# Variance Header line

## Variance Header Line

The variance header line is required whenever random effects in the residual or each random model term are not identically and independently distributed.

It defines three quantities Sections , Dimensions and Number of G structure definitions

## Layout of Variance structure lines.

A variance structure relates to an ordered list of random effects. Some typical examples
• residuals from a field trial
• order ranges x rows (or rows x columns),
• residuals from a multivariate analysis ordered
• units x traits,
• random effects for model term
• Trait.animal ordered Trait x animal,
• random effects for model term
• site.variety ordered site x variety.

In ASReml, ordered A x B means that the levels of B are sorted within levels of A.

Structures for Residuals are called R-structures. Structures for random model terms are called G-structures.

The structure lines are arranged as follows:
• Variance header line
• R-structure definitions
•  Sections sets of variance structure definitions, each set having a definition for each Dimensions,
• G-structure definitions.
•  Each G-structure definition consists of G-structure header which identifies a model term and the number of components in the direct product structure, variance structure definitions for each component.

A variance structure definition consists of
Size Sortkey VCODE initial_values [ qualifiers ]
• Size is the number of levels in the component. Often the
• component will be associated with a factor defined in the data set in which case the name of the factor rather than the levels in the factor may be supplied, and ASReml will take the number from the factor definition.
• Sortkey supplies the information required to ensure the
• effects are in the correct order. When they are known to be in the correct order, Sortkey may be given as 0. It is primarily used in conjunction with spatial analyses.
• VCODE is a
• keyword which defines the variance model required.
• qualifiers control whether the variance parameters are to be kept in some theoretical bounds (e.g. positive)
• initial_values must be supplied for each parameter
• to be estimated. The parameters are defined in the VCODE list.
 The initial_values are read from the following lines if there are not enough initial values on the model line. Each variance model has a certain number of parameters. If insufficient non zero values are found on the model line ASReml expects to find them on the following line(s), initial values of 0.0 may be ignored if they are on the model line but are accepted on subsequent lines, the notation n*v (for example, 5 * 0.1) is permitted on subsequent lines (but not the model line) when there are n repeats of a particular initial value v, only in a few specified cases is 0 permitted as an initial value of a non-zero parameter.

## Examples

This example is for a variance structure for the spatial analysis of a field trial with plots laid out in a regular indexed by two factors row and column. No variance structures are explicitly defined for random terms in the model.
1 2 0 # 1 experiment,
row row AR1 0.1
column column AR1 0.1