rlq {ade4} | R Documentation

## 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 Q correspond to the rows of Q. RLQ analysis is an extension of coinertia analysis (see as.coinertia function).

### Usage

    rlq(dudiR, dudiL, dudiQ, scannf = TRUE, nf = 2)
    print.rlq(x, ...)
    plot.rlq(x, xax = 1, yax = 2, ...)
    summary.rlq(object, ...)
    as.coinertia (dudiRLQ, fixed="R")
    randtest.rlq(xtest,nrepet = 999, RV = TRUE, ...)

### 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
`dudiRLQ` | an rlq object
`object` | an rlq object
`fixed` | "R" indicates that dudiR is not modified, otherwise "Q"
`RV` | a logical value indicating whether the test is based on RV or inertia
`xtest` | an rlq object
`nrepet` | the number of permutations
`...` | 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

`as.coinertia` transforms a `rlq` object into a `coinertia` object but user must specify which `dudi` is fixed and not modified.

### Author(s)

Stephane Dray dray@biomserv.univ-lyon1.fr

### 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.

### See Also

`coinertia`

### 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.rlq(rlq1)

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