AMMI procedure

Allows exploratory analysis of genotype × environment interactions (M. Talbot, K. Brown & M.F. Smith).

Options

PRINT = strings

Results to be output (aovtable, genotype, environment, graph, estimates, envtable, cluster); default * i.e. none

NROOTS = scalar

Number of IPCA scores required; default is to take as many roots as possible up to a maximum of 9

GRAPHICS = string

Controls the form of graphs produced (lineprinter, highresolution); default high

Parameters

DATA = variates

Provides the data to be analysed

GENOTYPES = factors

Specifies the genotypes

ENVIRONMENTS = factors

Specifies the environments

REPLICATES = factors

Replication factor; this should be omitted if the data comprises just the genotype by environment means

GSCORES = pointers

Pointer containing a set of variates (each of length equal to the number of genotypes) to save the genotype IPCA scores

ESCORES = pointers

Pointer to a set of variates to save the environment IPCA scores

Description

AMMI is a procedure for fitting, to data classified by two factors, a model which involves the Additive Main effects of ANOVA along with the Multiplicative Interaction effects of principal components analysis (PCA). The method is used when analysing data from a series of trials with crop genotypes.

A principal components model is fitted to the residuals from the ANOVA and the resulting scores, called the I (for interaction) PCA are calculated for both the genotypes and the trials or environments.

The DATA parameter specifies a variate holding the data values to be analysed. The genotype and environment factors must also be given, using the GENOTYPES and ENVIRONMENTS parameters. AMMI can handle the replicate observations that make up the genotype × environment means if the user supplies the replicate observations, and specifies a replicate factor using the REPLICATES parameter. When constructing the analysis-of-variance table, AMMI assumes that the replicates arise from the use of a randomized block design within each environment. No missing values are allowed, and there must be equal replication. If you have a more complicated structure, you can form the means (using ANOVA and AKEEP or REML and VKEEP), and then use procedure VTABLE to form a DATA variate containing just the means, together with corresponding GENOTYPES and ENVIRONMENTS factors.

The NROOTS option allows the number of roots (sets of scores) for the principal component analysis to be specified.

The PRINT option allows a choice of results to be requested by settings:

aovtable

analysis-of-variance table summarising the contribution of each component to the interaction term,

genotype

genotype means and scores,

environment

environment means and scores,

envtable

table of environment means and variances,

estimates

genotype estimates for each environment

cluster

hierarchical clustering of AMMI genotype estimates over environments (using the average link method and Euclidean test for the similarity matrix),

graph

plots of genotype and environment means against their corresponding IPCA scores.

The GRAPHICS option controls whether the plots are produced in high-resolution of line-printer format. By default GRAPHICS=highresolution.

Options: PRINT, NROOTS, GRAPHICS.

Parameters: DATA, GENOTYPES, ENVIRONMENTS, REPLICATES, GSCORES, ESCORES.

Method

The data are averaged over replicates, and the genotype by environment means are calculated. ANOVA is used to provide the main effects, sums of squares and degrees of freedom. The matrix of residuals from ANOVA are then decomposed by singular value decomposition to generate the AMMI analysis (see, for example, Gauch 1992).

Action with RESTRICT

If the DATA variate is restricted the analysis will involve only the units not excluded by the restriction.

Reference

Gauch, H.G. (1992). Statistical Analysis of Regional Yield Trials - AMMI analysis of factorial designs. Elsevier, Amsterdam.