rlq: RLQ analysis

In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

RLQ analysis

Description

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.

Usage

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

Value

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)

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.

Author(s)

Stéphane Dray [e-mail]

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.

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")

ade4 documentation built on Feb. 16, 2023, 7:58 p.m.