of dependence in your effect sizes. In site
B, you have experiments 9 and 11 labelled as "Andesite1controlWeek1" and "
Andesite1controlWeek6." Are these truly independent samples, or are these
the same organisms measured over time? If it is the latter, then there will
again be dependence in the sampling errors due to repeated measurement of
the same units.

Regardless, a good reference for Wolfgang's suggestion and on the more
complicated case with dependence do to repeated measurements is Lajeunesse
(2011): https://doi.org/10.1890/11-0423.1

James

On Wed, Mar 25, 2020 at 9:44 AM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Hi Cesar,
>
> When the same group is used to compute multiple estimates (i.e., a common
> control), then this also induces dependency on the sampling errors. For the
> log response ratio, the covariance is then:
>
> SD_C^2 / (n_C*M_C^2)
>
> where M_C and SD_C are the mean and SD of the common control group and n_C
> the control group size.
>
> So, you ideally should construct a proper V matrix that includes these
> covariances and that you can then pass to rma.mv().
>
> But yes, random=~1|Site/exp/obs would be sensible.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of César Terrer
> Sent: Wednesday, 25 March, 2020 15:34
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] Random effects structure
>
> Dear community,
>
> I am conducting a meta-analysis to study the growth rate of bacterial
> predators as compared to their prey, using the log response ratio.
> Furthermore, I want to study if this effect varies across different
> predators. The dataset has the following structure, here showing a subset:
>
> Site  CommonControl  exp   obs   Predator lnR   var
> A  Alaska  155 1  1  Bdello   -0.6713152  0.03785708
> A  Alaska  155 1  2  Cytoph   -0.0702467  0.05763364
> A  Alaska  155 1  3  Myxo  -0.148982   0.00748768
> A  Alaska  1510   2  4  Bdello   -0.4926361  0.01691187
> A  Alaska  1510   2  5  Cytoph   -0.213787   0.01045785
> B  Andesite1controlWeek1   9  6  Bdello   0.27873598  0.14129722
> B  Andesite1controlWeek1   9  7  Cytoph   -0.3243682  0.01466085
> B  Andesite1controlWeek1   9  8  Lyso  1.18302506  0.11663149
> B  Andesite1controlWeek6   11 9  Bdello   -0.8465128  0.03701618
> B  Andesite1controlWeek6   11 10 Cytoph   -0.1559056  0.0283173
> B  Andesite1controlWeek6   11 11 Lyso  -0.8039415  0.04926915
>
> 1. There are different sites, thus a potential source of non-independency
> 2. Within each site, we use the value for preys in the denominator
> multiple times. I guess rows of data using the same denominator
> (CommonControl) are also potentially correlated and should be also added as
> a random-effect.
>
> Based on 1., 2., and what I have understood from the Konstantopoulos
> (2011) tutorial, I think I should use the following model:
>
> res <-rma.mv(yi=lnR, V=var, random=~1|Site/exp/obs, mods=~Predator,
> data=data)
>
> Could you please let me know if the structure of random effects seems
> appropriate, and help me understand why I need to include "obs"?
> Thank you.
> Cesar
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