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

Gram, Gil (IITA) G@Gr@m @end|ng |rom cg|@r@org
Tue Feb 18 12:12:34 CET 2020

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