MSEP, RMSEP and R2 of PLSR and PCR models

Functions to estimate the mean squared error of prediction (MSEP), root mean squared error of prediction (RMSEP) and $R^2$ (A.K.A. coefficient of multiple determination) for fitted PCR and PLSR models. Test-set, cross-validation and calibration-set estimates are implemented.

multivariate, regression
MSEP(object, ...)
## S3 method for class 'mvr':
MSEP(object, estimate, newdata, ncomp = 1:object$ncomp, comps,
     intercept = cumulative, se = FALSE, \dots)

RMSEP(object, ...) ## S3 method for class 'mvr': RMSEP(object, ...)

R2(object, estimate, newdata, ncomp = 1:object$ncomp, comps, intercept = cumulative, se = FALSE, ...)

mvrValstats(object, estimate, newdata, ncomp = 1:object$ncomp, comps, intercept = cumulative, se = FALSE, ...)


RMSEP simply calls MSEP and takes the square root of the estimates. It therefore accepts the same arguments as MSEP.

Several estimators can be used. "train" is the training or calibration data estimate, also called (R)MSEC. For R2, this is the unadjusted $R^2$. It is overoptimistic and should not be used for assessing models. "CV" is the cross-validation estimate, and "adjCV" (for RMSEP and MSEP) is the bias-corrected cross-validation estimate. They can only be calculated if the model has been cross-validated. Finally, "test" is the test set estimate, using newdata as test set.

Which estimators to use is decided as follows (see below for mvrValstats). If estimate is not specified, the test set estimate is returned if newdata is specified, otherwise the CV and adjusted CV (for RMSEP and MSEP) estimates if the model has been cross-validated, otherwise the training data estimate. If estimate is "all", all possible estimates are calculated. Otherwise, the specified estimates are calculated.

Several model sizes can also be specified. If comps is missing (or is NULL), length(ncomp) models are used, with ncomp[1] components, ..., ncomp[length(ncomp)] components. Otherwise, a single model with the components comps[1], ..., comps[length(comps)] is used. If intercept is TRUE, a model with zero components is also used (in addition to the above).

The $R^2$ values returned by "R2" are calculated as $1 - SSE/SST$, where $SST$ is the (corrected) total sum of squares of the response, and $SSE$ is the sum of squared errors for either the fitted values (i.e., the residual sum of squares), test set predictions or cross-validated predictions (i.e., the $PRESS$). For estimate = "train", this is equivalent to the squared correlation between the fitted values and the response. For estimate = "train", the estimate is often called the prediction $R^2$. mvrValstats is a utility function that calculates the statistics needed by MSEP and R2. It is not intended to be used interactively. It accepts the same arguments as MSEP and R2. However, the estimate argument must be specified explicitly: no partial matching and no automatic choice is made. The function simply calculates the types of estimates it knows, and leaves the other untouched.




Mevik, B.-H., Cederkvist, H. R. (2004) Mean Squared Error of Prediction (MSEP) Estimates for Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR). Journal of Chemometrics, 18(9), 422--429.

See Also

mvr, crossval, mvrCv, validationplot, plot.mvrVal

mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO")
Documentation reproduced from package pls, version 2.1-0, License: GPL-2

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