# Algebraic elliptical confidence regions in non symmetrical correspondence analysis

### Description

This function produces elliptical confidence regions when non symmetrical or ordered non symmetrical correspondence analysis is performed.
It superimposes the confidence ellipses on to the graphical displays, when the input parameter `catype`

of the main code `CAvariants`

is equal to `"NSCA", "SONSCA"`

or `"DONSCA"`

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

and uses the function `ellipse`

.

### Usage

1 2 3 4 |

### 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 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. |

`tauden` |
The denominator of tau index. |

`inertiapc` |
The percentage of explained inertia. |

`plottype` |
The kind of graphical display. By default, |

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

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

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

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

`graphy` |
The parameter for diplaying ellipses in plots or biplots. By default, |

`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 = "NSCA"`

, `catype = "SONSCA"`

or
`catype = "DONSCA"`

, 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.