# Variance Models

## Converting Correlation matrices to variance matrices

The
base correlation identifiers
are converted to the corresponding homogeneous
and
heterogeneous variance models by appending V
and H to the base identifiers respectively. This
convention holds for most models. However, no V
or H
should be appended to the base identifiers
for the other variance models (from DIAG on).
p
In summary, to specify
a correlation model, use the base identifier, for example

EXP .1
is an exponential correlation model,
an homogeneous
variance model, append a V to the base identifier and
provide an additional initial value for the variance, for
example,

EXPV .1 .3
is an exponential variance model,
a heterogeneous
variance model, append an H to the base identifier and
provide additional initial values for the diagonal variances, for
example,
3 0 CORUH .1 .3 .4 .2
is a ` 3 x 3` matrix with uniform correlations of 0.1 and
heterogeneous variances 0.3, 0.4 and 0.2.
There are
important considerations
when combining variance matrices to define a variance structure.
The algebraic forms of the homogeneous and heterogeneous variance
models are determined as follows.
Let **C**
denote the correlation matrix for a particular correlation model. Then
**S**=`v`**C**
is the corresponding homogeneous
variance matrix where `v` is the variance parameter.
For example, the homogeneous
variance model corresponding to the ID correlation
model has variance matrix **S**=`v`**I** specified
IDV in the ASReml command file) and one parameter.
The initial values for the variance parameters are listed after the
initial values for the correlation parameters. For example, in
AR1V 0.3 0.5,
0.3 is the initial spatial correlation parameter
and 0.5 is the initial variance parameter value.
p
Similarly, the heterogeneous variance matrix corresponding to **C** is
**S**=**DCD**
where **D** is a diagonal matrix whose values are the square roots of the variance
parameters.
For example,
the heterogeneous variance model corresponding to ID
is IDH which is the same as
the DIAG structure and has variance matrix
**S**=**DID**.
Similarly, the CORGH model is equivalent to
a US model although
parameterized differently,
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