# [R-meta] Random effects structure

César Terrer ce@@r@terrer @end|ng |rom me@com
Wed Mar 25 15:33:48 CET 2020

```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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