R: Partial Least Squares and Principal Component Regression

mvr {pls} | R Documentation

## Partial Least Squares and Principal Component Regression

### Description

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.

### Usage

    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 arguments, passed to the underlying fit functions, and `mvrCv`.

### 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`.

### 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.

### Author(s)

Ron Wehrens and Bjørn-Helge Mevik

### 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")

    ## 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).

[Package pls version 2.7-0 Index]