plsdepot (version 0.2.0)

plsreg1: PLS-R1: Partial Least Squares Regression 1

Description

The function plsreg1 performs Partial Least Squares Regression for the univariate case (i.e. one response variable)

Usage

plsreg1(predictors, response, comps = 2, crosval = TRUE)

Value

An object of class "plsreg1", basically a list with the following elements:

x.scores

PLS components (also known as T-components)

x.loads

loadings of the predictor variables

y.scores

scores of the response variable (also known as U-components)

y.loads

loadings of the response variable

cor.xyt

Correlations between the variables and the PLS components

raw.wgs

weights to calculate the PLS scores with the deflated matrices of predictor variables

mod.wgs

modified weights to calculate the PLS scores with the matrix of predictor variables

std.coefs

Vector of standardized regression coefficients

reg.coefs

Vector of regression coefficients (used with the original data scale)

R2

Vector of PLS R-squared

R2Xy

explained variance of variables by PLS-components

y.pred

Vector of predicted values

resid

Vector of residuals

T2

Table of Hotelling T2 values (used to detect atypical observations)

Q2

Table with the cross validation results. Includes: PRESS, RSS, Q2, and cummulated Q2. Only available when crosval=TRUE

Arguments

predictors

A numeric matrix or data frame with the predictor variables (which may contain missing data).

response

A numeric vector for the reponse variable. No missing data allowed.

comps

The number of extracted PLS components (2 by default).

crosval

Logical indicating whether cross-validation should be performed (TRUE by default). No cross-validation is done if there is missing data or if there are less than 10 observations.

Author

Gaston Sanchez

Details

The minimum number of PLS components (comps) to be extracted is 2.

The data is scaled to standardized values (mean=0, variance=1).

The argument crosval gives the option to perform cross-validation. This parameter takes into account how comps is specified. When comps=NULL, the number of components is obtained by cross-validation. When a number of components is specified, cross-validation results are calculated for each component.

References

Geladi, P., and Kowalski, B. (1986) Partial Least Squares Regression: A Tutorial. Analytica Chimica Acta, 185, pp. 1-17.

Tenenhaus, M. (1998) La Regression PLS. Theorie et Pratique. Editions TECHNIP, Paris.

Tenenhaus, M., Gauchi, J.-P., and Menardo, C. (1995) Regression PLS et applications. Revue de statistique appliquee, 43, pp. 7-63.

See Also

plot.plsreg1, plsreg2.

Examples

if (FALSE) {
 ## example of PLSR1 with the vehicles dataset
 # predictand variable: price of vehicles
 data(vehicles)

 # apply plsreg1 extracting 2 components (no cross-validation)
 pls1_one = plsreg1(vehicles[,1:12], vehicles[,13,drop=FALSE], comps=2, crosval=FALSE)

 # apply plsreg1 with selection of components by cross-validation
 pls1_two = plsreg1(vehicles[,1:12], vehicles[,13,drop=FALSE], comps=NULL, crosval=TRUE)

 # apply plsreg1 extracting 5 components with cross-validation
 pls1_three = plsreg1(vehicles[,1:12], vehicles[,13,drop=FALSE], comps=5, crosval=TRUE)

 # plot variables
 plot(pls1_one)
 }