# Algebraic elliptical confidence regions

### Description

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

of the main code `CAvariants`

is equal to `"CA", "SOCA"`

or `"DOCA"`

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

.
It uses the function `ellipse`

.

### Usage

1 2 3 4 5 |

### Arguments

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

`a1` |
The dimension reflected along the horizontal axis. |

`a2` |
The dimension reflected along the vertical axis. |

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

`cols` |
The graphical parameter for setting the colours of the points in the graphical displays. |

`M` |
The number of axes used when drawing ellypse. By default, |

`cex` |
The parameter for setting the size of character labels of points in graphical displays. By default, |

`cex.lab` |
The parameter for setting the size of character labels of axes in graphical displays. By default, |

`mar` |
The parameter for setting the size of the plotting area. |

`prop` |
The scaling parameter for specifying the limits of the plotting area. By default, |

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

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

`a` |
The row principal or polynomial axes. |

`b` |
The column principal or polynomial axes. |

`fr` |
The row coordinates. |

`g` |
The column coordinates. |

`dmu` |
The squared singular values or inertia of each axis. |

`inertiapc` |
The percentage of explained inertia. |

`pos` |
The parameter that specifies the position of point symbols in the graphical displays. By default, |

`plottype` |
The parameter for specifying the type of plot. By default, |

`biptype` |
The parameter for specifying the type of biplot. By default, |

`arrow` |
The parameter used for diplaying arrows in biplot in correspondence of points in principal coordinates. By default, |

`length` |
The parameter used for setting the length of the arrow end in biplot. By default, |

`graphy` |
The flag parameter used for diplaying ellipses when using |

`ell` |
The flag parameter used for displaying ellipse. By default, |

### Details

The output values of this function.

### Value

`eccentricity` |
Value of ellipse eccentricity. This is the distance between the ellipse center and either of its two foci, which can be thought of as a measure of how much the conic section deviates from being circular (when it is equal to zero then the region becomes circular). |

`HL Axis 1` |
Value of ellipse semi-axis 1 for each row and column points. |

`HL Axis 2` |
Value of ellipse semi-axis 2 for each row and column points. |

`Area` |
Ellipse area for each row and column points. |

`pvalcol` |
P-value for each row and column points. |

### Note

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

and is executed when
`catype = "CA"`

, `catype = "SOCA"`

or `catype = "DOCA"`

, only if `ell = TRUE`

.

### 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.

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