# [R-meta] Differences in calculation of CVR in escalc()

Samuel Knapp samuel.knapp at tum.de
Mon Oct 9 14:12:26 CEST 2017

```Dear all,

I am conducting a meta-analysis on the stability of crop yields. I now
follow the approach suggeted by Nakagawa et al. (2015) approach and its
implementation in the metafor package, which helps me a lot!

As I first step I compared the estimates of the escalc function for ROM,
VR and CVR to the actual formulas (actually I used the functions in the
supplement of Nakagawa). Fortunately, they all yielded the same
estimates, except for the variance estimate of CVR. I did the
calculations on the gibson example data. The respective code (only for
CVR) is:

data <- get(data(dat.gibson2002))

metadat <- escalc(measure="CVR", m1i=m1i, m2i=m2i, sd1i=sd1i, sd2i=sd2i,
n1i=n1i, n2i=n2i, data=data)

# functions from Nakagawa et al. (2015)
Calc.lnCVR<-function(CMean, CSD, CN, EMean, ESD, EN){
ES<-log(ESD) - log(EMean) + 1 / (2*(EN - 1)) - (log(CSD) - log(CMean)
+ 1 / (2*(CN - 1)))
return(ES)
}
Calc.var.lnCVR<-function(CMean, CSD, CN, EMean, ESD, EN, Equal.E.C.Corr=T){
if(Equal.E.C.Corr==T){
mvcorr<-cor.test(log(c(CMean, EMean)), log(c(CSD, ESD)))\$estimate
S2<- CSD^2 / (CN * (CMean^2)) + 1 / (2 * (CN - 1)) - 2 * mvcorr *
sqrt((CSD^2 / (CN * (CMean^2))) * (1 / (2 * (CN - 1)))) +
ESD^2 / (EN * (EMean^2)) + 1 / (2 * (EN - 1)) - 2 * mvcorr *
sqrt((ESD^2 / (EN * (EMean^2))) * (1 / (2 * (EN - 1))))
}  else{
Cmvcorr<-cor.test(log(CMean), log(CSD))\$estimate  # corrected
(missing log()), was "cor.test(log(EMean), (ESD))\$estimate"
Emvcorr<-cor.test(log(EMean), log(ESD))\$estimate
S2<- CSD^2 / (CN * (CMean^2)) + 1 / (2 * (CN - 1)) - 2 *Cmvcorr *
sqrt((CSD^2 / (CN * (CMean^2))) * (1 / (2 * (CN - 1)))) +
ESD^2 / (EN * (EMean^2)) + 1 / (2 * (EN - 1)) - 2 *Emvcorr *
sqrt((ESD^2 / (EN * (EMean^2))) * (1 / (2 * (EN - 1))))
}
return(S2)
}

# compare

with(data,Calc.lnCVR(m2i,sd2i,n2i,m1i,sd1i,n1i))
# with pooled correlation
with(data,Calc.var.lnCVR(m2i,sd2i,n2i,m1i,sd1i,n1i,Equal.E.C.Corr = T))
# with separate correlations for E and C
with(data,Calc.var.lnCVR(m2i,sd2i,n2i,m1i,sd1i,n1i,Equal.E.C.Corr = F))
metadat\$vi # ALSO NOT THE SAME!!!

I checked all the equations in the Nakagawa functions and couldn't find
any error. Also, I tried the pooled and separate correlation.
Unfortunately, I didn't manage to access the code behind the escalc
function in order to check the underlying calculations.

Does anybody have a suggestion, what this difference could be due to?

(Versions: R 3.4.2, metafor 2.0)

Many thanks,

Sam

Reference: Nakagawa et al. , 2015. Meta-analysis of variation:
ecological and evolutionary applications and beyond. Methods Ecol Evol
6, 143–152. doi:10.1111/2041-210X.12309

--
Samuel Knapp

Lehrstuhl für Pflanzenernährung
Technische Universität München
(Chair of Plant Nutrition
Technical University of Munich)

Emil-Ramann-Strasse 2
D-85354 Freising

Tel. +49 8161 71-3578
samuel.knapp at tum.de
www.researchgate.net/profile/Samuel_Knapp

[[alternative HTML version deleted]]

```