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

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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)

Stephanie Bougeard (stephanie.bougeard@anses.fr) and Stephane 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

See Also

mbpls, testdim.multiblock, randboot.multiblock

Examples

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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)

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