oca3basic: Three-way Ordered Symmetrical Correspondence Analysis

In CA3variants: Three-Way Correspondence Analysis Variants

Three-way Ordered Symmetrical Correspondence Analysis

Description

This function is used in the main function CA3variants when the input parameter is ca3type="OCA3".
It performs the three-way symmetric correspondence analysis by TUCKALS3.

Usage

oca3basic(x, p, q, r, test = 10^-6, ctr = T, std = T, norder = 3, sign = TRUE)

Arguments

x	The three-way contingency table.
p	The number of components of the first mode.
q	The number of components of the second mode.
r	The number of components of the third mode.
test	The treshold used in the algorithm TUCKALS3.
ctr	The flag parameter (T or F), if F the analysis is not centered.
std	The flag parameter (T or F) if F the analysis is not standardized.
norder	The number of ordered variables considered.
sign	The input parameter for changing the sign to the components according to the core sign.

Value

x	The original three-way contingency table.
xs	The weighted three-way contingency table.
xhat	Three-way contingency table reconstructed after Tuckals3 by principal components and core array
nxhat2	The inertia of three-way symmetric correspondence analysis (Three-way Pearson ratio).
prp	The proportion of inertia reconstructed using the p, q, r principal components and the core array to the total inertia. To select the model dimensions (number of principal components), we examine the inertia explained by the p, q, r principal components with respect to the overall fit.
a	The row principal components.
b	The column principal coordinates.
cc	The tube principal coordinates.
g	The core array calculated by using the Tuckals3 algorithm and can be interpreted as generalised singular value table. They help to explain the strength of the association between the three principal components.
iteration	The number of iterations that are required for the TUCKALS3 algorithm to converge.

Author(s)

Rosaria Lombardo, Eric J Beh.

References

Lombardo R, Beh EJ and Kroonenberg PM (2021) Symmetrical and Non-Symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables. Statistical Science, 36 (4), 542-561.

CA3variants documentation built on Oct. 10, 2022, 5:07 p.m.