Cross-validation

Performs the cross-validation calculations for mvr.

mvrCv(X, Y, ncomp, Y.add = NULL, weights = NULL,
      method = pls.options()$mvralg, scale = FALSE,
      segments = 10, segment.type = c("random", "consecutive", "interleaved"),
      length.seg, jackknife = FALSE, trace = FALSE, ...)

Arguments

X	a matrix of observations. NAs and Infs are not allowed.
Y	a vector or matrix of responses. NAs and Infs are not allowed.
ncomp	the number of components to be used in the modelling.
Y.add	a vector or matrix of additional responses containing relevant information about the observations. Only used for cppls.
weights	a vector of individual weights for the observations. Only used for cppls. (Optional)
method	the multivariate regression method to be used.
scale	logical. If TRUE, the learning \(X\) data for each segment is scaled by dividing each variable by its sample standard deviation. The prediction data is scaled by the same amount.
segments	the number of segments to use, or a list with segments (see below).
segment.type	the type of segments to use. Ignored if segments is a list.
length.seg	Positive integer. The length of the segments to use. If specified, it overrides segments unless segments is a list.
jackknife	logical. Whether jackknifing of regression coefficients should be performed.
trace	logical; if TRUE, the segment number is printed for each segment.
...	additional arguments, sent to the underlying fit function.

Details

This function is not meant to be called directly, but through the generic functions pcr, plsr, cppls or mvr with the argument validation set to "CV" or "LOO". All arguments to mvrCv can be specified in the generic function call.

If segments is a list, the arguments segment.type and length.seg are ignored. The elements of the list should be integer vectors specifying the indices of the segments. See cvsegments for details.

Otherwise, segments of type segment.type are generated. How many segments to generate is selected by specifying the number of segments in segments, or giving the segment length in length.seg. If both are specified, segments is ignored.

If jackknife is TRUE, jackknifed regression coefficients are returned, which can be used for for variance estimation (var.jack) or hypothesis testing (jack.test).

X and Y do not need to be centered.

Note that this function cannot be used in situations where \(X\) needs to be recalculated for each segment (except for scaling by the standard deviation), for instance with msc or other preprocessing. For such models, use the more general (but slower) function crossval.

Also note that if needed, the function will silently(!) reduce ncomp to the maximal number of components that can be cross-validated, which is \(n - l - 1\), where \(n\) is the number of observations and \(l\) is the length of the longest segment. The (possibly reduced) number of components is returned as the component ncomp.

By default, the cross-validation will be performed serially. However, it can be done in parallel using functionality in the parallel package by setting the option parallel in pls.options. See pls.options for the different ways to specify the parallelism.

Value

A list with the following components:

method

equals "CV" for cross-validation.

pred

an array with the cross-validated predictions.

coefficients

(only if jackknife is TRUE) an array with the jackknifed regression coefficients. The dimensions correspond to the predictors, responses, number of components, and segments, respectively.

PRESS0

a vector of PRESS values (one for each response variable) for a model with zero components, i.e., only the intercept.

PRESS

a matrix of PRESS values for models with 1, ..., ncomp components. Each row corresponds to one response variable.

adj

a matrix of adjustment values for calculating bias corrected MSEP. MSEP uses this.

segments

the list of segments used in the cross-validation.

ncomp

the actual number of components used.

gamma

if method cppls is used, gamma values for the powers of each CV segment are returned.

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.

Note

The PRESS0 is always cross-validated using leave-one-out cross-validation. This usually makes little difference in practice, but should be fixed for correctness.

The current implementation of the jackknife stores all jackknife-replicates of the regression coefficients, which can be very costly for large matrices. This might change in a future version.

See also

mvr crossval cvsegments MSEP var.jack jack.test

Examples

data(yarn)
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV", segments = 10)
if (FALSE) plot(MSEP(yarn.pcr))