# Canonical analysis of several sets with another set

### Description

Relative proximities of several subsets of variables Yj with another set X. SUCCESSIVE SOLUTIONS

### Usage

1 | ```
concorcano(x,y,py,r)
``` |

### Arguments

`x` |
is a n x p matrix of p centered variables |

`y` |
is a n x q matrix of q centered variables |

`py` |
is a row vector which contains the numbers qi, i=1,...,ky, of
the ky subsets yi of y : |

`r` |
is the wanted number of successive solutions |

### Details

The first solution calculates a standardized canonical component
cx[,1] of x associated to ky standardized components cyi[,1] of yi by
maximizing *∑_i ρ(cx[,1],cy_i[,1])^2*.

The second solution is obtained from the same criterion, with ky orthogonality constraints for having rho(cyi[,1],cyi[,2])=0 (that implies rho(cx[,1],cx[,2])=0). For each of the 1+ky sets, the r canonical components are 2 by 2 zero correlated.

The ky matrices (cx)'*cyi are triangular.

This function uses concor function.

### Value

list with following components

`cx` |
is n x r matrix of the r canonical components of x |

`cy` |
is n.ky x r matrix. The ky blocks cyi of the rows n*(i-1)+1 : n*i contain the r canonical components relative to Yi |

`rho2` |
is a ky x r matrix; each column k contains ky squared
canonical correlations |

### References

Hanafi & Lafosse (2001) Generalisation de la regression lineaire simple pour analyser la dependance de K ensembles de variables avec un K+1 eme. Revue de Statistique Appliquee vol.49, n.1

### Examples

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