tauMbootQQ {chi2x3way}R Documentation

Simulations for observing the Marcotorchino's index distribution

Description

It allows 1) the generation of nboots=1000 randomly tables where the row, column, tube probabilities are set equal to the observed margins of the three-way table considered for the partition under Scenario 2. While under Scenario 1, the row, column, tube probabilities are prescribed by the analyst. By default, they are homogeneous.

Usage

tauMbootQQ(rows = 3, cols = 3, tubs = 3, nboots = 1000, nran = 10000, digits = 3, 
scen=2, pi, pj, pk)

Arguments

rows

The number of rows is set equal to the rows of the input table X.

cols

The number of cols is set equal to the columns of the input table X.

tubs

The number of tubs is set equal to the tubes of the input three-way table X.

nboots

The number of three-way tables randomly generated.

nran

The total number of individuals of each generated three-way table.

digits

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

scen

The input parameter for specifying the Scenario under which the theoretical probabilities are computed. Under Scenario 1 the probabilities are prescribed by the analyst, by default they are set homogeneous.

pi

The prescribed row probabilities. By default they are equal to the row margins of the input three-way table X.

pj

The prescribed column probabilities. By default they are equal to the column margins of the input three-way table X.

pk

The prescribed tube probabilities. By default they are equal to the tube margins of the input three-way table X.

Value

XG

The nboots=1000 randomly generated three-way tables.

margI

The row observed margins of the randomly generated three-way table.

margJ

The column observed margins of the randomly generated three-way table.

margK

The tube observed margins of the randomly generated three-way table.

ytau

The table of the terms of the Marcotorchino's index and of the $C_M$-statistic partition, associated to each of the randomly generated three-way table.

ytauNew

The table of the new expression of the terms of the $C_M$-statistic partition, associated to each of the randomly generated three-way table.

ychi

The table of the terms of the chi-square index partition associated to each of the randomly generated three-way table.

chidf

The table of the degree of freedom related to each terms of the chi-square index partition of the randomly generated three-way table.

cont

The number of the randomly generated three-way table whose margin products is less than 5.

Note

This function allows the generation of random tables under different theoretical probabilities. It allow to depict graphically the three-way index distribution. From calling the function QQplot, a QQ-plot is produced for each term of the partition of three indices: the Pearson's index, the classic $C_M$-statistic and of the revised $C_M$-statistic.

Author(s)

Lombardo R, Takane Y and Beh EJ

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

tauMbootQQ(rows = 3, cols = 3, tubs = 3, nboots = 10, nran = 1000, digits = 3, 
pi=rep(1/3,3), pj=rep(1/3,3), pk=rep(1/3,3)) 

[Package chi2x3way version 1.1 Index]