CA3variants | R Documentation |

This function performs four variants of three-way correspondence analysis (CA). It does the three-way symmetrical CA, when `ca3type = "CA3"`

, and three-way non-symmetrical
CA, when `ca3type = "NSCA3"`

, by using the Tucker3 decomposition.
It also performs ordered three-way symmetrical CA, when `ca3type = "OCA3"`

, and ordered
three-way non-symmetrical CA, when `ca3type = "ONSCA3"`

,
by using the Trivariate Moment Decomposition. The non-symmetrical variants consider 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.
Furthermore, it allows to look at the index (Pearson's chi-squared or Marcotorchino's tau) partition.

CA3variants(Xdata, dims = c(p, q, r), ca3type = "CA3", test = 10^-6, resp = "row", norder = 3, sign = TRUE)

`Xdata` |
The three-way data. It can be a |

`dims` |
The number of components for the first, second and third mode. By default, no |

`ca3type` |
The specification of the analysis to be performed.
If |

`test` |
Threshold used in the algorithm for stopping it after the convergence of the solutions. |

`resp` |
The input parameter for specifying in non-symmetrical three-way correspondence analysis variants ( |

`norder` |
The input parameter for specifying the number of ordered variable when |

`sign` |
The input parameter for changing the sign to the components according to the core sign. |

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`

.

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"`

Rosaria Lombardo, Eric J Beh and Michel van de Velden.

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.

Lombardo R, Beh EJ and Kroonenberg PM (2021) Symmetrical and Non-Symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables.
Statistical Science, 36 (4), 542-561.

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

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