[R-meta] Random effects structure

[Viechtbauer, Wolfgang (SP)]

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