Print of three-way correspondence analysis results
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.
## S3 method for class 'CA3variants' print(x, printall= FALSE, digits = 3,...)
x: The name of the output of the main function CA3variants.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.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.
Beh EJ and Lombardo R (2014) Correspondence Analysis, Theory, Practice and New Strategies. John Wiley & Sons.
Rosaria Lombardo, Eric J Beh and Michel van de Velden.
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)