CAvariants {CAvariants} | R Documentation |

## 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

```
CAvariants(Xtable, mj = NULL, mi = NULL, firstaxis = 1, lastaxis = 2,
catype = "CA", M = min(nrow(Xtable), ncol(Xtable)) - 1, alpha = 0.05)
```

### 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. It is used for the construction of the Inner product table. By default |

`lastaxis` |
The vertical polynomial, or principal, axis. It is used for the construction of the Inner product table. By default |

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

`M` |
The number of axes used for determining the structure of the elliptical confidence regions.
By default, |

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

### Value

Description of the output returned

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

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

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

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

`n` |
The total number of observations of the two-way contingency table. |

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

`collabels` |
The labels 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 denominator of the Goodman-Kruskal tau index is given when the input parameter |

`tau` |
The index of Goodman and Kruskal is given when the input parameter |

`inertiasum` |
The total inertia of the analysis based on Pearson's chi-squared when catype is |

`singvalue` |
The singular values of the two-way contingency table. |

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

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

`t.inertia` |
The total inertia of the two-way contingency table. |

`comps` |
The polynomial components of inertia when the variables are ordered. |

`catype` |
The type of correspondence analysis chosen by the analyst. By default, |

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

`mi` |
The ordered scores of the 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. |

`Innprod` |
The inner product, |

`Z` |
The generalised correlation matrix when |

`M` |
The number of axes used for determining the structure of the elliptical confidence regions.
By default, |

`eccentricity` |
When |

`row.summ` |
When |

`col.summ` |
When |

### 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`

.

### Author(s)

Rosaria Lombardo and Eric J Beh

### References

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

Lombardo R Beh EJ 2016 Variants of Simple Correspondence Analysis. The R Journal, 8 (2), 167–184.

Lombardo R Beh EJ and Kroonenberg PM 2016 Modelling Trends in Ordered Correspondence Analysis Using Orthogonal
Polynomials. Psychometrika, 81(2), 325–349.

### Examples

```
data(asbestos)
CAvariants(asbestos, catype = "CA")
CAvariants(asbestos, catype = "DOCA", mi = c(1:nrow(asbestos)), mj =c(4.5,14.5,24.5,34.5,44.5),
firstaxis = 1, lastaxis = 2, M = min(nrow(asbestos), ncol(asbestos)) - 1)
CAvariants(asbestos, catype = "DONSCA")
data(shopdataM)
CAvariants(shopdataM, catype = "NSCA")
CAvariants(shopdataM, catype = "SONSCA")
CAvariants(shopdataM, catype = "SOCA")
```

*CAvariants*version 6.0 Index]