# Six variants of correspondence analysis

### Description

It performs

1) simple correspondence analysis

2) doubly ordered correspondence analysis

3) singly ordered correspondence analysis

4) non symmetrical correspondence analysis

5) doubly ordered non symmetrical correspondence analysis

6) singly ordered non symmetrical correspondence analysis

### Usage

1 2 3 |

### Arguments

`Xtable` |
The two-way contingency table. |

`mi` |
The assigned ordered scores for the row categories. By default, |

`mj` |
The assigned ordered scores for the column categories, By default, |

`firstaxis` |
The horizontal polynomial or principal axis. By default |

`lastaxis` |
The vertical polynomial or principal axis. By default |

`catype` |
The input parameter for specifying what variant of correspondence analysis is considered. By default, |

`ellcomp` |
This input parameter ensures that the characteristics of the algebraic confidence ellipses are computed and stored.
When (when it is equal to zero then the region becomes circular).
The semi-major axis length of the ellipse for each row and column
point is given by |

`Mell` |
The number of axes |

`alpha` |
The confidence level of the elliptical regions. By default, |

### Details

This function belongs to the object class called `cacorporateplus`

### Value

Description of the output returned

`Xtable ` |
The two-way contingency table. |

`rows` |
The row number of the two-way contingency table. |

`cols` |
The column number of the two-way contingency table. |

`r` |
The rank of the two-way contingency table. |

`rowlabels` |
The label of the row variable. |

`collabels` |
The label of the column variable. |

`Rprinccoord` |
The row principal coordinates. When the input parameter |

`Cprinccoord` |
The column principal coordinates. When the input parameter |

`Rstdcoord ` |
The row standard coordinates. When the input parameter |

`Cstdcoord ` |
The column standard coordinates. When the input parameter |

`tauden` |
The tau denominator is given when the input parameter |

`tau` |
The tau index is given when the input parameter |

`inertiasum` |
The total inertia of the classical correspondence analysis when catype is |

`inertias` |
The associated inertia in absolute value and percentage, in the row space for each principal or polynomial axis. |

`inertias2` |
The associated inertia in absolute value and percentage, in the column space for each principal or polynomial axis.
When |

`comps` |
The polynomial components of inertia when the variables are ordered. The inertia of row and/or column space is partitioned in terms of polynomial components in ordered CA variants. |

`catype` |
The kind of correspondence analysis chosen. |

`mj` |
The ordered scores of a column variable. When |

`mi` |
The ordered scores of a row variable. When |

`pcc` |
The weighted centered column profile matrix. |

`Jmass` |
The weight matrix of the column variable. |

`Imass` |
The weight matrix of the row variable. |

`Trend` |
The inner product, |

`Z` |
The generalized correlation matrix when catype is |

`ellcomp` |
The flag parameter, |

`risell` |
When the input parameter, |

`Mell` |
The number of axes |

### Note

This function recalls internally many other functions, depending on the setting of the input parameter `catype`

, it recalls
one of the six functions which does a variant of correspondence analysis.
After performing a variant of correspondence analysis, it gives the output object necessary for printing and plotting the results. These two
important functions are `print.CAvariants`

and `plot.CAvariants`

.
This function belongs to the class `cacorporateplus`

.

### Author(s)

Rosaria Lombardo and Eric J Beh

### References

Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons.

### Examples

1 2 3 4 5 6 7 8 | ```
data(asbestos)
CAvariants(asbestos, catype = "CA", firstaxis = 1, lastaxis = 2)
CAvariants(asbestos, catype = "DOCA", firstaxis = 1,lastaxis = 2)
CAvariants(asbestos, catype = "DONSCA",firstaxis=1, lastaxis = 2, ellcomp = FALSE)
data(shopdataM)
CAvariants(shopdataM, catype = "NSCA", firstaxis = 1, lastaxis = 2)
CAvariants(shopdataM, catype = "SONSCA", firstaxis = 1, lastaxis = 2)
CAvariants(shopdataM, catype = "SOCA", firstaxis = 1, lastaxis = 2)
``` |

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