plsdof: benchmark.regression – R documentation

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benchmark.regression

Comparison of Partial Least Squares Regression, Principal Components Regression and Ridge Regression.

Description

This function computes the test error over several runs for (a) PLS, (b) PCR (c) Ridge Regression and (d) the null model, that is the mean of y. In the first three cases, the optimal model is selected via cross-validation.

Usage

benchmark.regression(
  X,
  y,
  m = ncol(X),
  R = 20,
  ratio = 0.8,
  verbose = TRUE,
  k = 10,
  nsamples = nrow(X),
  use.kernel = FALSE,
  supervised = FALSE
)

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 components for PLS. Default is `m=ncol(X)`.
`R`	number of runs. Default is 20.
`ratio`	ratio no of training examples/(no of training examples + no of test examples). Default is 0.8
`verbose`	If `TRUE`, the functions plots the progress of the function. Default is `TRUE`.
`k`	number of cross-validation splits. Default is 10.
`nsamples`	number of data points. Default is `nrow(X)`.
`use.kernel`	Use kernel representation for PLS? Default is `use.kernel=FALSE`.
`supervised`	Should the principal components be sorted by decreasing squared correlation to the response? Default is FALSE.

Details

The function computes the test error, the cross-validation-optimal model parameters, their corresponding Degrees of Freedom, and the sum-of-squared-residuals (SSR) for PLS and PCR.

Value

`MSE`	data frame of size R x 4. It contains the test error for the four different methods for each of the R runs.
`M`	data frame of size R x 4. It contains the optimal model parameters for the four different methods for each of the R runs.
`DoF`	data frame of size R x 4. It contains the Degrees of Freedom (corresponding to `M`) for the four different methods for each of the R runs.
`res.pls`	matrix of size R x (ncol(X+1)). It contains the SSR for PLS for each of the R runs.
`res.pcr`	matrix of size R x (ncol(X+1)). It contains the SSR for PCR for each of the R runs.
`DoF.all`	matrix of size R x (ncol(X+1)). It contains the Degrees of Freedom for PLS for all components for each of the R runs.

Author(s)

Nicole Kraemer

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

Examples

# Boston Housing data
library(MASS)
data(Boston)
X<-as.matrix(Boston[,1:4]) # select the first 3 columns as predictor variables
y<-as.vector(Boston[,14])

my.benchmark<-benchmark.regression(X,y,ratio=0.5,R=10,k=5)

# boxplot of the mean squared error

boxplot(my.benchmark$MSE,outline=FALSE)

# boxplot of the degrees of freedom, without the null model

boxplot(my.benchmark$DoF[,-4])

plsdof

Degrees of Freedom and Statistical Inference for Partial Least Squares Regression

v0.3-0

GPL (>= 2)

Authors

Nicole Kraemer, Mikio L. Braun

Initial release

2021-03-13