Univariate Partial Least Squares Regression

Usage

svdpls1c(X, y, K=r)

Arguments

X Matrix of explanatory variables. Each column represents a variable and each row an observation. The columns of this matrix are assumed to have been centred. The number of rows of X should equal the number of observations in y. NAs and Infs are not allowed.
y Vector of responses. y is assumed to have been centred. NAs and Infs are not allowed.
K Number of PLS factors to fit in the PLS regression. This must be less than or equal to the rank of X.

Description

Performs univariate partial least squares (PLS) regression of a vector on a matrix of explanatory variables using a modified version of an algorithm given in Helland (1988)

Details

Univariate Partial Least Squares Regression is an example of a regularised regression method. It creates a lower dimensional representation of the original explanatory variables and uses this representation in an ordinary least squares regression of the response variables. (cf. Principal Components Regression). Unlike Principal Components Regression, PLS regression chooses the lower dimensional representation of the original explanatory variables with reference to the response variable y.

Value

a vector of regression coefficients

References

Denham, M. C. (1992). Implementing partial least squares. Technical Report. Liverpool University

Helland, I. S. (1988). On the Structure of partial least squares regression, Communications in Statistics, 17, pp. 581-607

Martens, H. and Naes, T. (1989). Multivariate Calibration. Wiley, New York.

See Also

pls1a,pls1b,svdpls1a,svdpls1b,svdpls1c

Examples

data(crimes)
attach(crimes)
svdpls1c(scale(cbind(Murder, Assault, UrbanPop),scale=FALSE), 
      scale(Rape,scale=FALSE), 2)


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