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

[Viechtbauer Wolfgang (SP)]

Dear Samuel,

Eq. 12 in Nakagawa et al (2015) is not correct. For normally distributed data, the mean and variance are independent and so are ln(mean) and ln(SD). Hence, the correlation term should be omitted.

For data that cannot be assumed to be (approximately) normally distributed, the mean and variance are no longer independent and then one would need to account for their correlation in the computation of the sampling variance. However, the correlation between the means and variances (or ln(mean) and ln(SD) values) across studies is not the same thing as the correlation within the bivariate sampling distribution. In fact, those are really different things.

One would have to derive what the correlation is depending on the type of distribution one wants to assume for the data. The correct equation would differ for each type of distribution.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and 
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD 
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com 

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Samuel Knapp
Sent: Monday, 09 October, 2017 18:35
To: Michael Dewey; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Differences in calculation of CVR in escalc()

Dear Michael and others,

thanks for your reply.

I discovered the difference: in escalc(), in the calculation of the 
variance of lnCVR (vi), the subtraction of term including the 
correlation (Eqn 12 in Nakagawa et al 2015) is ommited. Does anybody 
know, if this Is this due due to any mathematical reasons, or just to 
keep it simple? Or should/could this be adjusted in the function?

The values for vi estimated by escalc() differ from the values based on 
the original equation, on average by a factor of 2.6 assessed on the 
gibson example dataset.

Best regards,

Samuel

On 09/10/17 16:17, Michael Dewey wrote:
> Dear Samuel
>
> Not sure what the issue is but the code from escalc is
>
>           if (measure == "CVR") {
>                 yi <- log(sd1i/m1i) + 1/(2 * (n1i - 1)) - log(sd2i/m2i) -
>                   1/(2 * (n2i - 1))
>                 vi <- 1/(2 * (n1i - 1)) + sd1i^2/(n1i * m1i^2) +
>                   1/(2 * (n2i - 1)) + sd2i^2/(n2i * m2i^2)
>             }
>
> Note you can obtain this by going
> library(metafor)
> sink("escalc.txt")
> escalc.default
> sink()
>
> and examining escalc.txt with your favourite text editor
>
> Michael
>
> On 09/10/2017 13:12, Samuel Knapp wrote:
>> 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))
>> metadat$yi # is the same
>> # with pooled correlation
>> with(data,Calc.var.lnCVR(m2i,sd2i,n2i,m1i,sd1i,n1i,Equal.E.C.Corr = T))
>> metadat$vi # NOT THE SAME!!!
>> # 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