ade4: mbpcaiv – R documentation

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mbpcaiv

Multiblock principal component analysis with instrumental variables

Description

Function to perform a multiblock redundancy analysis of several explanatory blocks (X_1, …, X_k), defined as an object of class ktab, to explain a dependent dataset $Y$, defined as an object of class dudi

Usage

mbpcaiv(dudiY, ktabX, scale = TRUE, option = c("uniform", "none"), scannf = TRUE, nf = 2)

Arguments

`dudiY`	an object of class `dudi` containing the dependent variables
`ktabX`	an object of class `ktab` containing the blocks of explanatory variables
`scale`	logical value indicating whether the explanatory variables should be standardized
`option`	an option for the block weighting. If `uniform`, the block weight is equal to $1/K$ for (X_1, …, X_K) and to $1$ for $X$ and $Y$. If `none`, the block weight is equal to the block inertia
`scannf`	logical value indicating whether the eigenvalues bar plot should be displayed
`nf`	integer indicating the number of kept dimensions

Value

A list containing the following components is returned:

`call`	the matching call
`tabY`	data frame of dependent variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
`tabX`	data frame of explanatory variables centered, eventually scaled (if scale=TRUE) and weighted (if option="uniform")
`TL, TC`	data frame useful to manage graphical outputs
`nf`	numeric value indicating the number of kept dimensions
`lw`	numeric vector of row weights
`X.cw`	numeric vector of column weighs for the explanalatory dataset
`blo`	vector of the numbers of variables in each explanatory dataset
`rank`	maximum rank of the analysis
`eig`	numeric vector containing the eigenvalues
`lX`	matrix of the global components associated with the whole explanatory dataset (scores of the individuals)
`lY`	matrix of the components associated with the dependent dataset
`Yc1`	matrix of the variable loadings associated with the dependent dataset
`Tli`	matrix containing the partial components associated with each explanatory dataset
`Tl1`	matrix containing the normalized partial components associated with each explanatory dataset
`Tfa`	matrix containing the partial loadings associated with each explanatory dataset
`cov2`	squared covariance between lY and Tl1
`Yco`	matrix of the regression coefficients of the dependent dataset onto the global components
`faX`	matrix of the regression coefficients of the whole explanatory dataset onto the global components
`XYcoef`	list of matrices of the regression coefficients of the whole explanatory dataset onto the dependent dataset
`bip`	block importances for a given dimension
`bipc`	cumulated block importances for a given number of dimensions
`vip`	variable importances for a given dimension
`vipc`	cumulated variable importances for a given number of dimensions

Author(s)

Stéphanie Bougeard (stephanie.bougeard@anses.fr) and Stéphane Dray (stephane.dray@univ-lyon1.fr)

References

Bougeard, S., Qannari, E.M. and Rose, N. (2011) Multiblock Redundancy Analysis: interpretation tools and application in epidemiology. Journal of Chemometrics, 23, 1-9

Bougeard, S. and Dray S. (2018) Supervised Multiblock Analysis in R with the ade4 Package. Journal of Statistical Software, 86 (1), 1-17. https://doi.org/10.18637/jss.v086.i01

Examples

data(chickenk)
Mortality <- chickenk[[1]]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpcaiv.chick <- mbpcaiv(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
summary(resmbpcaiv.chick)
if(adegraphicsLoaded())
plot(resmbpcaiv.chick)

ade4

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

v1.7-16

GPL (>= 2)

Authors

Stéphane Dray <stephane.dray@univ-lyon1.fr>, Anne-Béatrice Dufour <anne-beatrice.dufour@univ-lyon1.fr>, and Jean Thioulouse <jean.thioulouse@univ-lyon1.fr>, with contributions from Thibaut Jombart, Sandrine Pavoine, Jean R. Lobry, Sébastien Ollier, Daniel Borcard, Pierre Legendre, Stéphanie Bougeard and Aurélie Siberchicot. Based on earlier work by Daniel Chessel.

Initial release