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

[Samuel Knapp]

Dear Wolfgang,

that sounds like a tricky problem. I agree with you, that the best (or 
the worst) assumption about the distribution we can make is normal 
distribution. However, in observations the mean and sd covary very often 
(e.g. Döring et al. 2015), which is also the motivation to use CV=sd/mean.

Nagakawa et al. (2015) in their appendix assume normal distribution of 
the means and sds, but also assume covariation of mean and sd (without 
giving references, but I guess because of above mentioned observation).

I understand your point about the different kinds of correlation between 
studies and the bivariate sampling distribution. However, would it not 
be better to still include the correlation in order to account for the 
often observed covariation of mean and sd (and still being a good 
approximation independent of the real distribution), and also with the 
argument if there is no correlation (because of a assumed normal 
distribution), it will be estimated to zero and thus have no effect?

Looking forward to your reply!

Best regards,

Samuel

References: Döring, T.F., Knapp, S., Cohen, J.E., 2015. Taylor’s power 
law and the stability of crop yields. Field Crops Research 183, 294–302. 
doi:10.1016/j.fcr.2015.08.005


On 10/10/17 11:38, Viechtbauer Wolfgang (SP) wrote:
> 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


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