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# Multivariate and cluster analysis

Several standard multivariate methods are provided by Genstat directives. These include methods that analyse data in the form of units-by-variates, and methods that use a similarity or distance matrix.

The following directives carry out standard multivariate analyses:

    `CVA` canonical variates analysis factor analysis non-metric multidimensional scaling principal components analysis principal coordinates analysis Procrustes rotation

Other directives and procedures are available to process results from multivariate analyses:

`ADDPOINTS` adds points for new objects to a `PCO` plots the mean and unit scores from a canonical variates analysis calculates scores for individual units in canonical variates analysis plots a biplot from an analysis by `PCP`, `CVA` or `PCO` gives a high resolution plot of an ordination with minimum spanning tree rotates factor loadings from a `PCP`, `CVA` or `FCA`     `ADDPOINTS` prints a scree diagram and/or a difference table of latent roots relates principal coordinates to original data variables

The following directives are used for hierarchical or non-hierarchical cluster analysis:

`CLUSTER` non-hierarchical clustering from a data matrix forms a similarity matrix or a between-group similarity matrix from a units-by-variates data matrix forms a reduced similarity matrix (by groups) hierarchical cluster analysis from a similarity matrix

Other directives and procedures that process the results from hierarchical cluster analyses are:

`DDENDROGRAM` draws dendrograms with control over structure and style labels clusters in a single-page dendrogram plotted by `DDENDROGRAM` performs bootstrap analyses to assess the reliability of clusters from hierarchical cluster analysis compares groupings generated, for example, from cluster analyses displays results associated with hierarchical clustering forms an amalgamations forms a set of clusters from an amalgamations matrix lists a data matrix in abbreviated form prints a set of clusters summarizes data variates by clusters

Other multivariate techniques are provided by procedures in the Library:

    `AMMI` allows exploratory analysis of genotype × environment interactions constructs a classification tree displays a classification tree identifies specimens using a classification tree saves information from a classification tree forms values for nodes of a classification tree constructs a random classification forest displays information about a random classification forest identifies specimens using a random classification forest produces a biplot from a set of variates constructs an identification key displays an identification key identifies specimens using a key saves information from an identification key does canonical correlation analysis performs canonical correspondence analysis plots correlation or distance biplots after `CCA` or `RDA` plots ordination biplots or triplots after `CCA` or `RDA` clusters rows and columns of a two-way interaction table obtains a starting classification for non-hierarchical clustering finds the points of a single or a full peel of convex-hulls does correspondence analysis, or reciprocal averaging does multiple correspondence analysis plots results from correspondence analysis or multiple correspondence analysis performs discriminant analysis selects the best set of variates to discriminate between groups performs quadratic discrimination between groups i.e. allowing for different variance-covariance matrices displays multivariate data using parallel coordinates calculates stability coefficients for genotype-by-environment data plots displays to assess genotype + genotype-by-environment variation performs a generalized Procrustes analysis identifies an unknown specimen from a defined set of objects performs multivariate analysis of variance and covariance assesses the association between similarity matrices estimates missing values for units in a multivariate data set does an analysis of distance of multivariate data performs tests of univariate and/or multivariate normality performs orthogonal partial least squares regression performs a multiple Procrustes analysis fits a partial least squares regression model performs redundancy analysis produces ridge regression and principal component regression analyses does logistic ridge regression fits a linear functional relationship model performs multivariate linear regression with accumulated testing of terms forms robust estimates of sum-of-squares-and-products matrices produces statistics and graphs for checking sensory panel performance provides an analysis of skew-symmetry for an asymmetric matrix
Updated on September 3, 2019