Algebraic elliptical confidence regions in non symmetrical correspondence analysis

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Description

This function produces elliptical confidence regions when non symmetrical or ordered non symmetrical correspondence analysis is performed. It superimposes the confidence ellipses on to the graphical displays, when the input parameter catype of the main code CAvariants is equal to "NSCA", "SONSCA" or "DONSCA". It is called from the main plot function plot.CAvariants and uses the function ellipse.

Usage

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nscaellipse(Xtable, a1 = 1, a2 = 2, alpha = 0.05, cols = c(2, 4), 
M = 2, cex = 0.8, cex.lab = 0.8, mar = c(5, 4, 4, 2) + 0.1, prop = 0.8,  Imass, Jmass,
a, b, fr, g, dmu, tauden, inertiapc, plottype = "biplot", 
biptype = "row", pos = 2, arrow = TRUE, length = 0, graphy = TRUE, ell = TRUE)

Arguments

Xtable

The two-way contingency table.

a1

The dimension reflected along the horizontal axis.

a2

The dimension reflected along the vertical axis.

alpha

The confidence level of the elliptical regions. By default, alpha = 0.05.

cols

The graphical parameter for setting the colours of the points in graphical displays.

M

The number of axes used when drawing ellypse. By default, M = 2. Its maximum value is equal to the rank of the data matrix.

cex

The parameter for setting the size of character labels of points in graphical displays. By default, cex = 0.8.

cex.lab

The parameter for setting the size of character labels of axes in graphical displays. By default, cex.lab = 0.8.

mar

The parameter for setting the size of the plotting area.

prop

The scaling parameter for specifying the limits of the plotting area. By default, prop = 1.

Imass

The weight matrix of the row variable.

Jmass

The weight matrix of the column variable.

a

The row principal or polynomial axes.

b

The column principal or polynomial axes.

fr

The row coordinates.

g

The column coordinates.

dmu

The squared singular values or inertia of each axis.

tauden

The denominator of tau index.

inertiapc

The percentage of explained inertia.

plottype

The kind of graphical display. By default, plottype = "biplot".

biptype

The parameter for specifying the type of biplot. By default, biptype = "row".

pos

The parameter that specifies the position of the point symbols in the graphical displays. By default, pos = 2.

arrow

The parameter for diplaying arrows in biplot in correspondence of points in principal coordinates. By default, arrow = TRUE.

length

The parameter for setting the length of the arrow end in biplot. By default, length = 0.

graphy

The parameter for diplaying ellipses in plots or biplots. By default, graphy = TRUE.

ell

The flag parameter used for displaying ellipse. By default, ell = TRUE.

Details

The output values of this function

Value

eccentricity

Value of ellipse eccentricity. This is the distance between the ellipse center and either of its two foci, which can be thought of as a measure of how much the conic section deviates from being circular (when it is equal to zero then the region becomes circular)

HL Axis 1

Value of ellipse semi-axis 1 for each row and column points.

HL Axis 2

Value of ellipse semi-axis 2 for each row and column points.

Area

Ellipse area for each row and column points.

pvalcol

P-value for each row and column points.

Note

This function is called from the main plot function plot.CAvariants and is executed when catype = "NSCA", catype = "SONSCA" or catype = "DONSCA", only if ell = TRUE.

Author(s)

Rosaria Lombardo and Eric J Beh

References

Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons.