CPPLS (Indahl et al.)

Fits a PLS model using the CPPLS algorithm.

Usage

cppls.fit(
  X,
  Y,
  ncomp,
  Y.add = NULL,
  center = TRUE,
  stripped = FALSE,
  lower = 0.5,
  upper = 0.5,
  trunc.pow = FALSE,
  weights = NULL,
  ...
)

Arguments

X: a matrix of observations. NAs and Infs are not allowed.
Y: a vector or matrix of responses. NAs and Infs are not allowed.
ncomp: the number of components to be used in the modelling.
Y.add: a vector or matrix of additional responses containing relevant information about the observations.
center: logical, determines if the \(X\) and \(Y\) matrices are mean centered or not. Default is to perform mean centering.
stripped: logical. If TRUE the calculations are stripped as much as possible for speed; this is meant for use with cross-validation or simulations when only the coefficients are needed. Defaults to FALSE.
lower: a vector of lower limits for power optimisation. Defaults to 0.5.
upper: a vector of upper limits for power optimisation. Defaults to 0.5.
trunc.pow: logical. If TRUE an experimental alternative power algorithm is used. (Optional)
weights: a vector of individual weights for the observations. (Optional)
...: other arguments. Currently ignored.

Value

A list containing the following components is returned:

coefficients: an array of regression coefficients for 1, ..., ncomp components. The dimensions of coefficients are c(nvar, npred, ncomp) with nvar the number of X variables and npred the number of variables to be predicted in Y.
scores: a matrix of scores.
loadings: a matrix of loadings.
loading.weights: a matrix of loading weights.
Yscores: a matrix of Y-scores.
Yloadings: a matrix of Y-loadings.
projection: the projection matrix used to convert X to scores.
Xmeans: a vector of means of the X variables.
Ymeans: a vector of means of the Y variables.
fitted.values: an array of fitted values. The dimensions of fitted.values are c(nobj, npred, ncomp) with nobj the number samples and npred the number of Y variables.
residuals: an array of regression residuals. It has the same dimensions as fitted.values.
Xvar: a vector with the amount of X-variance explained by each component.
Xtotvar: total variance in X.
gammas: gamma-values obtained in power optimisation.
canonical.correlations: Canonical correlation values from the calculations of loading weights.
A: matrix containing vectors of weights a from canonical correlation (cor(Za,Yb)).
smallNorms: vector of indices of explanatory variables of length close to or equal to 0.

If stripped is TRUE, only the components coefficients, Xmeans, Ymeans and gammas are returned.

Details

This function should not be called directly, but through the generic functions cppls or mvr with the argument method="cppls". Canonical Powered PLS (CPPLS) is a generalisation of PLS incorporating discrete and continuous responses (also simultaneously), additional responses, individual weighting of observations and power methodology for sharpening focus on groups of variables. Depending on the input to cppls it can produce the following special cases:

PLS: uni-response continuous Y
PPLS: uni-response continuous Y, (lower || upper) != 0.5
PLS-DA (using correlation maximisation - B/W): dummy-coded descrete response Y
PPLS-DA: dummy-coded descrete response Y, (lower || upper) != 0.5
CPLS: multi-response Y (continuous, discrete or combination)
CPPLS: multi-response Y (continuous, discrete or combination), (lower || upper) != 0.5

The name "canonical" comes from canonical correlation analysis which is used when calculating vectors of loading weights, while "powered" refers to a reparameterisation of the vectors of loading weights which can be optimised over a given interval.

References

Indahl, U. (2005) A twist to partial least squares regression. Journal of Chemometrics, 19, 32–44.

Liland, K.H and Indahl, U.G (2009) Powered partial least squares discriminant analysis, Journal of Chemometrics, 23, 7–18.

Indahl, U.G., Liland, K.H. and Næs, T. (2009) Canonical partial least squares - a unified PLS approach to classification and regression problems. Journal of Chemometrics, 23, 495–504.

Author

Kristian Hovde Liland

Examples


data(mayonnaise)
# Create dummy response
mayonnaise$dummy <-
    I(model.matrix(~y-1, data.frame(y = factor(mayonnaise$oil.type))))

# Predict CPLS scores for test data
may.cpls <- cppls(dummy ~ NIR, 10, data = mayonnaise, subset = train)
may.test <- predict(may.cpls, newdata = mayonnaise[!mayonnaise$train,], type = "score")

# Predict CPLS scores for test data (experimental used design as additional Y information)
may.cpls.yadd <- cppls(dummy ~ NIR, 10, data = mayonnaise, subset = train, Y.add=design)
may.test.yadd <- predict(may.cpls.yadd, newdata = mayonnaise[!mayonnaise$train,], type = "score")

# Classification by linear discriminant analysis (LDA)
library(MASS)
error <- matrix(ncol = 10, nrow = 2)
dimnames(error) <- list(Model = c('CPLS', 'CPLS (Y.add)'), ncomp = 1:10)
for (i in 1:10) {
    fitdata1 <- data.frame(oil.type = mayonnaise$oil.type[mayonnaise$train],
                           NIR.score = I(may.cpls$scores[,1:i,drop=FALSE]))
    testdata1 <- data.frame(oil.type = mayonnaise$oil.type[!mayonnaise$train],
                            NIR.score = I(may.test[,1:i,drop=FALSE]))
    error[1,i] <-
        (42 - sum(predict(lda(oil.type ~ NIR.score, data = fitdata1),
                  newdata = testdata1)$class == testdata1$oil.type)) / 42
    fitdata2 <- data.frame(oil.type = mayonnaise$oil.type[mayonnaise$train],
                           NIR.score = I(may.cpls.yadd$scores[,1:i,drop=FALSE]))
    testdata2 <- data.frame(oil.type = mayonnaise$oil.type[!mayonnaise$train],
                            NIR.score = I(may.test.yadd[,1:i,drop=FALSE]))
    error[2,i] <-
        (42 - sum(predict(lda(oil.type ~ NIR.score, data = fitdata2),
                  newdata = testdata2)$class == testdata2$oil.type)) / 42
}
round(error,2)
#>               ncomp
#> Model             1    2    3    4    5    6    7    8 9 10
#>   CPLS         0.29 0.29 0.19 0.17 0.24 0.14 0.05 0.02 0  0
#>   CPLS (Y.add) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0  0