# mvrVal

##### 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.

- Keywords
- multivariate, regression

##### Usage

```
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, ...)

R2(object, ...)
# S3 method for mvr
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, …)

##### Arguments

- 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`

##### Details

`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.

##### Value

`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

##### References

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

##### Examples

```
# NOT RUN {
data(oliveoil)
mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO")
RMSEP(mod)
# }
# NOT RUN {
plot(R2(mod))
# }
```

*Documentation reproduced from package pls, version 2.7-2, License: GPL-2*