# [R-meta] Random effects structure

César Terrer ce@@r@terrer @end|ng |rom me@com
Wed Mar 25 19:41:34 CET 2020

```Thanks Wolfgang,

dat\$Site.exp <- as.factor(paste0(dat\$Site,".",dat\$exp))
dat <- dat[order(dat\$Site, dat\$exp),]
calc.v <- function(x) {
v <- matrix(x\$NPSD^2[1] / (x\$NPN[1] * x\$NP[1]^2), nrow=nrow(x), ncol=nrow(x))
diag(v) <- x\$var
v
}
V <- bldiag(lapply(split(dat, dat\$Site.exp), calc.v))
res <-rma.mv(yi=lnR, V, random=~1|Site/exp/obs, mods=~Predator, data=dat)

But I get an error: "'V' must be a symmetric matrix."

The dataset has 297 rows, so V is "num [1:297, 1:297]", which seems symmetric to me. The blocks in V seem to be correct. What do you think is the source of the error?
Cheers,
Cesar

On March 25, 2020 at 10:25 AM, "Viechtbauer, Wolfgang (SP)" <wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

The Berkey code doesn't quite apply here. This is more relevant:

http://www.metafor-project.org/doku.php/analyses:gleser2009#multiple-treatment_studies

But your splitting variable is 'exp' within 'Site', so you need to first create a variable that is the combination of the two. This should do it:

dat\$Site.exp <- paste0(dat\$Site, ".", dat\$exp)

Also make sure that the data are sorted accordingly:

dat <- dat[order(dat\$Site, dat\$exp),]

Then:

calc.v <- function(x) {
v <- matrix(x\$NPSD^2[1] / (x\$NPN[1] * dat\$NP[1]^2), nrow=nrow(x), ncol=nrow(x))
diag(v) <- x\$var
v
}
V <- bldiag(lapply(split(dat, dat\$Site.exp), calc.v))

You should double-check that the blocks in V are correct (with 'var' along the diagonal and the correct covariances along the off-diagonal) before trying to fit the model.

Best,
Wolfgang

-----Original Message-----
From: César Terrer [mailto:cesar.terrer using me.com]
Sent: Wednesday, 25 March, 2020 16:21
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Random effects structure

Hi Wolfgang,

Thank you for your quick response.

I have never constructed a V matrix. Based on the Berkey tutorial, I have tried to apply the following

dat\$v2i <- dat\$NPSD^2 / (dat\$NPN*dat\$NP^2)
V <- bldiag(lapply(split(dat[,c("var", "v2i")], dat\$exp), as.matrix))
res <-rma.mv(yi=lnR, V=V, random=~1|Site/exp/obs, mods=~Predator, data=dat)

But it gives me an error that  'V' must be a square matrix. Is this because the split in V has to be done at the "obs" level? I used "exp" because that indicates the level at which all effect sizes use the same control.

Thank you
Cesar

On March 25, 2020 at 7:44 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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