d.spls.pls: Univariate Partial Least Squares regression
In dual.spls: Dual Sparse Partial Least Squares Regression

d.spls.pls

R Documentation

Univariate Partial Least Squares regression

Description

The function d.spls.pls performs the PLS1 dimensional reduction methodology using Wold's NIPALS algorithm. It is a Dual-SPLS regression with the norm

\Omega(w)=||w||_2.

Usage

d.spls.pls(X,y,ncp,verbose=TRUE)

Arguments

`X`	a numeric matrix of predictors values of dimension `(n,p)`. Each row represents one observation and each column one predictor variable.
`y`	a numeric vector or a one column matrix of responses. It represents the response variable for each observation.
`ncp`	a positive integer. `ncp` is the number of Dual-SPLS components.
`verbose`	a Boolean value indicating whether or not to display the iterations steps. Default value is `TRUE`.

Details

The resulting solution for w and hence for the coefficients vector, in the PLS regression for one component is w=X^Ty. In order to compute the next components, a deflation step is performed only considering the parts of X that are orthogonal to the previous components.

Value

A list of the following attributes

`Xmean`	the mean vector of the predictors matrix `X`.
`scores`	the matrix of dimension `(n,ncp)` where `n` is the number of observations.The `scores` represents the observations in the new component basis computed by the compression step of the Dual-SPLS.
`loadings`	the matrix of dimension `(p,ncp)` that represents the Dual-SPLS components.
`Bhat`	the matrix of dimension `(p,ncp)` that regroups the regression coefficients for each component.
`intercept`	the vector of intercept values for each component.
`fitted.values`	the matrix of dimension `(n,ncp)` that represents the predicted values of `y`
`residuals`	the matrix of dimension `(n,ncp)` that represents the residuals corresponding to the difference between the responses and the fitted values.
`type`	a character specifying the Dual-SPLS norm used. In this case it is `ridge`.

Author(s)

Louna Alsouki François Wahl

References

H. Wold. Path Models with Latent Variables: The NIPALS Approach. In H.M. Blalock et al., editor, Quantitative Sociology: International Perspectives on Mathematical and Statistical Model Building, pages 307–357. Academic Press, 1975.

Examples

### load dual.spls library
library(dual.spls)
### constructing the simulated example
oldpar <- par(no.readonly = TRUE)
n <- 100
p <- 50
nondes <- 20
sigmaondes <- 0.5
data=d.spls.simulate(n=n,p=p,nondes=nondes,sigmaondes=sigmaondes)

X <- data$X
y <- data$y

#fitting the model
mod.dspls <- d.spls.pls(X=X,y=y,ncp=10,verbose=TRUE)

str(mod.dspls)

### plotting the observed values VS predicted values for 6 components
plot(y,mod.dspls$fitted.values[,6], xlab="Observed values", ylab="Predicted values",
 main="Observed VS Predicted for 6 components")
points(-1000:1000,-1000:1000,type='l')

### plotting the regression coefficients
par(mfrow=c(3,1))

i=6
plot(1:dim(X)[2],mod.dspls$Bhat[,i],type='l',
    main=paste(" PLS , ncp =", i),
    ylab='',xlab='' )
par(oldpar)

dual.spls documentation built on April 19, 2023, 1:07 a.m.