# Spatial Analysis of Multienvironment trials

## Generating/Checking spatial coding

Consider the simultaneous analysis of a series of trials
with similar treatments and layout. For field trials,
the residuals are independent between trials but may be spatially
within trials. At the treatment level there is the
average effect of treatments across trials and the interaction
of treatment with trial.
For analysis in ASReml, the data for each trial needs to be
arranged conformably in a single or
multiple files,
sorted by trial. The data also needs to be sorted into plot order
but this can be done by ASReml if the rows and columns
are coded in the data file. Assume we have a data field
site
which identifies the trial, and fields
row
and
column
which code for the spatial arrangement within trials.
## Syntax

When
!SECTION `site` !ROWFAC `row` !COLFAC `column `

is specified, ASReml generates the R-structure lines to fit
a separable first-order autoregressive (
AR1 x AR1
) variance structure for each site.
`column `
is the name of a factor or variate containing column numbers (1 ...
`nc` where `nc` is the number of columns) on which the data is to
be sorted.

`row `
is the name of a factor or variate containing row numbers (1 ...
`nr` where `nr` is the number of rows) on which the data is to
be sorted.

`site `
is the
name of a factor or variate containing site numbers (1 ...
`ns` where `ns` is the number of sites) on which the data is already sorted.
When
!SECTION `site `
is specified ASReml will check that sections have been correctly dimensioned
but assumes the data records are presorted with respect to
`site`.
When
!ROWFAC `row `
and
!COLFAC `column `
are also specified, ASReml will construct the R-structure lines
required to model the spatial variance as AR1 x AR1
with initial correlation parameters of 0.1,
such that the data is sorted into plot order: columns within rows within sites.
The R structure lines that a user would normally be
required to work out and type into the
.as
file
are written to the
.res
file. The user may then cut and paste them into the
.as
file for a later run if the structures need to be
modified.
The number of rows and columns within a trial does not
have to be the same across trials.
#### Example

The following is a basic example assuming 5 sites (sections).

Syntax Basic multi-environment trial analysis
site 5 # sites coded 1 ... 5
column * # columns coded 1 ...
row * # rows coded 1 ...
variety !A # variety names
yield
met.dat !SECTION site !ROWFAC row !COLFAC col
yield ~ site !r variety site.variety !f mv
site 2 0 # variance header line
# asreml inserts the 10 lines required to
# define the R structure lines for the five sites

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