CARenormalization: re-normalize CA factor scores to Asymetric and...

In HerveAbdi/PTCA4CATA: Partial Triadic Analysis (PTCA) for Check All That Apply (CATA) Data

re-normalize CA factor scores to Asymetric and True-Barycentric factor scores

Description

Re-normalize a set of CA factor scores to be 1) Asymmetric: points are the vertices of the simplex, (Inertia per dimension = Eigenvalues = 1); 2) True Barycentric: points of one set are at the true barycenter of the points of the other set (Inertia per dimension = Eigenvalues^2 of the standard-aka symmetric analysis); 3) Biplots (see Greenacre, 2007, p. 102): The asymetric set is rescaled by the inverse square root of its masses; 4) The strange SPSS renormalization where the factor scores have variance equal to the singular values. These re-normalizations schemes make sense only when the sets of items for rows and columns are asymmetric such as,for example, when one set represents an independent variable and the other one a dependent variable (e.g., "check all that apply" CATA data). When plotting both sets on the same map, the independent variable will be the set with the largest inertia. This type of plot is possible with two different configurations: 1) IV-set with Asymmetric and DV-set Symmetric, or 2) IV-set with symmetric and DV-set with True Barycentric.

Usage

CARenormalization(G, delta, singularValues = TRUE, masses = NULL)

Arguments

G	a set of factor scores from a correspondence analysis
delta	a vector of singular / eigen values
singularValues	do we have singular values or eigenvalues when TRUE (default) we have singular values, if FALSE we have eigenvalues
masses	a vector of masses for tor the observations. if NULL do not compute the Biplot normalization

Value

a list with G_A (Asymmetric factor scores), G_B (True Barycentric factor scores), G_S (SPSS Symmetric Biplot), and G_P (biPlot).

Author(s)

Herve Abdi

HerveAbdi/PTCA4CATA documentation built on July 17, 2022, 5:41 a.m.