ade4 (version 1.7-24)

dpcaiv: Double principal component analysis with respect to instrumental variables

Description

It includes double redundancy analysis (RDA, if dudi argument is created with dudi.pca) and double canonical correspondence analysis (CCA, if dudi argument is created with dudi.coa) as special cases. The function dvaripart computed associated double (by row and column) variation partitioning.

Usage

dpcaiv(dudi, dfR = NULL, dfQ = NULL, scannf = TRUE, nf = 2)
# S3 method for dpcaiv
plot(x, xax = 1, yax = 2, ...) 
# S3 method for dpcaiv
print(x, ...)
# S3 method for dpcaiv
summary(object, ...) 
# S3 method for dpcaiv
randtest(xtest, nrepet = 99, ...)
dvaripart(Y, dfR, dfQ, nrepet = 999, scale = FALSE, ...)
# S3 method for dvaripart
print(x, ...)

Value

returns an object of class dpcaiv, sub-class of class dudi

tab

a data frame with the modified array (predicted table)

cw

a numeric vector with the column weigths (from dudi)

lw

a numeric vector with the row weigths (from dudi)

eig

a vector with the all eigenvalues

rank

an integer indicating the rank of the studied matrix

nf

an integer indicating the number of kept axes

c1

a data frame with the Constrained Principal Axes (CPA)

faQ

a data frame with the loadings for Q to build the CPA as a linear combination

li

a data frame with the constrained (by R) row score (LC score)

lsR

a data frame with the unconstrained row score (WA score)

l1

data frame with the Constrained Principal Components (CPC)

faR

a data frame with the loadings for R to build the CPC as a linear combination

co

a data frame with the constrained (by Q) column score (LC score)

lsQ

a data frame with the unconstrained column score (WA score)

call

the matched call

Y

a data frame with the dependant variables

R

a data frame with the explanatory variables for rows

Q

a data frame with the explanatory variables for columns

asR

a data frame with the Principal axes of dudi$tab on CPA

asQ

a data frame with the Principal components of dudi$tab on CPC

corR

a data frame with the correlations between the CPC and R

corQ

a data frame with the correlations between the CPA and Q

Arguments

dudi

a duality diagram, object of class dudi

Y

a duality diagram, object of class dudi or a response data.frame

dfR

a data frame with external variables relative to rows of the dudi object

dfQ

a data frame with external variables relative to columns of the dudi object

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, object, xtest

an object of class dpcaiv or dvaripart

xax

the column number for the x-axis

yax

the column number for the y-axis

nrepet

an integer indicating the number of permutations

scale

If Y is not a dudi, a logical indicating if variables should be scaled

...

further arguments passed to or from other methods

Author

Stéphane Dray
Lisa Nicvert

References

Rao, C. R. (1964) The use and interpretation of principal component analysis in applied research. Sankhya, A 26, 329--359.

Obadia, J. (1978) L'analyse en composantes explicatives. Revue de Statistique Appliquee, 24, 5--28.

Lebreton, J. D., Sabatier, R., Banco G. and Bacou A. M. (1991) Principal component and correspondence analyses with respect to instrumental variables : an overview of their role in studies of structure-activity and species- environment relationships. In J. Devillers and W. Karcher, editors. Applied Multivariate Analysis in SAR and Environmental Studies, Kluwer Academic Publishers, 85--114.

Ter Braak, C. J. F. (1986) Canonical correspondence analysis : a new eigenvector technique for multivariate direct gradient analysis. Ecology, 67, 1167--1179.

Ter Braak, C. J. F. (1987) The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio, 69, 69--77.

Chessel, D., Lebreton J. D. and Yoccoz N. (1987) Propriétés de l'analyse canonique des correspondances. Une utilisation en hydrobiologie. Revue de Statistique Appliquée, 35, 55--72.

Examples

# example of a double canonical correspondence analysis
data(aviurba)
coa <- dudi.coa(aviurba$fau, scannf = FALSE)
dcca <- dpcaiv(coa, aviurba$mil, aviurba$trait, scannf = FALSE)
dcca
summary(dcca)
plot(dcca)
randtest(dcca)
dvaripart(coa, aviurba$mil, aviurba$trait, nrepet = 99)