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
`FCA`	factor analysis
`MDS`	non-metric multidimensional scaling
`PCP`	principal components analysis
`PCO`	principal coordinates analysis
`ROTATE`	Procrustes rotation

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

`ADDPOINTS`	adds points for new objects to a `PCO`
`CVAPLOT`	plots the mean and unit scores from a canonical variates analysis
`CVASCORES`	calculates scores for individual units in canonical variates analysis
`CVATRELLIS`	displays the distribution of groups over 2 dimensions from a `CVA`analysis using a trellis of bar or pie charts
`DBIPLOT`	plots a biplot from an analysis by `PCP`, `CVA` or `PCO`
`DMST`	gives a high resolution plot of an ordination with minimum spanning tree
`FACROTATE`	rotates factor loadings from a `PCP`, `CVA` or `FCA` `ADDPOINTS`
`LRVSCREE`	prints a scree diagram and/or a difference table of latent roots
`PCORELATE`	relates principal coordinates to original data variables

The following commands carry out hierarchical and non-hierarchical cluster analysis:

`CLUSTER`	non-hierarchical clustering from a data matrix
`FSIMILARITY`	forms a similarity matrix or a between-group similarity matrix from a units-by-variates data matrix
`HREDUCE`	forms a reduced similarity matrix (by groups)
`HCLUSTER`	hierarchical cluster analysis from a similarity matrix
`PCPCLUSTER`	forms groups of units using the densities of their `PCP` scores
`PTFCLUSTERS`	forms clusters of points from their densities in multi-dimensional space

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

`DDENDROGRAM`	draws dendrograms with control over structure and style
`DCLUSTERLABELS`	labels clusters in a single-page dendrogram plotted by `DDENDROGRAM`
`HBOOTSTRAP`	performs bootstrap analyses to assess the reliability of clusters from hierarchical cluster analysis
`HCOMPAREGROUPINGS`	compares groupings generated, for example, from cluster analyses
`HDISPLAY`	displays results associated with hierarchical clustering
`HFAMALGAMATIONS`	forms an amalgamations
`HFCLUSTERS`	forms a set of clusters from an amalgamations matrix
`HLIST`	lists a data matrix in abbreviated form
`HPCLUSTERS`	prints a set of clusters
`HSUMMARIZE`	summarizes data variates by clusters
`PTFILLCLUSTERS`	fills holes within clusters of points in multi-dimensional space

Other multivariate techniques are provided by procedures in the Library:

`AMMI`	allows exploratory analysis of genotype × environment interactions
`BCLASSIFICATION`	constructs a classification tree
`BCDISPLAY`	displays a classification tree
`BCIDENTIFY`	identifies specimens using a classification tree
`BCKEEP`	saves information from a classification tree
`BCVALUES`	forms values for nodes of a classification tree
`BCFOREST`	constructs a random classification forest
`BCFDISPLAY`	displays information about a random classification forest
`BCFIDENTIFY`	identifies specimens using a random classification forest
`BIPLOT`	produces a biplot from a set of variates
`BKEY`	constructs an identification key
`BKDISPLAY`	displays an identification key
`BKIDENTIFY`	identifies specimens using a key
`BKKEEP`	saves information from an identification key
`CANCORRELATION`	does canonical correlation analysis
`CCA`	performs canonical correspondence analysis
`CRBIPLOT`	plots correlation or distance biplots after `CCA` or `RDA`
`CRTRIPLOT`	plots ordination biplots or triplots after `CCA` or `RDA`
`CINTERACTION`	clusters rows and columns of a two-way interaction table
`CLASSIFY`	obtains a starting classification for non-hierarchical clustering
`CONVEXHULL`	finds the points of a single or a full peel of convex-hulls
`CORANALYSIS`	does correspondence analysis, or reciprocal averaging
`MCORANALYSIS`	does multiple correspondence analysis
`CABIPLOT`	plots results from correspondence analysis or multiple correspondence analysis
`DISCRIMINATE`	performs discriminant analysis
`SDISCRIMINATE`	selects the best set of variates to discriminate between groups
`QDISCRIMINATE`	performs quadratic discrimination between groups i.e. allowing for different variance-covariance matrices
`DPARALLEL`	displays multivariate data using parallel coordinates
`GESTABILITY`	calculates stability coefficients for genotype-by-environment data
`GGEBIPLOT`	plots displays to assess genotype + genotype-by-environment variation
`GENPROCRUSTES`	performs a generalized Procrustes analysis
`IDENTIFY`	identifies an unknown specimen from a defined set of objects
`KNEARESTNEIGHBOURS`	classifies items or predicts their responses by examining their k nearest neighbours
`MANOVA`	performs multivariate analysis of variance and covariance
`MANTEL`	assesses the association between similarity matrices
`MULTMISSING`	estimates missing values for units in a multivariate data set
`MVAOD`	does an analysis of distance of multivariate data
`NORMTEST`	performs tests of univariate and/or multivariate normality
`OPLS`	performs orthogonal partial least squares regression
`PCOPROCRUSTES`	performs a multiple Procrustes analysis
`PLS`	fits a partial least squares regression model
`RDA`	performs redundancy analysis
`RIDGE`	produces ridge regression and principal component regression analyses
`LRIDGE`	does logistic ridge regression
`RLFUNCTIONAL`	fits a linear functional relationship model
`RMULTIVARIATE`	performs multivariate linear regression with accumulated testing of terms
`ROBSSPM`	forms robust estimates of sum-of-squares-and-products matrices
`SAGRAPES`	produces statistics and graphs for checking sensory panel performance
`SKEWSYMMETRY`	provides an analysis of skew-symmetry for an asymmetric matrix

Updated on February 7, 2023

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