# CA3variants: Correspondence Analysis variants for three-way contingency... In CA3variants: Three-Way Correspondence Analysis Variants

## Description

This function performs the three-way symmetrical (when `ca3type = "CA3"`) and non-symmetrical correspondence analysis (when `ca3type = "NSCA3"`) by using the Tucker3 decomposition and an ordered variant of three-way symmetrical correspondence analysis (when `ca3type = "OCA3"`) by using the Trivariate Moment Decomposition. The non-symmetrical variant considers the three variables asymmetrically related, such that one of the variables is the response to be predicted given the other two variables. It calculates the coordinates and inertia values of the chosen analyses.

## Usage

 ```1 2``` ```CA3variants(Xtable, p = dim(Xtable)[[1]], q = dim(Xtable)[[2]], r = dim(Xtable)[[3]], ca3type = "CA3", test = 10^-6, norder = 3) ```

## Arguments

 `Xtable` The three-way data array. It must be an `R` object array. When non-symmetrical analysis for one response variable is performed, the response mode is the row variable. `p` The number of components for the first mode. By default, `p = dim(Xtable)[[1]]`. `q` The number of components for the second mode. By default, `q = dim(Xtable)[[2]]`. `r` The number of components for the third mode. By default, `r = dim(Xtable)[[3]]`. `ca3type` The specification of the analysis to be performed. If `ca3type = "CA3"`, then a three-way symmetrical correspondence analysis will be performed (default analysis). If `ca3type = "NSCA3"`, then three-way non-symmetrical correspondence analysis will be performed. If `ca3type = "OCA3"`, then ordered three-way symmetrical correspondence analysis will be performed. If `ca3type = "ONSCA3"`, then ordered three-way non-symmetrical correspondence analysis will be performed. `test` Threshold used in the algorithm for stopping it after the convergence of the solutions. `norder` The input parameter for specifying the number of ordered variable when `ca3type = "OCA3"`.

## Details

This function recall internally many other functions, depending on the setting of the input parameters. After performing three-way symmetric or non-symmetric correspondence analysis, it recall two functions for printing and plotting the results. These two important functions are `print.CA3variants` and `plot.CA3variants`.

## Value

The value of output returned depends on the kind of analysis performed. For a detailed description of the output one can see:
the output value of `ca3basic` if the input parameter is `ca3type="CA3"`; the output value of `nsca3basic` if the input parameter is `ca3type="NSCA3"`; the output value of `oca3basic` if the input parameter is `ca3type="OCA3"` the output value of `onsca3basic` if the input parameter is `ca3type="ONSCA3"`

## Author(s)

Rosaria Lombardo, Eric J Beh, Ida Camminatiello.

## References

Beh EJ and Lombardo R (2014). Correspondence Analysis, Theory, Practice and New Strategies. John Wiley & Sons.
Kroonenberg PM (1994). The TUCKALS line: a suite of programs for three-way data analysis. Computational Statistics and Data Analysis, 18, 73–96.

## Examples

 ```1 2 3 4 5``` ```data(happy) CA3variants(happy,p=2,q=2,r=2, ca3type = "CA3") CA3variants(happy,p=2,q=2,r=2, ca3type = "OCA3") CA3variants(happy,p=2,q=2,r=2, ca3type = "NSCA3") CA3variants(happy,p=2,q=2,r=2, ca3type = "ONSCA3") ```

CA3variants documentation built on Aug. 1, 2019, 5:06 p.m.