gpls: A function to fit Generalized partial least squares models.

Description

Partial least squares is a commonly used dimension reduction technique. The paradigm can be extended to include generalized linear models in several different ways. The code in this function uses the extension proposed by Ding and Gentleman, 2004.

Usage

gpls(x, ...)
"gpls"(x, y, K.prov=NULL, eps=1e-3, lmax=100, b.ini=NULL, denom.eps=1e-20, family="binomial", link=NULL, br=TRUE, ...)
"gpls"(formula, data, contrasts=NULL, K.prov=NULL,
eps=1e-3, lmax=100, b.ini=NULL, denom.eps=1e-20, family="binomial",
link=NULL, br=TRUE, ...)

Arguments

The matrix of covariates.

formula

A formula of the form 'y ~ x1 + x2 + ...', where y is the response and the other terms are covariates.

The vector of responses

data

A data.frame to resolve the forumla, if used

K.prov

number of PLS components, default is the rank of X

eps

tolerance for convergence

lmax

maximum number of iteration allowed

b.ini

initial value of regression coefficients

denom.eps

small quanitity to guarantee nonzero denominator in deciding convergence

family

glm family, binomial is the only relevant one here

link

link function, logit is the only one practically implemented now

TRUE if Firth's bias reduction procedure is used

...

Additional arguements.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

Value

coefficients: The estimated coefficients.
convergence: A boolean indicating whether convergence was achieved.
niter: The total number of iterations.
bias.reduction: A boolean indicating whether Firth's procedure was used.
family: The family argument that was passed in.
link: The link argument that was passed in.
terms: The constructed terms object.
call: The call
levs: The factor levels for prediction.

Details

This is a different interface to the functionality provided by glpls1a. The interface is intended to be simpler to use and more consistent with other matchine learning code in R.

The technology is intended to deal with two class problems where there are more predictors than cases. If a response variable (y) is used that has more than two levels the behavior may be unusual.

References

Ding, B.Y. and Gentleman, R. (2003) Classification using generalized partial least squares.
Marx, B.D (1996) Iteratively reweighted partial least squares estimation for generalized linear regression. Technometrics 38(4): 374-381.

Examples

Run this code

library(MASS)
m1 = gpls(type~., data=Pima.tr, K=3)

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