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"` or `"NSCA"`. It is called internally from the main plot function `plot.CAvariants`. It uses the function `ellipse`.

### Usage

```vcaellipse(row.summ, col.summ, inertiapc, cord1, cord2, a, b,
firstaxis, lastaxis, eccentricity)
```

### Arguments

 `row.summ` The matrix where the first column represents the row semi-major axis of ellipses, the second column the row semi-minor axis of ellipses, the third column contains the ellipse area and the last column the relative row p.values. `col.summ` The matrix where the first column represents the column semi-major axis of ellipses, the second column the column semi-minor axis of ellipses, the third column contains the ellipse area and the last column the relative column p.values. `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, `firstaxis` is that given in `plot.CAvariants`. `lastaxis` The vertical polynomial, or principal, axis. By default, `lastaxis` is that given in `plot.CAvariants`. `eccentricity` The eccentricity of ellipses.

### 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.

[Package CAvariants version 5.6 Index]