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.
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
Several estimators can be used.
"train" is the training
or calibration data estimate, also called (R)MSEC. For
this is the unadjusted $R^2$. It is
overoptimistic and should not be used for assessing models.
"CV" is the cross-validation estimate, and
the bias-corrected cross-validation estimate. They can only be
calculated if the model has been cross-validated.
"test" is the test set estimate, using
as test set.
Which estimators to use is decided as follows (see below for
estimate is not specified, the test set estimate is returned if
newdata is specified, otherwise the CV and adjusted CV (for
estimates if the model has been cross-validated, otherwise the
training data estimate. If
possible estimates are calculated. Otherwise, the specified estimates
Several model sizes can also be specified. If
comps is missing
length(ncomp) models are used, with
ncomp components, ...,
components. Otherwise, a single model with the components
comps[length(comps)] is used.
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 $PRESS$).
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
mvrValstats is a utility function that calculates the
statistics needed by
R2. It is not intended to
be used interactively. It accepts the same arguments as
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.
data(oliveoil) mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO") RMSEP(mod) plot(R2(mod))