This function computes the optimal model parameters using one of three different model selection criteria (aic, bic, gmdl) and based on two different Degrees of Freedom estimates for PLS.
pls.ic( X, y, m = min(ncol(X), nrow(X) - 1), criterion = "bic", naive = FALSE, use.kernel = FALSE, compute.jacobian = FALSE, verbose = TRUE )
matrix of predictor observations.
vector of response observations. The length of
maximal number of Partial Least Squares components. Default is
Choice of the model selection criterion. One of the three options aic, bic, gmdl.
Use the naive estimate for the Degrees of Freedom? Default is
Use kernel representation? Default is
Should the first derivative of the regression
coefficients be computed as well? Default is
The function returns an object of class "plsdof".
Degrees of Freedom
optimal number of components
vector of estimated model errors
vector of regression coefficients
use.kernel=FALSE, the function returns the covariance matrix of the
optimal regression coefficients.
the number of components for which the algorithm returns negative Degrees of Freedom
There are two options to estimate the Degrees of Freedom of PLS:
naive=TRUE defines the Degrees of Freedom as the number of components
naive=FALSE uses the generalized notion of Degrees of
compute.jacobian=TRUE, the function uses the Lanczos
decomposition to derive the Degrees of Freedom, otherwise, it uses the
Krylov representation. (See Kraemer and Sugiyama (2011) for details.) The
latter two methods only differ with respect to the estimation of the noise
Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281.
Hansen, M., Yu, B. (2001). "Model Selection and Minimum Descripion Length Principle". Journal of the American Statistical Association, 96, 746 - 774
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
Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686.
Nicole Kraemer, Mikio L. Braun