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.

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, ...)

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
... 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)

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)

Worked out examples


> library(ade4)
> ### Name: rlq
> ### Title: RLQ analysis
> ### Aliases: rlq print.rlq plot.rlq summary.rlq randtest.rlq
> ### Keywords: multivariate spatial
> 
> ### ** 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)

Eigenvalues decomposition:
        eig     covar      sdR      sdQ      corr
1 0.4782826 0.6915798 1.558312 1.158357 0.3831293
2 0.1418508 0.3766308 1.308050 1.219367 0.2361331

Inertia & coinertia R:
    inertia      max     ratio
1  2.428337 2.996911 0.8102800
12 4.139332 5.345110 0.7744148

Inertia & coinertia Q:
    inertia      max     ratio
1  1.341791 2.603139 0.5154512
12 2.828648 4.202981 0.6730098

Correlation L:
       corr       max     ratio
1 0.3831293 0.6435487 0.5953384
2 0.2361331 0.5220054 0.4523576
>    randtest.rlq(rlq1)
Monte-Carlo test
Call: randtest.rlq(xtest = rlq1)

Observation: 0.7278339 

Based on 1000 replicates
Simulated p-value: 0.000999001 
Alternative hypothesis: greater 

     Std.Obs  Expectation     Variance 
12.218602634  0.195251670  0.001899898 
> 
> 
> 
> 

[Package ade4 Index]