Data generating function for univariate gamma plsR models

This function generates a single univariate gamma response value \(Ygamma\) and a vector of explanatory variables \((X_1,\ldots,X_{totdim})\) drawn from a model with a given number of latent components.

Usage

simul_data_UniYX_gamma(totdim, ncomp, jvar, lvar, link = "inverse", offset = 0)

Arguments

totdim: Number of columns of the X vector (from ncomp to hardware limits)
ncomp: Number of latent components in the model (to use noise, select ncomp=3)
jvar: First variance parameter
lvar: Second variance parameter
link: Character specification of the link function in the mean model (mu). Currently, "inverse", "log" and "identity" are supported. Alternatively, an object of class "link-glm" can be supplied.
offset: Offset on the linear scale

Value

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

Details

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

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 .

A new bootstrap-based stopping criterion in PLS component construction, J. Magnanensi, M. Maumy-Bertrand, N. Meyer and F. Bertrand (2016), in The Multiple Facets of Partial Least Squares and Related Methods, doi:10.1007/978-3-319-40643-5_18

A new universal resample-stable bootstrap-based stopping criterion for PLS component construction, J. Magnanensi, F. Bertrand, M. Maumy-Bertrand and N. Meyer, (2017), Statistics and Computing, 27, 757–774. doi:10.1007/s11222-016-9651-4

New developments in Sparse PLS regression, J. Magnanensi, M. Maumy-Bertrand, N. Meyer and F. Bertrand, (2021), Frontiers in Applied Mathematics and Statistics, doi:10.3389/fams.2021.693126
.

Author

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

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

Examples

set.seed(314)
ncomp=rep(3,100)
totdimpos=7:50
totdim=sample(totdimpos,100,replace=TRUE)
l=3.01
#for (l in seq(3.01,15.51,by=0.5)) {
j=3.01
#for (j in seq(3.01,9.51,by=0.5))  {
i=44
#for ( i in 1:100){
set.seed(i)
totdimi<-totdim[i]
ncompi<-ncomp[i]
datasim <- t(replicate(200,simul_data_UniYX_gamma(totdimi,ncompi,j,l)))
#}
#}
#}
pairs(datasim)

rm(i,j,l,totdimi,ncompi,datasim)