rlq | R Documentation |

RLQ analysis performs a double inertia analysis of two arrays (R and Q) with a link expressed by a contingency table (L). The rows of L correspond to the rows of R and the columns of L correspond to the rows of Q.

rlq(dudiR, dudiL, dudiQ, scannf = TRUE, nf = 2) ## S3 method for class 'rlq' print(x, ...) ## S3 method for class 'rlq' plot(x, xax = 1, yax = 2, ...) ## S3 method for class 'rlq' summary(object, ...) ## S3 method for class 'rlq' randtest(xtest,nrepet = 999, modeltype = 6,...)

`dudiR` |
a duality diagram providing from one of the functions dudi.hillsmith, dudi.pca, ... |

`dudiL` |
a duality diagram of the function dudi.coa |

`dudiQ` |
a duality diagram providing from one of the functions dudi.hillsmith, dudi.pca, ... |

`scannf` |
a logical value indicating whether the eigenvalues bar plot should be displayed |

`nf` |
if scannf FALSE, an integer indicating the number of kept axes |

`x` |
an rlq object |

`xax` |
the column number for the x-axis |

`yax` |
the column number for the y-axis |

`object` |
an rlq object |

`xtest` |
an rlq object |

`nrepet` |
the number of permutations |

`modeltype` |
the model used to permute data(2: permute rows of R, 4: permute rows of Q, 5: permute both, 6: sequential approach, see ter Braak et al. 2012) |

`...` |
further arguments passed to or from other methods |

Returns a list of class 'dudi', sub-class 'rlq' containing:

`call` |
call |

`rank` |
rank |

`nf` |
a numeric value indicating the number of kept axes |

`RV` |
a numeric value, the RV coefficient |

`eig` |
a numeric vector with all the eigenvalues |

`lw` |
a numeric vector with the rows weigths (crossed array) |

`cw` |
a numeric vector with the columns weigths (crossed array) |

`tab` |
a crossed array (CA) |

`li` |
R col = CA row: coordinates |

`l1` |
R col = CA row: normed scores |

`co` |
Q col = CA column: coordinates |

`c1` |
Q col = CA column: normed scores |

`lR` |
the row coordinates (R) |

`mR` |
the normed row scores (R) |

`lQ` |
the row coordinates (Q) |

`mQ` |
the normed row scores (Q) |

`aR` |
the axis onto co-inertia axis (R) |

`aQ` |
the axis onto co-inertia axis (Q) |

IMPORTANT : row weights for `dudiR`

and `dudiQ`

must be taken from `dudiL`

.

A testing procedure based on the total coinertia of the RLQ
analysis is available by the function `randtest.rlq`

. The
function allows to deal with various analyses for tables R and Q. Means and variances are recomputed for each
permutation (PCA); for MCA, tables are recentred and column weights are recomputed.The
case of decentred PCA (PCA where centers are entered by the user) for
R or Q is not yet implemented. If you want to use the testing
procedure for this case, you must firstly center the table and then perform a non-centered PCA on the modified table.

Stéphane Dray stephane.dray@univ-lyon1.fr

Doledec, S., Chessel, D., ter Braak, C.J.F. and Champely, S. (1996)
Matching species traits to environmental variables: a new three-table ordination method. *Environmental and Ecological Statistics*,
**3**, 143–166.

Dray, S., Pettorelli, N., Chessel, D. (2002) Matching data sets from two different spatial samplings.
*Journal of Vegetation Science*, **13**, 867–874.

Dray, S. and Legendre, P. (2008)
Testing the species traits-environment relationships: the fourth-corner
problem revisited. *Ecology*,
**89**, 3400–3412.

ter Braak, C., Cormont, A., Dray, S. (2012) Improved testing of species
traits-environment relationships in the fourth corner problem.
*Ecology*, **93**, 1525–1526.

`coinertia`

, `fourthcorner`

data(aviurba) coa1 <- dudi.coa(aviurba$fau, scannf = FALSE, nf = 2) dudimil <- dudi.hillsmith(aviurba$mil, scannf = FALSE, nf = 2, row.w = coa1$lw) duditrait <- dudi.hillsmith(aviurba$traits, scannf = FALSE, nf = 2, row.w = coa1$cw) rlq1 <- rlq(dudimil, coa1, duditrait, scannf = FALSE, nf = 2) plot(rlq1) summary(rlq1) randtest(rlq1) fourthcorner.rlq(rlq1,type="Q.axes") fourthcorner.rlq(rlq1,type="R.axes")

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