Package `pcv`

implements Procrustes
cross-validation in R language.

Last version of the package (*1.1.0*) was released in August,
2023 and contains small improvements, better test coverage, as well as a
new experimental feature — CV scope. See details in the overall project
description.

You can install the package directly from CRAN by running
`install.packages("pcv")`

. If you already have the package
installed and want to update it to the newest version use:
`update.packages("pcv")`

There three main functions in the package:

`pcvpca()`

is implementation of PCV for PCA/SIMCA models.`pcvpcr()`

is implementation of PCV for PCR models.`pcvpls()`

is implementation of PCV for PLS models.

All three functions return PV-set generated with given parameters. The PV-set has the same size as the calibration set. In case of regression (PCR or PLS) PV-set is generated only for predictors (X), the response values for PV-set are the same as for the calibration set.

The last two functions return the PV-set with additional attribute,
`"D"`

which is matrix containing scaling factors (\(c_k/c\)), for each segment and each
component. See all details in the paper. The matrix
can be visualized as a heatmap, similar to the ones shown in the paper,
using method `plotD()`

which is also a part of the
package.

Below are examples of the functions syntax with all parameters:

```
# for PCA/SIMCA models
<- pcvpca(X, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
Xpv
# for PCR models
<- pcvpcr(X, y, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
Xpv
# for PLS models
<- pcvpls(X, y, ncomp = 20, center = TRUE, scale = FALSE, cv = list("ven", 4))
Xpv
# show heatmap for D values
plotD(Xpv)
# get the matrix D and show its values as boxplot
<- attr(Xpv, "D")
D boxplot(D)
```

Here `X`

is a matrix with predictors for your calibration
set (as a numerical matrix, not a data frame). In case of regression
model you also need to provide a vector or a matrix with response values
for the training set, `y`

. As mentioned above, the method
generates PV-set only for predictors, the response values for the
calibration set and for the PV-set are the same.

Parameter `ncomp`

is a number of principal components in
case of PCA/PCR models or number of latent variables in case of PLS
based method. Number of components must be large enough, larger than the
expected optimal number. In case of PCA use components which explain at
least 99% of the data.

Parameters `center`

and `scale`

define if the
predictors must be mean centered and/or standardized. By default
`center = TRUE`

and `scale = FALSE`

. Regardless
which settings you use, the resulted PV-set will be in original units
(uncentered and unstandardized), so you can compare it directly with the
calibration set.

Finally, parameter `cv`

defines how to split the rows of
the training set. The split is similar to cross-validation splits, as
PCV is based on cross-validation resampling. This parameter can have the
following values:

A list with 2 values:

`list("name", nseg)`

. In this case`"name"`

defines the way to make the split, you can select one of the following:`"loo"`

for leave-one-out,`"rand"`

for random splits or`"ven"`

for Venetian blinds (systematic) splits. The second parameter,`nseg`

, is a number of segments for splitting the rows into. For example,`cv = list("ven", 4)`

, shown in the code examples above, tells PCV to use Venetian blinds splits with 4 segments.A vector with integer numbers, e.g.

`cv = c(1, 2, 3, 1, 2, 3, 1, 2, 3)`

. In this case number of values in this vector must be the same as number of rows in the training set. The values specify which segment a particular row will belong to. In case of the example shown here, it is assumed that you have 9 rows in the calibration set, which will be split into 3 segments. The first segment will consist of measurements from rows 1, 4 and 7.

As it is written above, from *1.1.0*, there is additional
parameter, `cv.scope`

, which can have one of the two values,
`"global"`

or `"local"`

. The default value is
`"global"`

, if you want to try the local scope, just add this
parameter when you call one of the functions, like shown below:

```
# PCV for PLS models with local CV scope
<- pcvpls(X, y, ncomp = 20, cv = list("ven", 4), cv.scope = "local") Xpv
```

File `demo.R`

, which you can download from this repository
contains a demo code based on *Corn* dataset from the paper to be
published. See comments in the code for more details.

The package code will be improved and extended gradually. If you found a bug please report using issues or send an email.