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, `mi = NULL`, which gives consecutive integer valued (natural) scores. `mj` The assigned ordered scores for the column categories, By default, `mj = NULL`, which gives consecutive integer valued (natural) scores.
 `firstaxis` The horizontal polynomial, or principal, axis. By default `firstaxis = 1`. `lastaxis` The vertical polynomial, or principal, axis. By default `lastaxis = 2`. `catype` The input parameter for specifying what variant of correspondence analysis is to be performed. By default, `catype = "CA"`. Other possible values are: `catype = "SOCA"`, `catype = "DOCA"`, `catype = "NSCA"`, `catype = "SONSCA"`, `catype = "DONSCA"`.
 `M` The number of axes used for determining the structure of the elliptical confidence regions. By default, `M = min(nrow(Xtable), ncol(Xtable)) - 1`, i.e. the rank of the data matrix. Note that the graphical representation of ellipses depend on this parameter. `alpha` The level of significance for the elliptical regions. By default, `alpha = 0.05`.

### 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 `catype` is `"DOCA"`, `"SOCA"`, `"DONSCA"` or `"SONSCA"`, they are row principal polynomial coordinates. `Cprinccoord` The column principal coordinates. When the input parameter `catype` is `"DOCA"`, `"SOCA"`, `"DONSCA"` or `"SONSCA"`, they are column principal polynomial coordinates. `Rstdcoord ` The row standard coordinates. When the input parameter `catype` is `"DOCA"`, `"SOCA"`, `"DONSCA"` or `"SONSCA"`, they are row standard polynomial coordinates. `Cstdcoord ` The column standard coordinates. When the input parameter `catype` is `"DOCA"`, `"SOCA"`, `"DONSCA"` or `"SONSCA"`, they are column standard polynomial coordinates. `tauden` The denominator of the Goodman-Kruskal tau index is given when the input parameter `catype` is `"NSCA"`, `"SONSCA"`, or `"DONSCA"`. Otherwise it is NULL. `tau` The index of Goodman and Kruskal is given when the input parameter `catype` is `"NSCA"`, `"SONSCA"`, or `"DONSCA"`. Otherwise it is NULL. `inertiasum` The total inertia of the analysis based on Pearson's chi-squared when catype is `"CA"`, `"DOCA"` or `"SOCA"`, or based on the Goodman-Kruskal tau when `catype` is `"NSCA"`, `"DONSCA"` or `"SONSCA"` (numerator of the Goodman-Kruskal tau index). `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 `catype` is `"CA"` or `"NSCA"` the associated inertia in the row and column spaces are the same for each principal axis. `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, `catype = "ca"`. `mj` The ordered scores of the column variable. When `mj = NULL`, the natural scores are used (`i = 1,...,cols`). `mi` The ordered scores of the row variable. When `mi = NULL`, the natural scores are used (`i = 1,...,rows`). `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, `Inner product`, of the biplot coordinates (for the two axes defined by `firstaxis = 1` and `lastaxis = 2`) `Z` The generalised correlation matrix when `catype = "SOCA"`, `catype = "DOCA"` , `catype = "SONSCA"`, `catype = "DONSCA"`, but when `catype = "CA"`, or `catype = "NSCA"`, it gives again the inner product matrix of biplot coordinates. `M` The number of axes used for determining the structure of the elliptical confidence regions. By default, `M = min(nrow(Xtable), ncol(Xtable)) - 1`, i.e. the rank of the data matrix.
 `eccentricity` When `ellcomp = TRUE`, the output gives the eccentricity of the confidence ellipses. `row.summ` When `ellcomp = TRUE`, the output gives for each row the summary results that contain the semi-major axis length of the ellipse, `HL Axis 1`, the semi-minor axis length for the ellipse, `HL Axis 2`, the area of the ellipse, `Area` and the p-value, `P-value`. `col.summ` When `ellcomp = TRUE`, the output gives for each column point, the summary results that contain the semi-major axis length of the ellipse, `HL Axis 1`, the semi-minor axis length for the ellipse, `HL Axis 2`, the area of the ellipse, `Area` and the p-value, `P-value`.

### 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", firstaxis = 1, lastaxis = 2)
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", firstaxis = 1, lastaxis = 2)
data(shopdataM)
CAvariants(shopdataM, catype = "NSCA", firstaxis = 1, lastaxis = 3)
CAvariants(shopdataM, catype = "SONSCA", firstaxis = 1, lastaxis = 2)
CAvariants(shopdataM, catype = "SOCA", firstaxis = 1, lastaxis = 2)
```

[Package CAvariants version 5.6 Index]