pls (version 2.9-0)

simpls.fit: Sijmen de Jong's SIMPLS

Description

Fits a PLSR model with the SIMPLS algorithm.

Usage

simpls.fit(
  X,
  Y,
  ncomp,
  center = TRUE,
  orthScores = FALSE,
  stripped = FALSE,
  ...
)

Value

A list containing the following components is returned:

coefficients

an array of regression coefficients for 1, ..., ncomp components. The dimensions of coefficients are c(nvar, npred, ncomp) with nvar the number of X variables and npred the number of variables to be predicted in Y.

scores

a matrix of scores.

loadings

a matrix of loadings.

Yscores

a matrix of Y-scores.

Yloadings

a matrix of Y-loadings.

projection

the projection matrix used to convert X to scores.

Xmeans

a vector of means of the X variables.

Ymeans

a vector of means of the Y variables.

fitted.values

an array of fitted values. The dimensions of fitted.values are c(nobj, npred, ncomp) with nobj the number samples and npred the number of Y variables.

residuals

an array of regression residuals. It has the same dimensions as fitted.values.

Xvar

a vector with the amount of X-variance explained by each component.

Xtotvar

Total variance in X.

If stripped is TRUE, only the components coefficients, Xmeans and Ymeans are returned.

Details

This function should not be called directly, but through the generic functions plsr or mvr with the argument method="simpls". SIMPLS is much faster than the NIPALS algorithm, especially when the number of X variables increases, but gives slightly different results in the case of multivariate Y. SIMPLS truly maximises the covariance criterion. According to de Jong, the standard PLS2 algorithms lie closer to ordinary least-squares regression where a precise fit is sought; SIMPLS lies closer to PCR with stable predictions.

References

de Jong, S. (1993) SIMPLS: an alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18, 251--263.

See Also

mvr plsr pcr kernelpls.fit widekernelpls.fit oscorespls.fit

Examples

## Simulation of SIMPLS stability
# The graphics produced, demonstrate the numeric instability of the original
# SIMPLS without score orthogonalization.
set.seed(42)
N <- 100
p <- 2000
ncomp <- 40
simData <- data.frame(X = I(matrix(rnorm(N*p),N)), y = rnorm(N))
pls    <- plsr(y ~ X, data=simData, ncomp=ncomp)
simps  <- plsr(y ~ X, data=simData, ncomp=ncomp, method="simpls")
simpsO <- plsr(y ~ X, data=simData, ncomp=ncomp, method="simpls", orthScores=TRUE)
normScores <- pls$scores
for(i in 1:ncomp)
  normScores[,i] <- normScores[,i]/sqrt(sum(normScores[,i]^2))

# Check number of equal digits
eqDig <- function(x,y){
  xy <- abs(x - y)
  xy[xy == 0] <- 10^-16
  -colMeans(log10(xy))
}
eqDig_PLS_oSIMPLS    <- eqDig(normScores, simpsO$scores)
eqDig_SIMPLS_PLS     <- eqDig(simps$scores, normScores)
eqDig_SIMPLS_oSIMPLS <- eqDig(simps$scores, simpsO$scores)
# Correlation between models
cor_PLS_oSIMPLS    <- diag(cor(pls$scores,simps$scores))
cor_SIMPLS_oSIMPLS <- diag(cor(pls$scores,simpsO$scores))
cor_SIMPLS_PLS     <- diag(cor(simps$scores,simpsO$scores))

par.old <- par(mfrow=c(2,1), mar=c(4,4,1,1), las=1)
matplot(2:ncomp,cbind(eqDig_PLS_oSIMPLS,eqDig_SIMPLS_PLS, eqDig_SIMPLS_oSIMPLS)[-1,],
        type="l", xlab="component", ylab="equal digits", ylim=c(0,17),
        panel.first=grid())
legend("bottomleft", legend=c("PLS, SIMPLS", "PLS, OrthSIMPLS", "SIMPLS, OrthSIMPLS"),
       col=1:3, lty=1:3)
matplot(1:ncomp,cbind(cor_PLS_oSIMPLS,cor_SIMPLS_oSIMPLS,cor_SIMPLS_PLS), type="l",
        ylab="correlation", xlab="component", panel.first=grid())
legend("bottomleft", legend=c("PLS, SIMPLS", "PLS, OrthSIMPLS", "SIMPLS, OrthSIMPLS"),
       col=1:3, lty=1:3)
par(par.old)