Degrees of Freedom and Statistical Inference for Partial Least Squares Regression
The plsdof package provides Degrees of Freedom estimates for Partial Least Squares (PLS) Regression.
Model selection for PLS is based on various information criteria (aic, bic, gmdl) or on cross-validation. Estimates for the mean and covariance of the PLS regression coefficients are available. They allow the construction of approximate confidence intervals and the application of test procedures.
Further, cross-validation procedures for Ridge Regression and Principal Components Regression are available.
| Package: | plsdof |
| Type: | Package |
| Version: | 0.2-9 |
| Date: | 2019-31-01 |
| License: | GPL (>=2) |
| LazyLoad: | yes |
Nicole Kraemer, Mikio L. Braun
Maintainer: Frederic Bertrand <frederic.bertrand@math.unistra.fr>
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
Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448
# Boston Housing data data(Boston) X<-as.matrix(Boston[,-14]) y<-as.vector(Boston[,14]) # compute PLS coefficients for the first 5 components and plot Degrees of Freedom my.pls1<-pls.model(X,y,m=5,compute.DoF=TRUE) plot(0:5,my.pls1$DoF,pch="*",cex=3,xlab="components",ylab="DoF",ylim=c(0,14)) # add naive estimate lines(0:5,1:6,lwd=3) # model selection with the Bayesian Information criterion mypls2<-pls.ic(X,y,criterion="bic") # model selection based on cross-validation. # returns the estimated covariance matrix of the regression coefficients mypls3<-pls.cv(X,y,compute.covariance=TRUE) my.vcov<-vcov(mypls3) my.sd<-sqrt(diag(my.vcov)) # standard deviation of the regression coefficients
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