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)formula |
a model formula. Most of the |
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 |
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 |
method |
the multivariate regression method to be used. If
|
scale |
numeric vector, or logical. If numeric vector, X
is scaled by dividing each variable with the corresponding element
of |
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 |
x |
a logical. If |
y |
a logical. If |
weights |
a vector of individual weights for the observations.
Only used for |
... |
additional optional arguments, passed to the underlying fit
functions, and Currently, the fit functions
and
See the functions' documentation for details. |
The functions fit PLSR, CPPLS or PCR models with 1, …,
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.
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 |
fit.time |
the elapsed time for the fit. This is used by
|
na.action |
if observations with missing values were removed,
|
ncomp |
the number of components of the model. |
method |
the method used to fit the model. See the argument
|
scale |
if scaling was requested (with |
call |
the function call. |
terms |
the model terms. |
model |
if |
x |
if |
y |
if |
Ron Wehrens and Bjørn-Helge Mevik
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.
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")
## Not run:
## 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()
## End(Not run)
## 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).Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.