# mbpls: Multiblock partial least squares In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

 mbpls R Documentation

## Multiblock partial least squares

### Description

Function to perform a multiblock partial least squares (PLS) 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

```mbpls(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 `cov2` squared covariance between lY and TlX `Tc1` matrix containing the partial loadings associated with each explanatory dataset (unit norm) `TlX` matrix containing the partial components associated with each explanatory dataset `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., Lupo, C. and Hanafi, M. (2011). From multiblock partial least squares to multiblock redundancy analysis. A continuum approach. Informatica, 22(1), 11-26

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

`mbpls`, `testdim.multiblock`, `randboot.multiblock`

### Examples

```data(chickenk)
Mortality <- chickenk[]
dudiY.chick <- dudi.pca(Mortality, center = TRUE, scale = TRUE, scannf =
FALSE)
ktabX.chick <- ktab.list.df(chickenk[2:5])
resmbpls.chick <- mbpls(dudiY.chick, ktabX.chick, scale = TRUE,
option = "uniform", scannf = FALSE)
summary(resmbpls.chick)