rlq function

RLQ analysis

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,...)

Arguments

• 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

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)

References

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.

Author(s)

Stéphane Dray stephane.dray@univ-lyon1.fr

WARNING

IMPORTANT : row weights for dudiR and dudiQ must be taken from dudiL.

Note

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.

See Also

coinertia, fourthcorner

Examples

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")