mbpcaiv {ade4} | R Documentation

## 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. http://doi.org/10.18637/jss.v086.i01

### 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)

[Package ade4 version 1.7-13 Index]