chi3scen1 {chi2x3way}R Documentation

Pearson's index for three-way contingency tables under Scenario 1 (prescribed probabilities)

Description

It provides the Pearson's index, e.g. chi-square index, partitioning under the Scenario 1 when probabilities are homogeneous.

Usage

chi3scen1(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 the output returned

z

The chi-square index partition under Scenario 1, we get seven terms of the chi-square partition, three main terms, two bivariate terms and a trivariate term. The output is in a matrix, the four rows of this matrix indicate the index, the percentage of the explained inertia, the degree of freedom, the p-value, respectively.

Note

This function belongs to the class chi3class.

Author(s)

Lombardo R and Takane Y

References

Beh EJ and Lombardo R (2014) Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons.
Carlier A Kroonenberg PM (1996) Biplots and decompositions in two-way and three-way correspondence analysis. Psychometrika, 61, 355-373.
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 (2016) Partitions of Pearson's chi-square ststistic for frequency tables: A comprehensive account. Computational Statistics, 31, 1429-1452.

Examples

##---- Should be DIRECTLY executable !! ----
data(olive)
chi3scen1(olive)

[Package chi2x3way version 1.1 Index]