Quasi-correspondence analysis

Transforms a symmetrical contingency table so that it can be used for quasi-correspondence analysis, also called correspondence analysis of incomplete contingency table.

quasindep(tab, order = 3, tol = 1e-6)

Arguments

tab

a symmetric table or matrix

order

numeric value. Order of reconstitution of the quasi-independence data. Default is 3.

tol

numeric value. The tolerance threshold to be considered for convergence to null during iteration process. Default is 1e-6.

Details

In order to carry out a "quasi-correspondence analysis", also called "correspondence analysis of incomplete table", the principle is to stop analyzing the differences between the observed data and the situation of independence between the variable in rows and the variable in columns, as it is the case in the classical correspondence analysis, and to consider the differences between the data and a situation of quasi-independence, i.e. independence for some cells of the table only. In the most common situation, it is therefore a matter of applying the independence hypothesis to the off-diagonal cells only and replacing the diagonal with values that do not influence the analysis. Such values are obtained in an iterative way by replacing the numbers of the cells of the diagonal by their third order reconstruction, then by recalculating the correspondence analysis until convergence is reached. The algorithm used is developed in van der Heijden (1992: 11-12).

Note

This function is adapted from Milan Bouchet-Valat's script in the supplementary material of his article indicated in the reference section.

Value

An object of the same class and dimensions as tab : the quasi-independence data to be analyzed with Correspondence Analysis.

References

De Leeuw J et van der Heijden PGM (1985) Quasi-Correspondence Analysis. Leiden: University of Leiden.

Van der Heijden PGM (1992) Three Approaches to Study the Departure from Quasi-independence. Statistica Applicata 4: 465-80.

Bouchet-Valat M (2015) L'analyse statistique des tables de contingence carrées - L'homogamie socioprofessionnelle en France - I, L'analyse des correspondances Bulletin de Méthodologie Sociologique 125: 65–88. <doi:10.1177/0759106314555655>

Examples

if (FALSE) {
tab <- matrix(c(165,49,70,100,48,223,
                6,201,226,212,90,216,
                4,96,446,214,72,77,
                5,84,305,317,126,188,
                3,52,151,190,110,189,
                17,234,310,601,309,1222),
                nrow = 6, ncol = 6, byrow = TRUE)
newtab <- quasindep(tab)
}