Data generating function for multivariate plsR models

This function generates a single multivariate response value \(\boldsymbol{Y}\) and a vector of explinatory variables \((X_1,\ldots,X_{totdim})\) drawn from a model with a given number of latent components.

Usage

simul_data_YX(totdim, ncomp)

Arguments

totdim: Number of column of the X vector (from ncomp to hardware limits)
ncomp: Number of latent components in the model (from 2 to 6)

Value

vector: \((Y_1,\ldots,Y_r,X_1,\ldots,X_{totdim})\)

Details

This function should be combined with the replicate function to give rise to a larger dataset. The algorithm used is a port of the one described in the article of Li which is a multivariate generalization of the algorithm of Naes and Martens.

Note

The value of \(r\) depends on the value of ncomp :

`ncomp`	\(r\)	2
3	3	3
4	4

References

T. Naes, H. Martens, Comparison of prediction methods for multicollinear data, Commun. Stat., Simul. 14 (1985) 545-576.
Morris, Elaine B. Martin, Model selection for partial least squares regression, Chemometrics and Intelligent Laboratory Systems 64 (2002) 79-89, doi:10.1016/S0169-7439(02)00051-5 .

Author

Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/

Examples


simul_data_YX(20,6)                          
#>         Y 1         Y 2         Y 3         Y 4          X1          X2 
#> -9.45176297 -9.47163207 -9.45084107 -9.45273015 -4.62074234  1.55320742 
#>          X3          X4          X5          X6          X7          X8 
#>  0.60935296  1.13612242 -4.91720188  0.58412558  0.32945918  0.17914794 
#>          X9         X10         X11         X12         X13         X14 
#> -0.06716894 -2.82980256 -3.25922979  2.71312870  0.63529298 -1.03698105 
#>         X15         X16         X17         X18         X19         X20 
#> -0.08041950 -2.83857700 -3.24731589  2.72213250  0.61117743 -1.05277089 

# \donttest{
if(require(plsdepot)){
dimX <- 6
Astar <- 2
(dataAstar2 <- t(replicate(50,simul_data_YX(dimX,Astar))))
library(plsdepot)
resAstar2 <- plsreg2(dataAstar2[,4:9],dataAstar2[,1:3],comps=5)
resAstar2$Q2
resAstar2$Q2[,4]>0.0975

dimX <- 6
Astar <- 3
(dataAstar3 <- t(replicate(50,simul_data_YX(dimX,Astar))))
library(plsdepot)
resAstar3 <- plsreg2(dataAstar3[,4:9],dataAstar3[,1:3],comps=5)
resAstar3$Q2
resAstar3$Q2[,4]>0.0975

dimX <- 6
Astar <- 4
(dataAstar4 <- t(replicate(50,simul_data_YX(dimX,Astar))))
library(plsdepot)
resAstar4 <- plsreg2(dataAstar4[,5:10],dataAstar4[,1:4],comps=5)
resAstar4$Q2
resAstar4$Q2[,5]>0.0975

rm(list=c("dimX","Astar"))
}
#> Loading required package: plsdepot
#> Warning: there is no package called ‘plsdepot’
# }