Six variants of correspondence analysis

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Description

It performs
1) simple correspondence analysis
2) doubly ordered correspondence analysis
3) singly ordered correspondence analysis
4) non symmetrical correspondence analysis
5) doubly ordered non symmetrical correspondence analysis
6) singly ordered non symmetrical correspondence analysis

Usage

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CAvariants(
Xtable, mj = NULL, mi = NULL, firstaxis = 1, lastaxis = 2,
catype = "CA", ellcomp = TRUE, Mell = min(nrow(Xtable), ncol(Xtable)) - 1, alpha = 0.05) 

Arguments

Xtable

The two-way contingency table.

mi

The assigned ordered scores for the row categories. By default, mi = NULL, which gives consecutive integer valued (natural) scores.

mj

The assigned ordered scores for the column categories, By default, mj = NULL, which gives consecutive integer valued (natural) scores.

firstaxis

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

lastaxis

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

catype

The input parameter for specifying what variant of correspondence analysis is considered. By default, catype = "CA". Other possible values are: catype = "SOCA", catype = "DOCA", catype = "NSCA", catype = "SONSCA", catype = "DONSCA".

ellcomp

This input parameter ensures that the characteristics of the algebraic confidence ellipses are computed and stored. When ellcomp = TRUE (which is by default), the output includes the characteristics of the ellipses. The eccentricity of the confidence ellipses is summarised by the quantity eccentricity, this is the distance between the 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). The semi-major axis length of the ellipse for each row and column point is given by HL Axis 1 while HL Axis 2 gives the semi-minor axis length of the points along the second axis. The area of the ellipse for each row and column category is given by Area while the p-value of each category is defined by P-value.

Mell

The number of axes Mell considered in determining the structure of the elliptical confidence regions. By default, Mell = min(nrow(Xtable), ncol(Xtable)) - 1, i.e. the rank of the data matrix.

alpha

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

Details

This function belongs to the object class called cacorporateplus

Value

Description of the output returned

Xtable

The two-way contingency table.

rows

The row number of the two-way contingency table.

cols

The column number of the two-way contingency table.

r

The rank of the two-way contingency table.

rowlabels

The label of the row variable.

collabels

The label of the column variable.

Rprinccoord

The row principal coordinates. When the input parameter catype is
"DOCA", "SOCA", "SONSCA" or "DONSCA", they are row principal polynomial coordinates.

Cprinccoord

The column principal coordinates. When the input parameter catype is
"DOCA" or "DONSCA", they are column principal polynomial coordinates.

Rstdcoord

The row standard coordinates. When the input parameter catype is
"DOCA" or "DONSCA", they are row standard polynomial coordinates.

Cstdcoord

The column standard coordinates. When the input parameter catype is
"DOCA", "SOCA", "SONSCA" or "DONSCA", they are column standard polynomial coordinates.

tauden

The tau denominator is given when the input parameter catype is "NSCA", "SONSCA", or "DONSCA", otherwise it is a null value.

tau

The tau index is given when the input parameter catype is "NSCA", "SONSCA", or "DONSCA", otherwise it is a null value.

inertiasum

The total inertia of the classical correspondence analysis when catype is "CA", "DOCA" or "SOCA" (the Pearson's index), or the inertia of non symmetrical correspondence analysis when catype is "NSCA", "DONSCA" or "SONSCA" (numerator of the Goodman-Kruskal tau index).

inertias

The associated inertia in absolute value and percentage, in the row space for each principal or polynomial axis.

inertias2

The associated inertia in absolute value and percentage, in the column space for each principal or polynomial axis. When catype is "CA" or "NSCA" the associated inertia in the row and column spaces are the same for each principal axis.

comps

The polynomial components of inertia when the variables are ordered. The inertia of row and/or column space is partitioned in terms of polynomial components in ordered CA variants.

catype

The kind of correspondence analysis chosen.

mj

The ordered scores of a column variable. When mj = NULL, the natural ordered numbers are shown.

mi

The ordered scores of a row variable. When mi = NULL, the natural ordered numbers are shown.

pcc

The weighted centered column profile matrix.

Jmass

The weight matrix of the column variable.

Imass

The weight matrix of the row variable.

Trend

The inner product, Inner product, of the biplot coordinates (concerning the first two axes when firstaxis=1 and lastaxis=2)

Z

The generalized correlation matrix when catype is "SOCA", "DOCA" , "SONSCA", "DONSCA", but when catype is "CA", "NSCA", it gives again the inner product matrix of biplot coordinates.

ellcomp

The flag parameter, ellcomp, specifies that the characteristics of the confidence ellipses (eccentricity, semi-axis, area, p-values) are computed.
By default, ellcomp = TRUE.

risell

When the input parameter, ellcomp, is set to ellcomp = TRUE, the output includes the characteristics risell of the confidence ellipses, the eccentricity of the confidence ellipses, risell$eccentricity, for each row and column point, the summary results, risell$row.summ and risell$col.summ, contain the semi-major axis length of the ellipse, HL Axis 1, the semi-minor axis length for the ellipse, HL Axis 2, the area of the ellipse, Area and the p-value, P-value.

Mell

The number of axes Mell considered in determining the structure of the elliptical confidence regions. By default, Mell = min(nrow(Xtable), ncol(Xtable)) - 1, i.e. the rank of the data matrix.

Note

This function recalls internally many other functions, depending on the setting of the input parameter catype, it recalls one of the six functions which does a variant of correspondence analysis. After performing a variant of correspondence analysis, it gives the output object necessary for printing and plotting the results. These two important functions are print.CAvariants and plot.CAvariants. This function belongs to the class cacorporateplus.

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.

Examples

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data(asbestos)
CAvariants(asbestos, catype = "CA", firstaxis = 1, lastaxis = 2) 
CAvariants(asbestos, catype = "DOCA", firstaxis = 1,lastaxis = 2) 
CAvariants(asbestos, catype = "DONSCA",firstaxis=1, lastaxis = 2, ellcomp = FALSE) 
data(shopdataM)
CAvariants(shopdataM, catype = "NSCA", firstaxis = 1, lastaxis = 2)
CAvariants(shopdataM, catype = "SONSCA", firstaxis = 1, lastaxis = 2)
CAvariants(shopdataM, catype = "SOCA", firstaxis = 1, lastaxis = 2)