[R-sig-ME] getting matrix-covariance matrices from a multivariate lme

[David Villegas Ríos]

Dear list,
I'm running a multivariate mixed model in lme. So far, I'm modeling only
two response variables (dataset in long format), but the questions below
applies as well to models with more response variables. I have been reading
some documents produced by Ben Bolker available online (e.g. this
<http://rstudio-pubs-static.s3.amazonaws.com/3336_03636030d93d47de9131e625b72f58c6.html>)
but still I have some doubts.

This is my model. I hope it is correctly specified: there is a single fixed
effect ("month", continuous variable), different variances between traits
and a correlation term to account for the temporal correlation of the
replicates. "tim" is a timer variable, "id" is individual identity and
"trait" is a factor variable with two levels in this simple case (the two
response traits).

lme21=lme(value~trait*poly(month,3)-1,data=long21,random=~trait-1|id,weights=varIdent(form=~1|trait),correlation=corAR1(form=~tim|id/trait))

The summary:
Linear mixed-effects model fit by REML
 Data: long21
       AIC      BIC   logLik
  12364.22 12453.96 -6168.11

Random effects:
 Formula: ~trait - 1 | id
 Structure: General positive-definite, Log-Cholesky parametrization
         StdDev    Corr
traitdvm 1.6190039 trtdvm
traitsdl 0.1730272 0.702
Residual 3.2393785

Correlation Structure: ARMA(1,0)
 Formula: ~tim | id/trait
 Parameter estimate(s):
     Phi1
0.5775275
Variance function:
 Structure: Different standard deviations per stratum
 Formula: ~1 | trait
 Parameter estimates:
      dvm       sdl
1.0000000 0.1166486
Fixed effects: value ~ trait * poly(month, 3) - 1
                             Value Std.Error   DF   t-value p-value
traitdvm                   2.85966  0.154334 4217 18.529065  0.0000
traitsdl                   0.03629  0.017347 4217  2.092108  0.0365
poly(month, 3)1           41.34481  5.323865 4217  7.765939  0.0000
poly(month, 3)2          -14.49704  6.118856 4217 -2.369241  0.0179
poly(month, 3)3          -30.73276  4.157736 4217 -7.391707  0.0000
traitsdl:poly(month, 3)1 -44.68770  5.355425 4217 -8.344380  0.0000
traitsdl:poly(month, 3)2  13.13565  6.149759 4217  2.135962  0.0327
traitsdl:poly(month, 3)3  33.08326  4.183701 4217  7.907655  0.0000
 Correlation:
                         trtdvm trtsdl p(,3)1 p(,3)2 p(,3)3 t:(,3)1 t:(,3)2
traitsdl                  0.297
poly(month, 3)1           0.025 -0.001
poly(month, 3)2           0.063  0.017 -0.006
poly(month, 3)3          -0.037  0.001 -0.462  0.051
traitsdl:poly(month, 3)1 -0.025  0.004 -0.993  0.006  0.459
traitsdl:poly(month, 3)2 -0.060 -0.010  0.006 -0.993 -0.050 -0.006
traitsdl:poly(month, 3)3  0.037 -0.006  0.459 -0.050 -0.993 -0.462   0.051

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max
-7.48299422 -0.52498105 -0.03120914  0.53723986  5.96432196

Number of Observations: 4498
Number of Groups: 274

And these are my questions:
1- How can I get the random and residual variance-covariance matrices? Can
they be extracted using VarCorr somehow? This is part of the output in
MCMCglmm but in lme I haven't found the way to do it in lme so far...
2- How can I test the significance of the random covariances, i.e, if it is
statistically different from zero? I guess a solution would be to fit a
model with a constrained covariance (fixed to zero) and then compare
models, but how would this be specified in the model?

Thanks!!

David

	[[alternative HTML version deleted]]