biplot.measures: Biplot quality measures

In tpepler/cpc: Common principal component (CPC) analysis and applications

Biplot quality measures

Description

Calculates a number of quality measures for principal component biplots of grouped data.

Usage

biplot.measures(datalist, projectmat, rdim)

Arguments

datalist	List of the data for which the biplot is to be constructed, created with a command such as list(group1, group2, ...).
projectmat	Orthogonal projection matrix used in constructing the biplot.
rdim	Number of dimensions of the biplot representation.

Details

For the plain PCA biplot, use the eigenvectors of the pooled data (not centred per group before pooling) as the projection matrix.

Value

Returns a list with the values:

overall.quality	Overall quality of the biplot display, a scalar value in the[0-1] range.
within.quality	Quality of the within-group variation per group, a vector of values in the [0-1] range.
within.quality.mean	Mean quality of the within-group variation displayed in the biplot, a scalar value in the [0-1] range.
between.quality	Quality of the between-group variation as displayed in the biplot, a scalar value in the [0-1] range.
adequacies	Vector containing the adequacies of the variables (values in the [0-1] range).
adequacies.median	Median of the variable adequacies.
axis.predictivities	Vector containing the axis predictivities (values in the [0-1] range, but see the notes below).
axis.predictivities.mean	Mean of the axis predicitivities.
sample.predictivities	Vector containing the sample predictivities (values in the [0-1] range).
sample.predictivities.mean	Mean of the sample predictivities.
mspe	Vector containing the mean standard predictive errors (MSPE) of the variables.
mspe.mean	Mean of the MSPE values.

Note

The median (instead of the mean) adequacy of the variables is calculated, as the mean adequacy of the variables will always be equal to r/p (r = number of dimensions; p = number of variables), and is therefore uninformative as a quality measure.

The axis predictivities of the variables are only valid if the Type B orthogonality condition holds. It is thus a valid measure for the plain PCA biplot, but not for other types of principal component biplots.

Author(s)

Theo Pepler

References

Pepler, P.T. (2014). The identification and application of common principal components. PhD dissertation in the Department of Statistics and Actuarial Science, Stellenbosch University.

See Also

biplot.choice

Examples

# The Iris data
data(iris)
setosa <- iris[1:50, 1:4]
versicolor <- iris[51:100, 1:4]
virginica <- iris[101:150, 1:4]

project.matrix <- eigen(cov(rbind(setosa, versicolor, virginica)))$vectors

# For a 2-dimensional biplot
biplot.measures(datalist = list(setosa, versicolor, virginica), projectmat = project.matrix, rdim = 2)

# For a 3-dimensional biplot
biplot.measures(datalist = list(setosa, versicolor, virginica), projectmat = project.matrix, rdim = 3)

tpepler/cpc documentation built on July 7, 2022, 2:13 a.m.