mvr_dcv: Repeated double-cross-validation for PLS and PCR

In chemometrics: Multivariate Statistical Analysis in Chemometrics

Repeated double-cross-validation for PLS and PCR

Description

Performs a careful evaluation by repeated double-CV for multivariate regression methods, like PLS and PCR.

Usage

mvr_dcv(formula, ncomp, data, subset, na.action, 
  method = c("kernelpls", "widekernelpls", "simpls", "oscorespls", "svdpc"), 
  scale = FALSE, repl = 100, sdfact = 2, 
  segments0 = 4, segment0.type = c("random", "consecutive", "interleaved"), 
  length.seg0, segments = 10, segment.type = c("random", "consecutive", "interleaved"), 
  length.seg, trace = FALSE, plot.opt = FALSE, selstrat = "hastie", ...)

Arguments

formula	formula, like y~X, i.e., dependent~response variables
ncomp	number of PLS components
data	data frame to be analyzed
subset	optional vector to define a subset
na.action	a function which indicates what should happen when the data contain missing values
method	the multivariate regression method to be used, see mvr
scale	numeric vector, or logical. If numeric vector, X is scaled by dividing each variable with the corresponding element of 'scale'. If 'scale' is 'TRUE', X is scaled by dividing each variable by its sample standard deviation. If cross-validation is selected, scaling by the standard deviation is done for every segment.
repl	Number of replicattion for the double-CV
sdfact	factor for the multiplication of the standard deviation for the determination of the optimal number of components
segments0	the number of segments to use for splitting into training and test data, or a list with segments (see mvrCv)
segment0.type	the type of segments to use. Ignored if 'segments0' is a list
length.seg0	Positive integer. The length of the segments to use. If specified, it overrides 'segments' unless 'segments0' is a list
segments	the number of segments to use for selecting the optimal number if components, or a list with segments (see mvrCv)
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
trace	logical; if 'TRUE', the segment number is printed for each segment
plot.opt	if TRUE a plot will be generated that shows the selection of the optimal number of components for each step of the CV
selstrat	method that defines how the optimal number of components is selected, should be one of "diffnext", "hastie", "relchange"; see details
...	additional parameters

Details

In this cross-validation (CV) scheme, the optimal number of components is determined by an additional CV in the training set, and applied to the test set. The procedure is repeated repl times. There are different strategies for determining the optimal number of components (parameter selstrat): "diffnext" compares MSE+sdfact*sd(MSE) among the neighbors, and if the MSE falls outside this bound, this is the optimal number. "hastie" searches for the number of components with the minimum of the mean MSE's. The optimal number of components is the model with the smallest number of components which is still in the range of the MSE+sdfact*sd(MSE), where MSE and sd are taken from the minimum. "relchange" is a strategy where the relative change is combined with "hastie": First the minimum of the mean MSE's is searched, and MSE's of larger components are omitted. For this selection, the relative change in MSE compared to the min, and relative to the max, is computed. If this change is very small (e.g. smaller than 0.005), these components are omitted. Then the "hastie" strategy is applied for the remaining MSE's.

Value

resopt	array [nrow(Y) x ncol(Y) x repl] with residuals using optimum number of components
predopt	array [nrow(Y) x ncol(Y) x repl] with predicted Y using optimum number of components
optcomp	matrix [segments0 x repl] optimum number of components for each training set
pred	array [nrow(Y) x ncol(Y) x ncomp x repl] with predicted Y for all numbers of components
SEPopt	SEP over all residuals using optimal number of components
sIQRopt	spread of inner half of residuals as alternative robust spread measure to the SEPopt
sMADopt	MAD of residuals as alternative robust spread measure to the SEPopt
MSEPopt	MSEP over all residuals using optimal number of components
afinal	final optimal number of components
SEPfinal	vector of length ncomp with final SEP values; use the element afinal for the optimal SEP

Author(s)

Peter Filzmoser <[e-mail]>

References

K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.

See Also

mvr

Examples

data(NIR)
X <- NIR$xNIR[1:30,]      # first 30 observations - for illustration
y <- NIR$yGlcEtOH[1:30,1] # only variable Glucose
NIR.Glc <- data.frame(X=X, y=y)
res <- mvr_dcv(y~.,data=NIR.Glc,ncomp=10,method="simpls",repl=10)

chemometrics documentation built on Aug. 25, 2023, 5:18 p.m.