tau3scen1: Marcotorchino's index for three-way contingency tables under...

In chi2x3way: Partitioning Chi-Squared and Tau Index for Three-Way Contingency Tables

Description

It provides the partition of the Marcotorchino's index and its related $C_M$-statistic under the Scenario 1 when probabilities are homogeneous.

Usage

tau3scen1(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 partition of the Marcotorchino's index, of the $C_M$-statistic and its revised formula, under Scenario 1. We get seven terms partitioning the Marcotorchino's index and the related $C_M$-statistic: three main terms, two bivariate terms and a trivariate term. The output is in a matrix, the six rows of this matrix indicate the tau index numerator, the tau index, the percentage of explained inertia, the $C_M$-statistic, 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.
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.
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)
tau3scen1(olive)

Example output

Loading required package: tools
$z
                  I     J     K     IJ     IK    JK    IJK       M
Numerator     0.005 0.000 0.000  0.008  0.004 0.000  0.002   0.019
Index         0.006 0.000 0.000  0.009  0.004 0.000  0.002   0.022
% of Inertia 28.636 0.744 0.035 41.404 19.702 0.433  9.046 100.000
C-statistic  20.515 0.533 0.025 29.662 14.115 0.310  6.481  71.640
df            5.000 2.000 1.000 10.000  5.000 2.000 10.000  35.000
p-value       0.001 0.766 0.875  0.001  0.015 0.856  0.773   0.000

chi2x3way documentation built on May 2, 2019, 4:16 a.m.