Linear Partial Least Squares Fit

This function computes the Partial Least Squares solution and the first derivative of the regression coefficients. This implementation scales mostly in the number of variables

Usage

linear.pls.fit(
  X,
  y,
  m = ncol(X),
  compute.jacobian = FALSE,
  DoF.max = min(ncol(X) + 1, nrow(X) - 1)
)

Arguments

X: matrix of predictor observations.
y: vector of response observations. The length of y is the same as the number of rows of X.
m: maximal number of Partial Least Squares components. Default is m=ncol(X).
compute.jacobian: Should the first derivative of the regression coefficients be computed as well? Default is FALSE
DoF.max: upper bound on the Degrees of Freedom. Default is min(ncol(X)+1,nrow(X)-1).

Value

coefficients: matrix of regression coefficients
intercept: vector of regression intercepts
DoF: Degrees of Freedom
sigmahat: vector of estimated model error
Yhat: matrix of fitted values
yhat: vector of squared length of fitted values
RSS: vector of residual sum of error

covarianceif compute.jacobian is TRUE, the function returns the array of covariance matrices for the PLS regression coefficients.

TT: matrix of normalized PLS components

Details

We first standardize X to zero mean and unit variance.

References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

Author

Nicole Kraemer

Examples


n<-50 # number of observations
p<-5 # number of variables
X<-matrix(rnorm(n*p),ncol=p)
y<-rnorm(n)

pls.object<-linear.pls.fit(X,y,m=5,compute.jacobian=TRUE)