Variance wrapper functions

Functional specification of variance structures.

The model line lists model terms, typically variables, functions of variables and interactions of these. Model terms are classified as fixed fixed or random random

Random terms have an associated variance structure. The default is IDV, independent, identically distributed effects (i.e. equal variance, no covariance). But ASReml allows many other variance structures, and ASReml 4 allows these to be specified using variance wrapper functions on the components of the model term. All the variance structures have a corresponding wrapper function. The function name is lower case.
The following list identifies some common cases.

Model Example Description
IDV 
   idv(blocks)
 independent effects with a common variance
AR1 
 ar1(row).ar1(column)
 autocorrelated rows and columns in a typical spatial residual model
AR1V 
 ar1v(time)
 autocorrelated effects across time with a scaler variance
CORUV 
 coruv(Trial).Genotype
or 
 coru(Trial).idv(Genotype)
 uniformly correlated genetic effects, with common variance.
CORUH 
 coruh(Trial).Genotype
 uniformly correlated genetic effects, with Trial specific variance variance.
XFAk 
 XFA1(Trial).Genotype
 One factor covariance structure with trial specific loadings and variance.
US 
 units.us(Trait)
 Typical residual structure for multitrait analysis 

 us(pol(X,2)).Subject
Typical quadratic random regression model term
NRM 
nrm(Animal)
uses relationship matrix based on the pedigree 

us(Trait).nrm(Animal)
 typical multivariate animal model 

!{ Animal Dam us(2).nrm(Animal) !}  ide(Dam)
 typical maternal effects model with direct/maternal genetic covariance. In this case, the variance structure cannot be expressed as a function of the model terms and so, inside !{ !} we list the model terms, followed by the structure that applies to the set of terms.
GRMk 
GRM1(Animal)
 uses the first General Relationship matrix
EXPV 
  expv(fac(X))
 fits the exponential correlation structure calculated at the design points in X, with a variance parameter.

Variance structure qualifiers

Sometimes the user will wish to supply initial parameter values or other qualifiers for the variance structure. These are typically supplied as a list after the model term. When the list is long, making the model line excessively messy, the list may be placed in an !ASSIGN string.

Variance structure qualifiers are discussed here.

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