R structure in bivariate analysis

Dear Auther and others:

 I am working on bivariate analysis using tree (or animal) model
and in a puzzle about the R structure. In my data, trait A was
measured at sites 2-3-4, and trait B was measured at sites 1-3-4.
I would like to fit heterogeneous residual variances for different
sites. I therefore set the covariances to 0 for sites 1 and 2,
and also fix the variances to 0 for the combinations of site and
trait without data.

 I first tried the following code:

 !PART 1
trait_a trait_b ~ Trait Tr.site !r Tr.site.rep Tr.tree Tr.site.fam
 4 2 3
1200 0 IDEN
Trait 0 US 0.1E-7 0.0 0.6748 !GFFU
1221 0 IDEN
Trait 0 US 0.8250 0.0 0.1E-7 !GUFF
3519 0 IDEN
Trait 0 US 0.8242 0.2106 0.5981
3507 0 IDEN
Trait 0 US 0.8286 0.2127 0.6065
......

and it worked as I expected:

Covariance/Variance/Correlation Matrix UnStructured Residual
 0.1000E-07 0.000
  0.000 0.6741
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8353 0.000
  0.000 0.1000E-07
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8245 -0.1306
-0.9180E-01 0.5996
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8289 -0.7723E-01
-0.5487E-01 0.6090

 Then I changed the residual variance for trait A at site 1 from
0.1E-7 to 0.0.

 !PART 2
trait_a trait_b ~ Trait Tr.site !r Tr.site.rep Tr.tree Tr.site.fam
 4 2 3
1200 0 IDEN
Trait 0 US 0.0 0.0 0.6748 !GFFU
1221 0 IDEN
Trait 0 US 0.8250 0.0 0.1E-7 !GUFF
3519 0 IDEN
Trait 0 US 0.8242 0.2106 0.5981
3507 0 IDEN
Trait 0 US 0.8286 0.2127 0.6065
......

 I noticed that instead of fixing it to 0, ASReml filled the first
variance with a non-zero value (0.3885):

 Covariance/Variance/Correlation Matrix UnStructured Residual
 0.3885 0.000
  0.000 0.6741
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8353 0.000
  0.000 0.1000E-07
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8245 -0.1306
-0.9180E-01 0.5996
Covariance/Variance/Correlation Matrix UnStructured Residual
 0.8289 -0.7723E-01
-0.5487E-01 0.6090

I further changed the another 0.1E-7 to 0 as well, and ASReml failed
with the message: "REQUIRE !ASUV qualifier for this R structure". The
error message changed to "Error structures are wrong size" once I used
!ASUV qualifier (and added !f mv in the model as well).

 So, how does ASReml treat 0s in R structure? What is the real
difference between 0 and a very small number like 0.1E-7? Why 0s are
ok for covariances but not for variances?

Thanks!
 Peter Adam
Received on Fri Jun 18 2008 - 02:39:38 EST