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]