chi2x3way (version 1.1)

tau3scen1new: Marcotorchino's index for three-way contingency tables under Scenario 1. Revised formulation.

Description

It provides the partition of the Marcotorchino's index and of the $C_M$-statistic, revised formula, under the Scenario 1 when probabilities are set homogeneous.

Usage

tau3scen1new(X, pi=rep(1/dim(X)[[1]],dim(X)[[1]]), pj=rep(1/dim(X)[[2]],dim(X)[[2]]), 
pk=rep(1/dim(X)[[3]],dim(X)[[3]]), digits = 3)

Arguments

X

The three-way contingency table.

pi

The input parameter for specifying the theoretical probabilities of rows categories. When scen = 1, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is pi = rep(1/dim(X)[[1]],dim(X)[[1]]).

pj

The input parameter for specifying the theoretical probabilities of columns categories. When scen = 1, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is pj = rep(1/dim(X)[[2]],dim(X)[[2]]).

pk

The input parameter for specifying the theoretical probabilities of tube categories. When scen = 1, they can be prescribed by the analyst. By default, they are set equal among the categories, homogeneous margins (uniform probabilities), that is pk = rep(1/dim(X)[[3]],dim(X)[[3]]).

digits

The minimum number of decimal places, digits, used for displaying the numerical summaries of the analysis. By default, digits = 3.

Value

Description of of the output returned Description of of the output returned

References

Beh EJ and Lombardo R (2014) Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons. Lancaster H O (1951) Complex contingency tables treated by the partition of the chi-square. Journal of Royal Statistical Society, Series B, 13, 242-249. Loisel S and Takane Y (2015) Partitions of Pearson's chi-square statistic for frequency tables: A comprehensive account. Computational Statistics, 31, 1429-1452. Lombardo R Carlier A D'Ambra L (1996) Nonsymmetric correspondence analysis for three-way contingency tables. Methodologica, 4, 59-80. Marcotorchino F (1985) Utilisation des comparaisons par paires en statistique des contingencies: Partie III. Etude du Centre Scientifique, IBM, France. No F 081

Examples

data(olive)
tau3scen1new(olive)