[R-meta] extracting variances

[Viechtbauer, Wolfgang (SP)]

Dear Gil,

You seem to interpret 0.00775 as 0.77% but the variances (or contrasts thereof) are not percentages. They are variances (in the units of whatever effect size / outcome measure you are using).

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Gram, Gil (IITA)
>Sent: Tuesday, 14 July, 2020 11:38
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] extracting variances
>
>Dear all,
>
>I have a question regarding extracting the variances from my model.
>
>Say I want to analyse the yields (tonnes per hectare) of 4 treatments
>(control, OR, MR, ORMR) running across different sites and times. A
>simplified version of my model would then be:
>
>dat = escalc(measure="MN", mi=yield, sdi=sdYield, ni=nRep, data=temp)
>dat$yi = sqrt(dat$yi) # sqrt transformation
>dat$vi = dat$vi/(4*dat$yi) # variance adjustment to sqrt transformation
>
>mod = rma.mv(yi, as.matrix(vi), method = 'REML', struct="HCS", sparse=TRUE,
>data=dat,
>                               mods = ~ rateORone + kgMN + I(rateORone^2) +
>I(kgMN^2)
>                               + rateORone:kgMN + I(rateORone^2):I(kgMN^2) +
>[…],
>                               random = list(~1|ref, ~1|idRow, ~ treatment |
>idSite, ~ treatment | idSite.time))
>
>
>I’m interested in the yield variance responses over time, of OR and ORMR
>versus control. So I extract the variance-covariance matrix H = mod$H:
>
>          Control        MR        OR      ORMR
>Control 0.1098190 0.1179042 0.1055471 0.1216751
>MR      0.1179042 0.1360579 0.1174815 0.1354332
>OR      0.1055471 0.1174815 0.1090329 0.1212389
>ORMR    0.1216751 0.1354332 0.1212389 0.1449001
>
>The variance responses I then calculate with e.g. responseOR = varianceOR +
>varianceControl - 2*covar(OR, Control):
>
>resOR
>= (H['OR','OR'] + H['Control','Control'] - 2*H['Control','OR'])
>= 0.1090329 + 0.1098190 - 2* 0.1055471
>~ 0.00775
>
>resORMR
>~ 0.0114
>
>I understand therefore that the variance responses over time for treatments
>OR and ORMR are about 0.77% and 1.1%. These values are extremely small,
>hence my questions:
>
>- Am I correct that this was the correct way to estimate the yield
>variability (responses) over time?
>
>If this is all correct, then this means that there is hardly any variability
>associated with these components. And one could start wondering what the
>point is of even looking at this. I tried looking at the values of the other
>components, and see whether these are larger.
>
>- Keeping in mind the original data was sqrt transformed, can these values
>still be considered as variances? or as standard deviations instead?
>- If this makes up so little variance, then where is the variance coming
>from? How much variability is associated with the error term? Or the other
>components. Are these then magnitudes larger? How do I check if the sum of
>all variance components equals 100% with the model output below?
>
>I hope my questions are clear…
>
>Thanks a lot in advance for your help,
>
>Gil
>
>------
>
>Multivariate Meta-Analysis Model (k = 1161; method: REML)
>
>Variance Components:
>
>            estim    sqrt  nlvls  fixed  factor
>sigma^2.1  0.0604  0.2458     40     no     ref
>sigma^2.2  0.0285  0.1688   1161     no   idRow
>
>outer factor: idSite    (nlvls = 71)
>inner factor: treatment (nlvls = 4)
>
>            estim    sqrt  k.lvl  fixed    level
>tau^2.1    0.1285  0.3584    275     no  Control
>tau^2.2    0.0952  0.3086    374     no       MR
>tau^2.3    0.1217  0.3488    234     no       OR
>tau^2.4    0.0711  0.2666    278     no     ORMR
>rho        0.7172                    no
>
>outer factor: idSite.time (nlvls = 271)
>inner factor: treatment   (nlvls = 4)
>
>              estim    sqrt  k.lvl  fixed    level
>gamma^2.1    0.1098  0.3314    275     no  Control
>gamma^2.2    0.1361  0.3689    374     no       MR
>gamma^2.3    0.1090  0.3302    234     no       OR
>gamma^2.4    0.1449  0.3807    278     no     ORMR
>phi          0.9646                    no
>
>Test for Residual Heterogeneity:
>QE(df = 1151) = 501266.0717, p-val < .0001
>
>Test of Moderators (coefficients 2:10):
>QM(df = 9) = 441.0373, p-val < .0001
>
>Model Results:
>
>                          estimate      se     zval    pval    ci.lb
>ci.ub
>intrcpt                     1.2855  0.0691  18.6010  <.0001   1.1501
>1.4210  ***
>rateORone                   0.0059  0.0007   8.5224  <.0001   0.0045
>0.0072  ***
>kgMN                        0.0096  0.0009  10.5108  <.0001   0.0078
>0.0114  ***
>I(rateORone^2)             -0.0000  0.0000  -5.2103  <.0001  -0.0000  -
>0.0000  ***
>I(kgMN^2)                  -0.0000  0.0000  -6.6753  <.0001  -0.0000  -
>0.0000  ***
>[…]
>rateORone:kgMN             -0.0000  0.0000  -3.7035  0.0002  -0.0000  -
>0.0000  ***
>I(rateORone^2):I(kgMN^2)    0.0000  0.0000   2.5775  0.0100   0.0000
>0.0000   **