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.

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

# S3 method for mvr
R2(
object,
estimate,
newdata,
ncomp = 1:object$ncomp,
comps,
intercept = cumulative,
se = FALSE,
...
)

MSEP(object, ...)

# S3 method for mvr
MSEP(
object,
estimate,
newdata,
ncomp = 1:object$ncomp,
comps,
intercept = cumulative,
se = FALSE,
...
)

RMSEP(object, ...)

# S3 method for mvr
RMSEP(object, ...)

`mvrValstats`

returns a list with components

- SSE
three-dimensional array of SSE values. The first dimension is the different estimators, the second is the response variables and the third is the models.

- SST
matrix of SST values. The first dimension is the different estimators and the second is the response variables.

- nobj
a numeric vector giving the number of objects used for each estimator.

- comps
the components specified, with

`0`

prepended if`intercept`

is`TRUE`

.- cumulative
`TRUE`

if`comps`

was`NULL`

or not specified.

The other functions return an object of class `"mvrVal"`

, with
components

- val
three-dimensional array of estimates. The first dimension is the different estimators, the second is the response variables and the third is the models.

- type
`"MSEP"`

,`"RMSEP"`

or`"R2"`

.- comps
the components specified, with

`0`

prepended if`intercept`

is`TRUE`

.- cumulative
`TRUE`

if`comps`

was`NULL`

or not specified.- call
the function call

- object
an

`mvr`

object- estimate
a character vector. Which estimators to use. Should be a subset of

`c("all", "train", "CV", "adjCV", "test")`

.`"adjCV"`

is only available for (R)MSEP. See below for how the estimators are chosen.- newdata
a data frame with test set data.

- ncomp, comps
a vector of positive integers. The components or number of components to use. See below.

- intercept
logical. Whether estimates for a model with zero components should be returned as well.

- se
logical. Whether estimated standard errors of the estimates should be calculated. Not implemented yet.

- ...
further arguments sent to underlying functions or (for

`RMSEP`

) to`MSEP`

Ron Wehrens and Bjørn-Helge Mevik

`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.

`mvr`

, `crossval`

, `mvrCv`

,
`validationplot`

, `plot.mvrVal`

```
data(oliveoil)
mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO")
RMSEP(mod)
if (FALSE) plot(R2(mod))
```

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