Partial Least Squares and Principal Component Regression

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

multivariate, regression
mvr(formula, ncomp, data, subset, na.action,
    method = c("kernelpls", "simpls", "oscorespls", "svdpc", "model.frame"),
    scale = FALSE, validation = c("none", "CV", "LOO"),
    model = TRUE, x = FALSE, y = FALSE, ...)
plsr(..., method = c("kernelpls", "simpls", "oscorespls", "model.frame"))
pcr(..., method = c("svdpc", "model.frame"))
a model formula. Most of the lm formula constructs are supported. See below.
the number of components to include in the model (see below).
an optional data frame with the data to fit the model from.
an optional vector specifying a subset of observations to be used in the fitting process.
a function which indicates what should happen when the data contain missing values.
the multivariate regression method to be used. If "model.frame", the model frame is returned.
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 st
character. What kind of (internal) validation to use. See below.
a logical. If TRUE, the model frame is returned.
a logical. If TRUE, the model matrix is returned.
a logical. If TRUE, the response is returned.
additional arguments, passed to the underlying fit functions, and mvrCv.

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

Three PLSR algorithms are available: the kernel algorithm, SIMPLS and the classical orthogonal scores algorithm. One PCR algorithm is available: using the singular value decomposition. The type of regression is specified with the method argument. pcr and plsr 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 Ris 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).

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.

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:
  • validationif validation was requested, the results of the cross-validation. See mvrCv for details.
  • na.actionif 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.
  • ncompthe number of components of the model.
  • methodthe method used to fit the model. See the argument method for possible values.
  • scaleif scaling was requested (with scale), the scaling used.
  • callthe function call.
  • termsthe model terms.
  • modelif model = TRUE, the model frame.
  • xif x = TRUE, the model matrix.
  • yif y = TRUE, the model response.




Martens, H., N�s, T. (1989) Multivariate calibration. Chichester: Wiley.

See Also,,,, mvrCv, crossval, loadings, scores, loading.weights, coef.mvr, predict.mvr, R2, MSEP, RMSEP, plot.mvr

  • mvr
  • pcr
  • plsr
## Default methods:
NIR.pcr <- pcr(y ~ X, 6, data = NIR, validation = "CV")
NIR.pls <- plsr(y ~ X, 6, data = NIR, validation = "CV")

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

Pn <- scale(sensory$Panel)
Ql <- scale(sensory$Quality)
sens.pcr <- pcr(Ql ~ Pn, ncomp = 4)
sens.pls <- plsr(Ql ~ Pn, ncomp = 4)
Documentation reproduced from package pls, version 1.2-1, License: GPL version 2

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