[R-meta] Co-variances of the random structure

[Gram, Gil (IITA)]

Dear all,

I have the following question: is it possible to extract the covariances from random variance components of a rma.mv model? For example, from my model below this email.

Thanks in advance you for your help,

Gil

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My model design:

MOD = rma.mv(sqrt(yi), vi, method = 'REML', struct="HCS", sparse=TRUE, data=dat,
                              mods = ~ rateORone + rateORtwo + rateORthree + rateORManure + kgMN
                              + I(rateORone^2) + I(rateORtwo^2) + I(rateORthree^2) + I(rateORManure^2) + I(kgMN^2)
                              + rateORone:kgMN + rateORtwo:kgMN + rateORthree:kgMN + rateORManure:kgMN
                              + I(rateORone^2):I(kgMN^2) + I(rateORtwo^2):I(kgMN^2) + I(rateORthree^2):I(kgMN^2) + I(rateORManure^2):I(kgMN^2)
                              + cropSys + idF,
                              random = list(~1|ref, ~1|idRow, ~ treatment|idSite, ~ treatment|idSite.time))

Where ‘treatment’ in the random structure has 4 levels, Control, OR, MR and ORMR. 
I wish to evaluate the variances of the responses of the 3 last levels with the first. For instance with OR: Var_response = Var_OR + Var_control – 2 * Cov_OR:control.

My model output yields the following:

Multivariate Meta-Analysis Model (k = 2695; method: REML)

Variance Components:

           estim    sqrt  nlvls  fixed  factor 
sigma^2.1  0.0513  0.2264     34     no     ref 
sigma^2.2  0.0139  0.1178   2625     no   idRow 

outer factor: idSite    (nlvls = 62)
inner factor: treatment (nlvls = 4)

           estim    sqrt  k.lvl  fixed    level 
tau^2.1    0.1683  0.4103    255     no  Control 
tau^2.2    0.1403  0.3745    324     no       MR 
tau^2.3    0.1305  0.3612    993     no       OR 
tau^2.4    0.1094  0.3308   1123     no     ORMR 
rho        0.8343                    no          

outer factor: idSite.time (nlvls = 230)
inner factor: treatment   (nlvls = 4)

             estim    sqrt  k.lvl  fixed    level 
gamma^2.1    0.1061  0.3258    255     no  Control 
gamma^2.2    0.1272  0.3566    324     no       MR 
gamma^2.3    0.1052  0.3243    993     no       OR 
gamma^2.4    0.1344  0.3666   1123     no     ORMR 
phi          0.9229                    no          

Test for Residual Heterogeneity:
QE(df = 2673) = 115058.0204, p-val < .0001

Test of Moderators (coefficients 2:22):
QM(df = 21) = 754.8078, p-val < .0001