vcaellipse {CAvariants}

Algebraic elliptical confidence regions for symmetrical variants of correspondence analysis

Description

It produces elliptical confidence regions when symmetrical or ordered symmetrical correspondence analysis is performed. This function allows the analyst to superimpose confidence ellipses onto a graphical display when the input parameter catype of the main function CAvariants is set to "CA", "SOCA" or "DOCA". It is called internally from the main plot function plot.CAvariants. It uses the function ellipse.

Usage

vcaellipse(t.inertia, inertias, inertiapc, cord1, cord2, a, b, firstaxis=1,
lastaxis = 2, n, M = 2, Imass, Jmass)

Arguments

t.inertia

The total inertia of the two-way contingency table (Pearson's chi-squared or Goodman and Kruskal's index depends on the CA variant).

inertias

The explained inertia of each dimension.

inertiapc

The percentage of explained inertia for each dimension.

cord1

The row principal coordinates.

cord2

The column principal coordinates.

a

The row standard coordinates or, in case of the ordered variants of CA, the row standard polynomial coordinates.

b

The column standard coordinates or, in case of the ordered variants of CA, the column standard polynomial coordinates.

firstaxis

The horizontal polynomial, or principal, axis. By default, firstaxis = 1.

lastaxis

The vertical polynomial, or principal, axis. By default, lastaxis = 2.

n

The total number of observations.

M

The number of axes considered in determining the structure of the elliptical confidence regions.

Imass

The weight matrix of the row variable.

Jmass

The weight matrix of the column variable.

Details

The output values of this function.

Value

eccentricity

The eccentricity of the ellipses. This is the distance between the centre of the ellipse and its two foci, which can be thought of as a measure of how much the conic section deviates from being circular (when the region is perfectly circular, eccentricity is zero).

HL Axis 1

Value of the semi-major axis length for each row and column point.

HL Axis 2

Value of the semi-minor axis length for each row and column point.

Area

Area of the ellipse for each row and column point.

pvalcol

Approximate p-value for each of the row and column points.

Note

This function is called from the main plot function plot.CAvariants and is executed when in the main plot function the parameter ell = TRUE.

Author(s)

Rosaria Lombardo and Eric J Beh

References

Beh EJ 2010 Elliptical confidence regions for simple correspondence analysis. J. Stat. Plan. Inference 140, 2582–2588.
Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. Wiley.
Beh EJ Lombardo R 2015 Confidence regions and Approximate P-values for classical and non-symmetric correspondence analysis. Journal of Communications and Statistics, Theory and Methods. 44: 95–114.
Lombardo R Beh EJ 2016 Variants of Simple Correspondence Analysis. The R Journal, 8 (2), 167–184.