Partial Least Squares and Principal Component Regression

Functions to perform partial least squares regression (PLSR), canonical powered partial least squares (CPPLS) or principal component regression (PCR), with a formula interface. Cross-validation can be used. Prediction, model extraction, plot, print and summary methods exist.

mvr(formula, ncomp, Y.add, data, subset, na.action,
    method = pls.options()$mvralg,
    scale = FALSE, center = TRUE, validation = c("none", "CV", "LOO"),
    model = TRUE, x = FALSE, y = FALSE, ...)
plsr(..., method = pls.options()$plsralg)
cppls(..., Y.add, weights, method = pls.options()$cpplsalg)
pcr(..., method = pls.options()$pcralg)

Arguments

formula	a model formula. Most of the lm formula constructs are supported. See below.
ncomp	the number of components to include in the model (see below).
Y.add	a vector or matrix of additional responses containing relevant information about the observations. Only used for cppls.
data	an optional data frame with the data to fit the model from.
subset	an optional vector specifying a subset of observations to be used in the fitting process.
na.action	a function which indicates what should happen when the data contain missing values. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful. See na.omit for other alternatives.
method	the multivariate regression method to be used. If "model.frame", the model frame is returned.
scale	numeric vector, or logical. If numeric vector, \(X\) is scaled by dividing each variable with the corresponding element of scale. If scale is TRUE, \(X\) is scaled by dividing each variable by its sample standard deviation. If cross-validation is selected, scaling by the standard deviation is done for every segment.
center	logical, determines if the \(X\) and \(Y\) matrices are mean centered or not. Default is to perform mean centering.
validation	character. What kind of (internal) validation to use. See below.
model	a logical. If TRUE, the model frame is returned.
x	a logical. If TRUE, the model matrix is returned.
y	a logical. If TRUE, the response is returned.
weights	a vector of individual weights for the observations. Only used for cppls. (Optional)
...	additional optional arguments, passed to the underlying fit functions, and mvrCv. Currently, the fit functions oscorespls.fit and widekernelpls.fit implement these extra arguments: tol: numeric. Tolerance used for determining convergence. maxit: positive integer. The maximal number of iterations used. and cppls.fit implements: lower: a vector of lower limits for power optimisation. upper: a vector of upper limits for power optimisation. trunc.pow: logical. Whether to use an experimental alternative power algorithm. mvrCv implements several arguments; the following are probably the most useful of them: segments: the number of segments to use, or a list with segments. segment.type: the type of segments to use. length.seg: Positive integer. The length of the segments to use. jackknife: logical. Whether to perform jackknifing of regression coefficients. See the functions' documentation for details.

Details

The functions fit PLSR, CPPLS or PCR models with 1, \(\ldots\), ncomp number of components. Multi-response models are fully supported.

The type of model to fit is specified with the method argument. Four PLSR algorithms are available: the kernel algorithm ("kernelpls"), the wide kernel algorithm ("widekernelpls"), SIMPLS ("simpls") and the classical orthogonal scores algorithm ("oscorespls"). One CPPLS algorithm is available ("cppls") providing several extensions to PLS. One PCR algorithm is available: using the singular value decomposition ("svdpc"). If method is "model.frame", the model frame is returned. The functions pcr, plsr and cppls are wrappers for mvr, with different values for method.

The formula argument should be a symbolic formula of the form response ~ terms, where response is the name of the response vector or matrix (for multi-response models) and terms is the name of one or more predictor matrices, usually separated by +, e.g., water ~ FTIR or y ~ X + Z. See lm for a detailed description. The named variables should exist in the supplied data data frame or in the global environment. Note: Do not use mvr(mydata$y ~ mydata$X, ...), instead use mvr(y ~ X, data = mydata, ...). Otherwise, predict.mvr will not work properly. The chapter Statistical models in R of the manual An Introduction to R distributed with R is a good reference on formulas in R.

The number of components to fit is specified with the argument ncomp. It this is not supplied, the maximal number of components is used (taking account of any cross-validation).

All implemented algorithms mean-center both predictor and response matrices. This can be turned off by specifying center = FALSE. See Seasholtz and Kowalski for a discussion about centering in PLS regression.

If validation = "CV", cross-validation is performed. The number and type of cross-validation segments are specified with the arguments segments and segment.type. See mvrCv for details. If validation = "LOO", leave-one-out cross-validation is performed. It is an error to specify the segments when validation = "LOO" is specified.

By default, the cross-validation will be performed serially. However, it can be done in parallel using functionality in the parallel package by setting the option parallel in pls.options. See pls.options for the differnt ways to specify the parallelism. See also Examples below.

Note that the cross-validation is optimised for speed, and some generality has been sacrificed. Especially, the model matrix is calculated only once for the complete cross-validation, so models like y ~ msc(X) will not be properly cross-validated. However, scaling requested by scale = TRUE is properly cross-validated. For proper cross-validation of models where the model matrix must be updated/regenerated for each segment, use the separate function crossval.

Value

If method = "model.frame", the model frame is returned. Otherwise, an object of class mvr is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following components:

validation

if validation was requested, the results of the cross-validation. See mvrCv for details.

fit.time

the elapsed time for the fit. This is used by crossval to decide whether to turn on tracing.

na.action

if observations with missing values were removed, na.action contains a vector with their indices. The class of this vector is used by functions like fitted to decide how to treat the observations.

ncomp

the number of components of the model.

method

the method used to fit the model. See the argument method for possible values.

scale

if scaling was requested (with scale), the scaling used.

call

the function call.

terms

the model terms.

model

if model = TRUE, the model frame.

x

if x = TRUE, the model matrix.

y

if y = TRUE, the model response.

References

Martens, H., Næs, T. (1989) Multivariate calibration. Chichester: Wiley.

Seasholtz, M. B. and Kowalski, B. R. (1992) The effect of mean centering on prediction in multivariate calibration. Journal of Chemometrics, 6(2), 103--111.

See also

kernelpls.fit, widekernelpls.fit, simpls.fit, oscorespls.fit, cppls.fit, svdpc.fit, mvrCv, crossval, loadings, scores, loading.weights, coef.mvr, predict.mvr, R2, MSEP, RMSEP, plot.mvr

Examples

data(yarn)
## Default methods:
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.cppls <- cppls(density ~ NIR, 6, data = yarn, validation = "CV")

## Alternative methods:
yarn.oscorespls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",
                      method = "oscorespls")
yarn.simpls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",
                  method = "simpls")

if (FALSE) {
## Parallelised cross-validation, using transient cluster:
pls.options(parallel = 4) # use mclapply
pls.options(parallel = quote(makeCluster(4, type = "PSOCK"))) # use parLapply
## A new cluster is created and stopped for each cross-validation:
yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")

## Parallelised cross-validation, using persistent cluster:
library(parallel)
## This creates the cluster:
pls.options(parallel = makeCluster(4, type = "PSOCK"))
## The cluster can be used several times:
yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")
## The cluster should be stopped manually afterwards:
stopCluster(pls.options()$parallel)

## Parallelised cross-validation, using persistent MPI cluster:
## This requires the packages snow and Rmpi to be installed
library(parallel)
## This creates the cluster:
pls.options(parallel = makeCluster(4, type = "MPI"))
## The cluster can be used several times:
yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")
## The cluster should be stopped manually afterwards:
stopCluster(pls.options()$parallel)
## It is good practice to call mpi.exit() or mpi.quit() afterwards:
mpi.exit()
}

## Multi-response models:
data(oliveoil)
sens.pcr <- pcr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)
sens.pls <- plsr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)

## Classification
# A classification example utilizing additional response information
# (Y.add) is found in the cppls.fit manual ('See also' above).