mbpcaiv function

Multiblock principal component analysis with instrumental variables

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

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 $(X_1, \dots, X_K)$ 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

Returns

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

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. tools:::Rd_expr_doi("10.18637/jss.v086.i01")

Author(s)

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

See Also

mbpls, testdim.multiblock, randboot.multiblock

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)