R: MSEP, RMSEP and R2 of PLSR and PCR models

mvrVal {pls} | R Documentation

## MSEP, RMSEP and R2 of PLSR and PCR models

### Description

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.

### Usage

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

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

    R2(object, ...)
    ## S3 method for class '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

### Author(s)

Ron Wehrens and Bjørn-Helge Mevik

### 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

`mvr`, `crossval`, `mvrCv`, `validationplot`, `plot.mvrVal`

### Examples

    data(oliveoil)
    mod <- plsr(sensory ~ chemical, ncomp = 4, data = oliveoil, validation = "LOO")
    RMSEP(mod)
    ## Not run: plot(R2(mod))

[Package pls version 2.6-0 Index]