# mbregular: Regularized multiblock regression In mbclusterwise: Clusterwise Multiblock Analyses

## Description

Function to perform the regularized multiblock regression which gives results comprised the ones from multiblock Redundancy Analysis (`gamma=0`) and multiblock PLS (`gamma=1`). This method is applied to several explanatory blocks (X_1, …, X_K) defined as an object of class `ktab` (from `ade4`), to explain a dependent dataset Y defined as an object of class `dudi` (from `ade4`).

## Usage

 `1` ```mbregular(dudiY, ktabX, scale = FALSE, option = c("none", "uniform"), H, gamma) ```

## Arguments

 `dudiY` an object of class `dudi` (from `ade4`) containing the dependent variable(s) `ktabX` an object of class `ktab` (from `ade4`) containing the blocks of explanatory variables `scale` a logical value indicating whether the explanatory variables should be standardized `option` an option for the block weighting (by default, the first option is chosen): none the block weight is equal to the block inertia uniform the block weight is equal to 1/K for (X_1, …, X_K) and to 1 for X and Y `H` an integer giving the number of dimensions `gamma` a numeric value of the regularization parameter comprised between 0 and 1. The value (`gamma=0`) leads to multiblock Redundancy Analysis and (`gamma=1`) to multiblock PLS

## Value

A list containing the following components is returned:

 `crit.reg` the regression error `lX` a matrix of the global components associated with the whole explanatory dataset (scores of the individuals) `XYcoef` a list of matrices of the regression coefficients of the whole explanatory dataset onto the dependent dataset `intercept` a list of matrices of the regression intercepts of the whole explanatory dataset onto the dependent dataset `fitted` a list of matrices which contain the predicted dependent values

## Author(s)

Stephanie Bougeard (stephanie.bougeard@anses.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

`cw.multiblock`, `cw.tenfold`, `cw.predict`, `mbpcaiv`, `mbpls`
 ```1 2 3 4 5 6 7 8``` ``` data(simdata.red) Data.X <- simdata.red[c(1:15, 21:35), 1:10] Data.Y <- simdata.red[c(1:15, 21:35), 11:13] library(ade4) dudiy <- dudi.pca(df = Data.Y, center = FALSE, scale = FALSE, scannf = FALSE) ktabx <- ktab.data.frame(df = data.frame(Data.X), blocks = c(5,5), tabnames = paste("Tab", c(1:2), sep = ".")) res <- mbregular(dudiy, ktabx, scale = FALSE, option = "none", H = 2, gamma = 0.8) ```