print.CA3variants {CA3variants}R Documentation

Print of three-way correspondence analysis results

Description

This function prints the results of three-way symmetrical or non-symmetrical correspondence analysis. If the input parameter, in CA3variants, is ca3type="CA3", the function prints the results of three-way symmetrical correspondence analysis. If the input parameter, in CA3variants, is ca3type="NSCA3", the function prints the results of three-way non-symmetrical correspondence analysis. If the input parameter, in CA3variants, is ca3type="OCA3", the function prints the results of ordered three-way symmetrical correspondence analysis. If the input parameter, in CA3variants, is ca3type="ONSCA3", the function prints the results of ordered three-way non-symmetrical correspondence analysis. When the input parameter, in print.CA3variants, is digits = 3, the function prints all the results using three digital numbers.

Usage

## S3 method for class 'CA3variants'
print(x, printall= FALSE, digits = 3,...)

Arguments

x

The name of the output of the main function CAvariants.

printall

The logical parameter that specifies if to print all the results or some of them. By default, printall = FALSE.

digits

The input parameter specifying the digital number. By default, digits = 3.

...

Further arguments passed to or from other methods.

Value

The value of output returned depends on the kind of three-way correspondence analysis variant performed. It also gives the number of the iteration of the algorithm to reach the convergence of the solution. Depending on the variant of three-way correspondence analysis performed, it gives the related weighted contingency table, the reconstructed table by the components and core array, the explained inertia, the total inertia, the inertia in percentage, the proportion of explained inertia given the defined number of the components, the row standard and principal coordinates, the interactive column-tube standard and principal coordinates, the inner-product matrix of coordinates, the core array and index partitioning. In detail:

CA3variants

The output of the kind of three-way correspondence analysis analysis considered.

Data

The original three-way contingency table.

xs

The centred and weighted three-way contingency table when the input parameters are ctr=T and std=T.

xhat

The three-way contingency table approximated (reconstructed) by the three component matrices (of dimension Ixp, Jxq, and Kxr) and the core array.

nxhat2

The sum of squares of the approximated contingency table.

prp

The ratio between the inertia of the complete contingency table and the inertia of the approximated contingency table.

fi

The principal row coordinates.

fiStandard

The standard row coordinates.

gjk

The principal colum-tube coordinates.

gjkStandard

The standard colum-tube coordinates.

fj

The principal column coordinates.

fjStandard

The standard column coordinates.

gik

The principal row-tube coordinates.

gikStandard

The standard row-tube coordinates.

fk

The principal tube coordinates.

fkStandard

The standard tube coordinates.

gij

The principal row-colum coordinates.

gijStandard

The standard row-colum coordinates.

rows

The row marginals of the three-way data table.

cols

The column marginals of the three-way data table.

tubes

The tube marginals of the three-way data table.

flabels

The row category labels.

glabels

The column category labels.

maxaxes

The maximum dimension to consider.

inertia

The total inertia of a variant of three-way correspondence analysis.

inertiaRSS

The residual inertia of a variant of three-way correspondence analysis.

inertiapc

The percentage contribution of the three components to the total variation.

inertiacoltub

The vector of the percentage contributions of the interactively coded colum-tube components to the total inertia, useful for making interactively coded biplots.

inertiarow

The vector of the percentage contributions of the row components to the total inertia, useful for making response biplots.

iproduct

The inner product between the standard row coordinates (fi) and the column-tube principal coordinates (gjk).

g

The core array (i.e. the generalized singular values) calculated by using the Tuckals3 algorithm.

index3

When ca3type = "CA3" or ca3type = "OCA3", the index3 represents the partition of the Pearson index into three two-way association terms and one three-way association term. It also shows the C statistic of each term, its degrees of freedom and p-value. If ca3type = "NSCA3" or ca3type = "ONSCA3", the index3 returns the partition of the Marcotorchino index into three two-way association terms and one three-way association term. It also shows the C statistic of each term, its degrees of freedom and p-value.

ca3type

The specification of the analysis to be performed. When ca3type = "CA3", then a three-way symmetrical correspondence analysis will be performed (default analysis). If ca3type = "NSCA3", then three-way non-symmetrical correspondence analysis will be performed, where one of the variables is the response to be predicted given the other two variables. These two three-way variants use the Tucker3 method of decomposition. When ca3type = "OCA3" or ca3type = "ONSCA3", then an ordered three-way symmetrical or non-symmetrical correspondence analysis will be performed. Differently, these analysis use a new method of decomposition called Trivariate Moment Decomposition.

iteration

The number of iterations that are required for the Tuckals3 algorithm to converge.

Author(s)

Rosaria Lombardo, Eric J Beh and Michel van de Velden.

References

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

Examples

data(happy)
ris.ca3<-CA3variants(happy, dims= c(p=2,q=2,r=2), ca3type = "CA3") 
print(ris.ca3)
ris.nsca3<-CA3variants(happy, dims = c(p=2,q=2,r=2), ca3type = "NSCA3") 
print(ris.nsca3)
ris.oca3<-CA3variants(happy, dims = c(p=3,q=5,r=4), ca3type = "OCA3",norder=3) 
print(ris.oca3)
ris.onsca3<-CA3variants(happy, dims = c(p=3,q=5,r=4), ca3type = "ONSCA3",norder=3) 
print(ris.onsca3)


[Package CA3variants version 3.0 Index]