[R-sig-ME] Covariance matrix of random genetic effects

[Kassim Baba Yussif]

Dear mix modelers,
I am modeling genotype-by-environment interaction with environment (E) as
the fixed effect and genotype (G) as the random effect using nlme package.
The model assumes residual heterogeneity across environments and a random
genetic main effects that changes between groups of environments (group)
that are positively correlated.

The genetic main effects that changes between groups of environments has a
covariance matrix that consists of group specific variances on the
diagonals and pairwise-specific genetic covariance between groups on the
off-diagonals.

I fitted the following models:
fm3b <- lme(yield ~ E,
           random = list(G = pdDiag(~group)),
           weights = varIdent(form = ~ 1 | E), data = BABS , method =
"REML" )

summary(fm3b)Linear mixed-effects model fit by REML
 Data: BABS
       AIC      BIC    logLik
  3822.193 3925.297 -1892.096

Random effects:
 Formula: ~group | G
 Structure: Diagonal
        (Intercept)    group2  group3 Residual
StdDev:   0.2698093 0.5510772 1.05834 0.657899

Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | E
 Parameter estimates:
    SS92a     IS92a     NS92a     IS94a     SS94a     LN96a     LN96b
1.0000000 1.0274616 0.9887740 0.9880075 1.0702162 0.5393888 0.5381522
    HN96b
1.3293175
Fixed effects: yield ~ E
                Value  Std.Error   DF   t-value p-value
(Intercept)  3.234534 0.07354699 1470  43.97915       0
EIS92a       1.033065 0.07609483 1470  13.57602       0
EIS94a      -0.434446 0.07501537 1470  -5.79143       0
ELN96a      -2.009100 0.07523938 1470 -26.70276       0
ELN96b      -2.636272 0.07522121 1470 -35.04692       0
ENS92a       3.759188 0.11125709 1470  33.78830       0
ESS92a      -0.781158 0.07534063 1470 -10.36835       0
ESS94a      -0.477911 0.07729423 1470  -6.18301       0


fm3c <- lme(yield ~ E,
            random = list(G = pdSymm(~group)),
            weights = varIdent(form = ~ 1 | E) , data = BABS, method =
"REML")


summary(fm3c)Linear mixed-effects model fit by REML
 Data: BABS
       AIC      BIC    logLik
  3751.569 3870.953 -1853.785

Random effects:
 Formula: ~group | G
 Structure: General positive-definite
            StdDev    Corr
(Intercept) 0.2050822 (Intr) group2
group2      0.5137835 0.631
group3      1.0695264 0.335  0.671
Residual    0.6677121

Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | E
 Parameter estimates:
    SS92a     IS92a     NS92a     IS94a     SS94a     LN96a     LN96b
1.0000000 0.9988832 0.9509165 0.9799925 1.0669147 0.5698006 0.5565435
    HN96b
1.2884907
Fixed effects: yield ~ E
                Value  Std.Error   DF   t-value p-value
(Intercept)  3.234534 0.07475904 1470  43.26612       0
EIS92a       1.033065 0.07494170 1470  13.78491       0
EIS94a      -0.434446 0.07441283 1470  -5.83833       0
ELN96a      -2.009100 0.07379078 1470 -27.22697       0
ELN96b      -2.636272 0.07357668 1470 -35.83026       0
ENS92a       3.759188 0.09272196 1470  40.54258       0
ESS92a      -0.781158 0.07497316 1470 -10.41917       0
ESS94a      -0.477911 0.07689743 1470  -6.21491       0


The two models gives me the residual heterogeneity across environments. But
I don't get the group specific variances and covariance. Model fm3b gives
me only group specific variances whiles fm3c gives group specific variances
and some between groups correlations.

Is there a way I can get group specific variances and the pair-wise
covariance?
https://orcid.org/0000-0002-3994-5066

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