vcaellipse {CAvariants} | R Documentation |

## Algebraic elliptical confidence regions for symmetrical variants of correspondence analysis

### Description

It produces elliptical confidence regions when symmetrical or ordered symmetrical correspondence analysis is performed.
This function allows the analyst to superimpose confidence ellipses onto a graphical display when the input parameter `catype`

of the main function `CAvariants`

is set to `"CA", "SOCA"`

or `"DOCA"`

.
It is called internally from the main plot function `plot.CAvariants`

.
It uses the function `ellipse`

.

### Usage

```
vcaellipse(t.inertia, inertias, inertiapc, cord1, cord2, a, b, firstaxis=1,
lastaxis = 2, n, M = 2, Imass, Jmass)
```

### Arguments

`t.inertia` |
The total inertia of the two-way contingency table (Pearson's chi-squared or Goodman and Kruskal's index depends on the CA variant). |

`inertias` |
The explained inertia of each dimension. |

`inertiapc` |
The percentage of explained inertia for each dimension. |

`cord1` |
The row principal coordinates. |

`cord2` |
The column principal coordinates. |

`a` |
The row standard coordinates or, in case of the ordered variants of CA, the row standard polynomial coordinates. |

`b` |
The column standard coordinates or, in case of the ordered variants of CA, the column standard polynomial coordinates. |

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

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

`n` |
The total number of observations. |

`M` |
The number of axes considered in determining the structure of the elliptical confidence regions. |

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

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

### Details

The output values of this function.

### Value

`eccentricity` |
The eccentricity of the ellipses. This is the distance between the centre of the ellipse and its two foci, which can be thought of as a measure of how much the conic section deviates from being circular (when the region is perfectly circular, eccentricity is zero). |

`HL Axis 1` |
Value of the semi-major axis length for each row and column point. |

`HL Axis 2` |
Value of the semi-minor axis length for each row and column point. |

`Area` |
Area of the ellipse for each row and column point. |

`pvalcol` |
Approximate p-value for each of the row and column points. |

### Note

This function is called from the main plot function `plot.CAvariants`

and is executed when in the main plot function the parameter
`ell = TRUE`

.

### Author(s)

Rosaria Lombardo and Eric J Beh

### References

Beh EJ 2010 Elliptical confidence regions for simple correspondence analysis. J. Stat. Plan.
Inference 140, 2582–2588.

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

Beh EJ Lombardo R 2015 Confidence regions and Approximate P-values for classical and non-symmetric correspondence analysis.
Journal of Communications and Statistics, Theory and Methods. 44: 95–114.

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

*CAvariants*version 6.0 Index]