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.

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@utt.fr
https://fbertran.github.io/homepage/

Examples


simul_data_YX(20,6)                          
#>        Y 1        Y 2        Y 3        Y 4         X1         X2         X3 
#>  1.6521069  1.6767627  1.6346312  1.6132278  0.4990016  4.5452299 -3.2486510 
#>         X4         X5         X6         X7         X8         X9        X10 
#>  2.3508245  0.1799964  4.8791825 -3.5780348  2.6919449  1.0616228  4.3819963 
#>        X11        X12        X13        X14        X15        X16        X17 
#> -1.1678799  0.6185691  3.2516226 -1.9117334  1.0510836  4.3806368 -1.1590954 
#>        X18        X19        X20 
#>  0.6317238  3.2675463 -1.8953118 

# \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"))
}
#> Le chargement a nécessité le package : plsdepot
#> 
#> Attachement du package : ‘plsdepot’
#> The following object is masked from ‘package:chemometrics’:
#> 
#>     nipals
# }