This package is the R companion to the book "Introduction to Multivariate Statistical Analysis in Chemometrics" written by K. Varmuza and P. Filzmoser (2009).
Description
Included are functions for multivariate statistical methods, tools for diagnostics, multivariate calibration, cross validation and bootstrap, clustering, etc.
Details
The package can be used to verify the examples in the book. It can also be used to analyze own data.
Author(s)
P. Filzmoser <P.Filzmoser@tuwien.ac.at
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Plots classical and robust Mahalanobis distances
Description
For multivariate outlier detection the Mahalanobis distance can be used. Here a plot of the classical and the robust (based on the MCD) Mahalanobis distance is drawn.
Usage
Moutlier(X, quantile = 0.975, plot = TRUE, ...)
Arguments
X
numeric data frame or matrix
quantile
cut-off value (quantile) for the Mahalanobis distance
plot
if TRUE a plot is generated
...
additional graphics parameters, see par
Details
For multivariate normally distributed data, a fraction of 1-quantile of data can be declared as potential multivariate outliers. These would be identified with the Mahalanobis distance based on classical mean and covariance. For deviations from multivariate normality center and covariance have to be estimated in a robust way, e.g. by the MCD estimator. The resulting robust Mahalanobis distance is suitable for outlier detection. Two plots are generated, showing classical and robust Mahalanobis distance versus the observation numbers.
Value
md
Values of the classical Mahalanobis distance
rd
Values of the robust Mahalanobis distance
cutoff
Value with the outlier cut-off
...
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
data(glass.grp)
x=glass[,c(2,7)]
require(robustbase)
res <- Moutlier(glass,quantile=0.975,pch=glass.grp)
NIR data
Description
For 166 alcoholic fermentation mashes of different feedstock (rye, wheat and corn) we have 235 variables (X) containing the first derivatives of near infrared spectroscopy (NIR) absorbance values at 1115-2285 nm, and two variables (Y) containing the concentration of glucose and ethanol (in g/L).
Usage
data(NIR)Format
A data frame with 166 objects and 2 list elements:
xNIRdata frame with 166 rows and 235 columns
yGlcEtOHdata frame with 166 rows and 2 columns
Details
The data can be used for linear and non-linear models.
Source
B. Liebmann, A. Friedl, and K. Varmuza. Determination of glucose and ethanol in bioethanol production by near infrared spectroscopy and chemometrics. Anal. Chim. Acta, 642:171-178, 2009.
References
B. Liebmann, A. Friedl, and K. Varmuza. Determination of glucose and ethanol in bioethanol production by near infrared spectroscopy and chemometrics. Anal. Chim. Acta, 642:171-178, 2009.
Examples
data(NIR)
str(NIR)
GC retention indices
Description
For 209 objects an X-data set (467 variables) and a y-data set (1 variable) is available. The data describe GC-retention indices of polycyclic aromatic compounds (y) which have been modeled by molecular descriptors (X).
Usage
data(PAC)Format
A data frame with 209 objects and 2 list elements:
ynumeric vector with length 209
Xmatrix with 209 rows and 467 columns
Details
The data can be used for linear and non-linear models.
Source
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(PAC)
names(PAC)
Phenyl data set
Description
The data consist of mass spectra from 600 chemical compounds, where 300 contain a phenyl substructure (group 1) and 300 compounds do not contain this substructure (group 2). The mass spectra have been transformed to 658 variables, containing the mass spectral features. The 2 groups are coded as -1 (group 1) and +1 (group 2), and is provided as first last variable.
Usage
data(Phenyl)Format
A data frame with 600 observations on the following 659 variables.
grpa numeric vector
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Details
The data set can be used for classification in high dimensions.
Source
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(Phenyl)
str(Phenyl)
Generating random projection directions
Description
A matrix with pandom projection (RP) directions (columns) is generated according to a chosen distributions; optionally the random vectors are orthogonalized.
Usage
RPvectors(a, m, ortho = "none", distr = "uniform", par_unif = c(-1, 1),
par_norm = c(0, 1), par_eq = c(-1, 0, 1), par_uneq = c(-sqrt(3), 0, sqrt(3)),
par_uneqprob = c(1/6, 2/3, 1/6))
Arguments
a
number of generated vectors (>=1)
m
dimension of generated vectors (>=2)
ortho
orthogonalization of vectors: "none" ... no orthogonalization (default); "onfly" ... orthogonalization on the fly after each generated vector; "end" ... orthogonalization at the end, after the whole random matrix was generated
distr
distribution of generated random vector components: "uniform" ... uniformly distributed in range par_unif (see below); default U[-1, +1]; "normal" ... normally distributed with parameters par_norm (see below); typical N(0, 1); "randeq" ... random selection of values par_eq (see below) with equal probabilities; typically -1, 0, +1; "randuneq" ... random selection of values par_uneq (see below) with probabilties par_uneqprob (see below); typical -(3)^0.5 with probability 1/6; 0 with probability 2/3; +(3)^0.5 with probability 1/6
par_unif
parameters for range for distr=="uniform"; default to c(-1,1)
par_norm
parameters for mean and sdev for distr=="normal"; default to c(0,1)
par_eq
values for distr=="randeq" which are replicated; default to c(-1,0,1)
par_uneq
values for distr=="randuneq" which are replicated with probabilties par_uneqprob; default to c(-sqrt(3),0,sqrt(3))
par_uneqprob
probabilities for distr=="randuneq" to replicate values par_uneq; default to c(1/6,2/3,1/6)
Details
The generated random projections can be used for dimension reduction of multivariate data. Suppose we have a data matrix X with n rows and m columns. Then the call B <- RPvectors(a,m) will produce a matrix B with the random directions in its columns. The matrix product X times t(B) results in a matrix of lower dimension a. There are several options to generate the projection directions, like orthogonal directions, and different distributions with different parameters to generate the random numbers. Random Projection (RP) can have comparable performance for dimension reduction like PCA, but gives a big advantage in terms of computation time.
Value
The value returned is the matrix B with a columns of length m, representing the random vectors
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza, P. Filzmoser, and B. Liebmann. Random projection experiments with chemometric data. Journal of Chemometrics. To appear.
Examples
B <- RPvectors(a=5,m=10)
res <- t(B)
additive logratio transformation
Description
A data transformation according to the additive logratio transformation is done.
Usage
alr(X, divisorvar)
Arguments
X
numeric data frame or matrix
divisorvar
number of the column of X for the variable to divide with
Details
The alr transformation is one possibility to transform compositional data to a real space. Afterwards, the transformed data can be analyzed in the usual way.
Value
Returns the transformed data matrix with one variable (divisor variable) less.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
glass_alr <- alr(glass,1)
ash data
Description
Data from 99 ash samples originating from different biomass, measured on 9 variables; 8 log-transformed variables are added.
Usage
data(ash)Format
A data frame with 99 observations on the following 17 variables.
SOTa numeric vector
P2O5a numeric vector
SiO2a numeric vector
Fe2O3a numeric vector
Al2O3a numeric vector
CaOa numeric vector
MgOa numeric vector
Na2Oa numeric vector
K2Oa numeric vector
log(P2O5)a numeric vector
log(SiO2)a numeric vector
log(Fe2O3)a numeric vector
log(Al2O3)a numeric vector
log(CaO)a numeric vector
log(MgO)a numeric vector
log(Na2O)a numeric vector
log(K2O)a numeric vector
Details
The dependent variable Softening Temperature (SOT) of ash should be modeled by the elemental composition of the ash data. Data from 99 ash samples - originating from different biomass - comprise the experimental SOT (630-1410 centigrades), and the experimentally determined eight mass concentrations the listed elements. Since the distribution of the elements is skweed, the log-transformed variables have been added.
Source
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(ash)
str(ash)
Data from cereals
Description
For 15 cereals an X and Y data set, measured on the same objects, is available. The X data are 145 infrared spectra, and the Y data are 6 chemical/technical properties (Heating value, C, H, N, Starch, Ash). Also the scaled Y data are included (mean 0, variance 1 for each column). The cereals come from 5 groups B=Barley, M=Maize, R=Rye, T=Triticale, W=Wheat.
Usage
data(cereal)Format
A data frame with 15 objects and 3 list elements:
Xmatrix with 15 rows and 145 columns
Ymatrix with 15 rows and 6 columns
Yscmatrix with 15 rows and 6 columns
Details
The data set can be used for PLS2.
Source
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(cereal)
names(cereal)
centered logratio transformation
Description
A data transformation according to the centered logratio transformation is done.
Usage
clr(X)
Arguments
X
numeric data frame or matrix
Details
The clr transformation is one possibility to transform compositional data to a real space. Afterwards, the transformed data can be analyzed in the usual way.
Value
Returns the transformed data matrix with the same dimension as X.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
glass_clr <- clr(glass)
compute and plot cluster validity
Description
A cluster validity measure based on within- and between-sum-of-squares is computed and plotted for the methods k-means, fuzzy c-means, and model-based clustering.
Usage
clvalidity(x, clnumb = c(2:10))
Arguments
x
input data matrix
clnumb
range for the desired number of clusters
Details
The validity measure for a number k of clusters is
\sum_j W_j divided by \sum_{j<l} B_{jl} with
W_j is the sum of squared distances of the objects in each cluster
cluster to its center, and B_{jl} is the squared distance between
the cluster centers of cluster j and l.
Value
validity
vector with validity measure for the desired numbers of clusters
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
require(robustbase)
res <- pcaCV(glass,segments=4,repl=100,cex.lab=1.2,ylim=c(0,1),las=1)
Delete intercept from model matrix
Description
A utility function to delete any intercept column from a model matrix, and adjust the assign attribute correspondingly.
Usage
delintercept(mm)
Arguments
mm
Model matrix
Value
A model matrix without intercept column.
Author(s)
B.-H. Mevik and Ron Wehrens
See Also
Draws ellipses according to Mahalanobis distances
Description
For 2-dimensional data a scatterplot is made. Additionally, ellipses corresponding to certain Mahalanobis distances and quantiles of the data are drawn.
Usage
drawMahal(x, center, covariance, quantile = c(0.975, 0.75, 0.5, 0.25), m = 1000,
lwdcrit = 1, ...)
Arguments
x
numeric data frame or matrix with 2 columns
center
vector of length 2 with multivariate center of x
covariance
2 by 2 covariance matrix of x
quantile
vector of quantiles for the Mahalanobis distance
m
number of points where the ellipses should pass through
lwdcrit
line width of the ellipses
...
additional graphics parameters, see par
Details
For multivariate normally distributed data, a fraction of 1-quantile of data should be outside the ellipses. For center and covariance also robust estimators, e.g. from the MCD estimator, can be supplied.
Value
A scatterplot with the ellipses is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
data(glass.grp)
x=glass[,c(2,7)]
require(robustbase)
x.mcd=covMcd(x)
drawMahal(x,center=x.mcd$center,covariance=x.mcd$cov,quantile=0.975,pch=glass.grp)
glass vessels data
Description
13 different measurements for 180 archaeological glass vessels from different groups are included.
Usage
data(glass)Format
A data matrix with 180 objects and 13 variables.
Details
This is a matrix with 180 objects and 13 columns.
Source
Janssen, K.H.A., De Raedt, I., Schalm, O., Veeckman, J.: Microchim. Acta 15 (suppl.) (1998) 253-267. Compositions of 15th - 17th century archaeological glass vessels excavated in Antwerp.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(glass)
str(glass)
glass types of the glass data
Description
13 different measurements for 180 archaeological glass vessels from different groups are included. These groups are certain types of glasses.
Usage
data(glass.grp)Format
The format is: num [1:180] 1 1 1 1 1 1 1 1 1 1 ...
Details
This is a vector with 180 elements referring to the groups.
Source
Janssen, K.H.A., De Raedt, I., Schalm, O., Veeckman, J.: Microchim. Acta 15 (suppl.) (1998) 253-267. Compositions of 15th - 17th century archaeological glass vessels excavated in Antwerp.
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
Examples
data(glass.grp)
str(glass.grp)
Hyptis data set
Description
30 objects (Wild growing, flowering Hyptis suaveolens) and 7 variables (chemotypes), and 2 variables that explain the grouping (4 groups).
Usage
data(hyptis)Format
A data frame with 30 observations on the following 9 variables.
Sabinenea numeric vector
Pinenea numeric vector
Cineolea numeric vector
Terpinenea numeric vector
Fenchonea numeric vector
Terpinolenea numeric vector
Fenchola numeric vector
Locationa factor with levels
East-highEast-lowNorthSouthGroupa numeric vector with the group information
Details
This data set can be used for cluster analysis.
References
P. Grassi, M.J. Nunez, K. Varmuza, and C. Franz: Chemical polymorphism of essential oils of Hyptis suaveolens from El Salvador. Flavour and Fragrance, 20, 131-135, 2005. K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009
Examples
data(hyptis)
str(hyptis)
isometric logratio transformation
Description
A data transformation according to the isometric logratio transformation is done.
Usage
ilr(X)
Arguments
X
numeric data frame or matrix
Details
The ilr transformation is one possibility to transform compositional data to a real space. Afterwards, the transformed data can be analyzed in the usual way.
Value
Returns the transformed data matrix with one dimension less than X.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
glass_ilr <- ilr(glass)
kNN evaluation by CV
Description
Evaluation for k-Nearest-Neighbors (kNN) classification by cross-validation
Usage
knnEval(X, grp, train, kfold = 10, knnvec = seq(2, 20, by = 2), plotit = TRUE,
legend = TRUE, legpos = "bottomright", ...)
Arguments
X
standardized complete X data matrix (training and test data)
grp
factor with groups for complete data (training and test data)
train
row indices of X indicating training data objects
kfold
number of folds for cross-validation
knnvec
range for k for the evaluation of kNN
plotit
if TRUE a plot will be generated
legend
if TRUE a legend will be added to the plot
legpos
positioning of the legend in the plot
...
additional plot arguments
Details
The data are split into a calibration and a test data set (provided by "train"). Within the calibration set "kfold"-fold CV is performed by applying the classification method to "kfold"-1 parts and evaluation for the last part. The misclassification error is then computed for the training data, for the CV test data (CV error) and for the test data.
Value
trainerr
training error rate
testerr
test error rate
cvMean
mean of CV errors
cvSe
standard error of CV errors
cverr
all errors from CV
knnvec
range for k for the evaluation of kNN, taken from input
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(fgl,package="MASS")
grp=fgl$type
X=scale(fgl[,1:9])
k=length(unique(grp))
dat=data.frame(grp,X)
n=nrow(X)
ntrain=round(n*2/3)
require(class)
set.seed(123)
train=sample(1:n,ntrain)
resknn=knnEval(X,grp,train,knnvec=seq(1,30,by=1),legpos="bottomright")
title("kNN classification")
CV for Lasso regression
Description
Performs cross-validation (CV) for Lasso regression and plots the results in order to select the optimal Lasso parameter.
Usage
lassoCV(formula, data, K = 10, fraction = seq(0, 1, by = 0.05), trace = FALSE,
plot.opt = TRUE, sdfact = 2, legpos = "topright", ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data frame to be analyzed
K
the number of segments to use for CV
fraction
fraction for Lasso parameters to be used for evaluation, see details
trace
if 'TRUE', intermediate results are printed
plot.opt
if TRUE a plot will be generated that shows optimal choice for "fraction"
sdfact
factor for the standard error for selection of the optimal parameter, see details
legpos
position of the legend in the plot
...
additional plot arguments
Details
The parameter "fraction" is the sum of absolute values of the regression coefficients
for a particular Lasso parameter on the sum of absolute values of the regression
coefficients for the maximal possible value of the Lasso parameter (unconstrained
case), see also lars .
The optimal fraction is chosen according to the following criterion:
Within the CV scheme, the mean of the SEPs is computed, as well as their standard
errors. Then one searches for the minimum of the mean SEPs and adds
sdfact*standarderror. The optimal fraction is the smallest fraction with an MSEP
below this bound.
Value
cv
MSEP values at each value of fraction
cv.error
standard errors for each value of fraction
SEP
SEP value for each value of fraction
ind
index of fraction with optimal choice for fraction
sopt
optimal value for fraction
fraction
all values considered for fraction
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(PAC)
# takes some time: # res <- lassoCV(y~X,data=PAC,K=5,fraction=seq(0.1,0.5,by=0.1))
Plot Lasso coefficients
Description
Plots the coefficients of Lasso regression
Usage
lassocoef(formula, data, sopt, plot.opt = TRUE, ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data frame to be analyzed
sopt
optimal fraction from Lasso regression, see details
plot.opt
if TRUE a plot will be generated
...
additional plot arguments
Details
Using the function lassoCV for cross-validation, the optimal
fraction sopt can be determined. Besides a plot for the Lasso coefficients
for all values of fraction, the optimal fraction is taken to compute the
number of coefficients that are exactly zero.
Value
coefficients
regression coefficients for the optimal Lasso parameter
sopt
optimal value for fraction
numb.zero
number of zero coefficients for optimal fraction
numb.nonzero
number of nonzero coefficients for optimal fraction
ind
index of fraction with optimal choice for fraction
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(PAC)
res=lassocoef(y~X,data=PAC,sopt=0.3)
Repeated Cross Validation for lm
Description
Repeated Cross Validation for multiple linear regression: a cross-validation is performed repeatedly, and standard evaluation measures are returned.
Usage
lmCV(formula, data, repl = 100, segments = 4, segment.type = c("random", "consecutive",
"interleaved"), length.seg, trace = FALSE, ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data set including y and X
repl
number of replication for Cross Validation
segments
number of segments used for splitting into training and test data
segment.type
"random", "consecutive", "interleaved" splitting into training and test data
length.seg
number of parts for training and test data, overwrites segments
trace
if TRUE intermediate results are reported
...
additional plotting arguments
Details
Repeating the cross-validation with allow for a more careful evaluation.
Value
residuals
matrix of size length(y) x repl with residuals
predicted
matrix of size length(y) x repl with predicted values
SEP
Standard Error of Prediction computed for each column of "residuals"
SEPm
mean SEP value
RMSEP
Root MSEP value computed for each column of "residuals"
RMSEPm
mean RMSEP value
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(ash)
set.seed(100)
res=lmCV(SOT~.,data=ash,repl=10)
hist(res$SEP)
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 <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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)
PCA calculation with the NIPALS algorithm
Description
NIPALS is an algorithm for computing PCA scores and loadings.
Usage
nipals(X, a, it = 10, tol = 1e-04)
Arguments
X
numeric data frame or matrix
a
maximum number of principal components to be computed
it
maximum number of iterations
tol
tolerance limit for convergence of the algorithm
Details
The NIPALS algorithm is well-known in chemometrics. It is an algorithm for computing PCA scores and loadings. The advantage is that the components are computed one after the other, and one could stop at a desired number of components.
Value
T
matrix with the PCA scores
P
matrix with the PCA loadings
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
res <- nipals(glass,a=2)
Neural network evaluation by CV
Description
Evaluation for Artificial Neural Network (ANN) classification by cross-validation
Usage
nnetEval(X, grp, train, kfold = 10, decay = seq(0, 10, by = 1), size = 30,
maxit = 100, plotit = TRUE, legend = TRUE, legpos = "bottomright", ...)
Arguments
X
standardized complete X data matrix (training and test data)
grp
factor with groups for complete data (training and test data)
train
row indices of X indicating training data objects
kfold
number of folds for cross-validation
decay
weight decay, see nnet ,
can be a vector with several values - but then "size" can be only one value
size
number of hidden units, see nnet ,
can be a vector with several values - but then "decay" can be only one value
maxit
maximal number of iterations for ANN, see nnet
plotit
if TRUE a plot will be generated
legend
if TRUE a legend will be added to the plot
legpos
positioning of the legend in the plot
...
additional plot arguments
Details
The data are split into a calibration and a test data set (provided by "train"). Within the calibration set "kfold"-fold CV is performed by applying the classification method to "kfold"-1 parts and evaluation for the last part. The misclassification error is then computed for the training data, for the CV test data (CV error) and for the test data.
Value
trainerr
training error rate
testerr
test error rate
cvMean
mean of CV errors
cvSe
standard error of CV errors
cverr
all errors from CV
decay
value(s) for weight decay, taken from input
size
value(s) for number of hidden units, taken from input
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(fgl,package="MASS")
grp=fgl$type
X=scale(fgl[,1:9])
k=length(unique(grp))
dat=data.frame(grp,X)
n=nrow(X)
ntrain=round(n*2/3)
require(nnet)
set.seed(123)
train=sample(1:n,ntrain)
resnnet=nnetEval(X,grp,train,decay=c(0,0.01,0.1,0.15,0.2,0.3,0.5,1),
size=20,maxit=20)
Determine the number of PCA components with repeated cross validation
Description
By splitting data into training and test data repeatedly the number of principal components can be determined by inspecting the distribution of the explained variances.
Usage
pcaCV(X, amax, center = TRUE, scale = TRUE, repl = 50, segments = 4,
segment.type = c("random", "consecutive", "interleaved"), length.seg, trace = FALSE,
plot.opt = TRUE, ...)
Arguments
X
numeric data frame or matrix
amax
maximum number of components for evaluation
center
should the data be centered? TRUE or FALSE
scale
should the data be scaled? TRUE or FALSE
repl
number of replications of the CV procedure
segments
number of segments for CV
segment.type
"random", "consecutive", "interleaved" splitting into training and test data
length.seg
number of parts for training and test data, overwrites segments
trace
if TRUE intermediate results are reported
plot.opt
if TRUE the results are shown by boxplots
...
additional graphics parameters, see par
Details
For cross validation the data are split into a number of segments, PCA is computed (using 1 to amax components) for all but one segment, and the scores of the segment left out are calculated. This is done in turn, by omitting each segment one time. Thus, a complete score matrix results for each desired number of components, and the error martrices of fit can be computed. A measure of fit is the explained variance, which is computed for each number of components. Then the whole procedure is repeated (repl times), which results in repl numbers of explained variance for 1 to amax components, i.e. a matrix. The matrix is presented by boxplots, where each boxplot summarized the explained variance for a certain number of principal components.
Value
ExplVar
matrix with explained variances, repl rows, and amax columns
MSEP
matrix with MSEP values, repl rows, and amax columns
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
x.sc <- scale(glass)
resv <- clvalidity(x.sc,clnumb=c(2:5))
Diagnostics plot for PCA
Description
Score distances and orthogonal distances are computed and plotted.
Usage
pcaDiagplot(X, X.pca, a = 2, quantile = 0.975, scale = TRUE, plot = TRUE, ...)
Arguments
X
numeric data frame or matrix
X.pca
PCA object resulting e.g. from princomp
a
number of principal components
quantile
quantile for the critical cut-off values
scale
if TRUE then X will be scaled - and X.pca should be from scaled data too
plot
if TRUE a plot is generated
...
additional graphics parameters, see par
Details
The score distance measures the outlyingness of the onjects within the PCA space using Mahalanobis distances. The orthogonal distance measures the distance of the objects orthogonal to the PCA space. Cut-off values for both distance measures help to distinguish between outliers and regular observations.
Value
SDist
Score distances
ODist
Orthogonal distances
critSD
critical cut-off value for the score distances
critOD
critical cut-off value for the orthogonal distances
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
require(robustbase)
glass.mcd <- covMcd(glass)
rpca <- princomp(glass,covmat=glass.mcd)
res <- pcaDiagplot(glass,rpca,a=2)
PCA diagnostics for variables
Description
Diagnostics of PCA to see the explained variance for each variable.
Usage
pcaVarexpl(X, a, center = TRUE, scale = TRUE, plot = TRUE, ...)
Arguments
X
numeric data frame or matrix
a
number of principal components
center
centring of X (FALSE or TRUE)
scale
scaling of X (FALSE or TRUE)
plot
if TRUE make plot with explained variance
...
additional graphics parameters, see par
Details
For a desired number of principal components the percentage of explained variance is computed for each variable and plotted.
Value
ExplVar
explained variance for each variable
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
res <- pcaVarexpl(glass,a=2)
Plot results of Ridge regression
Description
Two plots from Ridge regression are generated: The MSE resulting from Generalized Cross Validation (GCV) versus the Ridge parameter lambda, and the regression coefficients versus lambda. The optimal choice for lambda is indicated.
Usage
plotRidge(formula, data, lambda = seq(0.5, 50, by = 0.05), ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data frame to be analyzed
lambda
possible values for the Ridge parameter to evaluate
...
additional plot arguments
Details
For all values provided in lambda the results for Ridge regression are computed.
The function lm.ridge is used for cross-validation and
Ridge regression.
Value
predicted
predicted values for the optimal lambda
lambdaopt
optimal Ridge parameter lambda from GCV
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(PAC)
res=plotRidge(y~X,data=PAC,lambda=seq(1,20,by=0.5))
Plot SEP from repeated DCV
Description
Generate plot showing SEP values for Repeated Double Cross Validation
Usage
plotSEPmvr(mvrdcvobj, optcomp, y, X, method = "simpls", complete = TRUE, ...)
Arguments
mvrdcvobj
object from repeated double-CV, see mvr_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
method
the multivariate regression method to be used, see
mvr
complete
if TRUE the SEPcv values are drawn and computed for the same range of components as included in the mvrdcvobj object; if FALSE only optcomp components are computed and their results are displayed
...
additional plot arguments
Details
After running repeated double-CV, this plot visualizes the distribution of the SEP values.
Value
SEPdcv
all SEP values from repeated double-CV
SEPcv
SEP values from classical CV
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(NIR)
X <- NIR$xNIR[1:30,] # first 30 observations - for illustration
y <- NIR$yGlcEtOH[1:30,1] # only variable Glucose
NIR.Glc <- data.frame(X=X, y=y)
res <- mvr_dcv(y~.,data=NIR.Glc,ncomp=10,method="simpls",repl=10)
plot1 <- plotSEPmvr(res,opt=7,y,X,method="simpls")
Plot trimmed SEP from repeated DCV of PRM
Description
Generate plot showing trimmed SEP values for Repeated Double Cross Validation for Partial RObust M-Regression (PRM)
Usage
plotSEPprm(prmdcvobj, optcomp, y, X, complete = TRUE, ...)
Arguments
prmdcvobj
object from repeated double-CV of PRM, see prm_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
complete
if TRUE the trimmed SEPcv values are drawn and computed from
prm_cv for the same range of components as included in the
prmdcvobj object; if FALSE only optcomp components are computed and their
results are displayed
...
additional arguments ofr prm_cv
Details
After running repeated double-CV for PRM, this plot visualizes the distribution of the SEP values. While the gray lines represent the resulting trimmed SEP values from repreated double CV, the black line is the result for standard CV with PRM, and it is usually too optimistic.
Value
SEPdcv
all trimmed SEP values from repeated double-CV
SEPcv
trimmed SEP values from usual CV
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(NIR)
X <- NIR$xNIR[1:30,] # first 30 observations - for illustration
y <- NIR$yGlcEtOH[1:30,1] # only variable Glucose
NIR.Glc <- data.frame(X=X, y=y)
res <- prm_dcv(X,y,a=4,repl=2)
plot1 <- plotSEPprm(res,opt=res$afinal,y,X)
Component plot for repeated DCV
Description
Generate plot showing optimal number of components for Repeated Double Cross-Validation
Usage
plotcompmvr(mvrdcvobj, ...)
Arguments
mvrdcvobj
object from repeated double-CV, see mvr_dcv
...
additional plot arguments
Details
After running repeated double-CV, this plot helps to decide on the final number of components.
Value
optcomp
optimal number of components
compdistrib
frequencies for the optimal number of components
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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)
plot2 <- plotcompmvr(res)
Component plot for repeated DCV of PRM
Description
Generate plot showing optimal number of components for Repeated Double Cross-Validation of Partial Robust M-regression
Usage
plotcompprm(prmdcvobj, ...)
Arguments
prmdcvobj
object from repeated double-CV of PRM, see prm_dcv
...
additional plot arguments
Details
After running repeated double-CV for PRM, this plot helps to decide on the final number of components.
Value
optcomp
optimal number of components
compdistrib
frequencies for the optimal number of components
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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 <- prm_dcv(X,y,a=4,repl=2)
plot2 <- plotcompprm(res)
Plot predictions from repeated DCV
Description
Generate plot showing predicted values for Repeated Double Cross Validation
Usage
plotpredmvr(mvrdcvobj, optcomp, y, X, method = "simpls", ...)
Arguments
mvrdcvobj
object from repeated double-CV, see mvr_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
method
the multivariate regression method to be used, see
mvr
...
additional plot arguments
Details
After running repeated double-CV, this plot visualizes the predicted values.
Value
A plot is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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)
plot3 <- plotpredmvr(res,opt=7,y,X,method="simpls")
Plot predictions from repeated DCV of PRM
Description
Generate plot showing predicted values for Repeated Double Cross Validation of Partial Robust M-regression
Usage
plotpredprm(prmdcvobj, optcomp, y, X, ...)
Arguments
prmdcvobj
object from repeated double-CV of PRM, see prm_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
...
additional plot arguments
Details
After running repeated double-CV for PRM, this plot visualizes the predicted values. The result is compared with predicted values obtained via usual CV of PRM.
Value
A plot is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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 <- prm_dcv(X,y,a=4,repl=2)
plot3 <- plotpredprm(res,opt=res$afinal,y,X)
Plot results from robust PLS
Description
The predicted values and the residuals are shown for robust PLS using the optimal number of components.
Usage
plotprm(prmobj, y, ...)
Arguments
prmobj
resulting object from CV of robust PLS, see prm_cv
y
vector with values of response variable
...
additional plot arguments
Details
Robust PLS based on partial robust M-regression is available at prm .
Here the function prm_cv has to be used first, applying cross-validation
with robust PLS. Then the result is taken by this routine and two plots are generated
for the optimal number of PLS components: The measured versus the predicted y, and
the predicted y versus the residuals.
Value
A plot is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(cereal)
set.seed(123)
res <- prm_cv(cereal$X,cereal$Y[,1],a=5,segments=4,plot.opt=FALSE)
plotprm(res,cereal$Y[,1])
Plot residuals from repeated DCV
Description
Generate plot showing residuals for Repeated Double Cross Validation
Usage
plotresmvr(mvrdcvobj, optcomp, y, X, method = "simpls", ...)
Arguments
mvrdcvobj
object from repeated double-CV, see mvr_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
method
the multivariate regression method to be used, see
mvr
...
additional plot arguments
Details
After running repeated double-CV, this plot visualizes the residuals.
Value
A plot is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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)
plot4 <- plotresmvr(res,opt=7,y,X,method="simpls")
Plot residuals from repeated DCV of PRM
Description
Generate plot showing residuals for Repeated Double Cross Validation for Partial Robust M-regression
Usage
plotresprm(prmdcvobj, optcomp, y, X, ...)
Arguments
prmdcvobj
object from repeated double-CV of PRM, see prm_dcv
optcomp
optimal number of components
y
data from response variable
X
data with explanatory variables
...
additional plot arguments
Details
After running repeated double-CV for PRM, this plot visualizes the residuals. The result is compared with predicted values obtained via usual CV of PRM.
Value
A plot is generated.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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 <- prm_dcv(X,y,a=4,repl=2)
plot4 <- plotresprm(res,opt=res$afinal,y,X)
Plot SOM results
Description
Plot results of Self Organizing Maps (SOM).
Usage
plotsom(obj, grp, type = c("num", "bar"), margins = c(3,2,2,2), ...)
Arguments
obj
result object from som
grp
numeric vector or factor with group information
type
type of presentation for output, see details
margins
plot margins for output, see par
...
additional graphics parameters, see par
Details
The results of Self Organizing Maps (SOM) are plotted either in a table with numbers (type="num") or with barplots (type="bar"). There is a limitation to at most 9 groups. A summary table is returned.
Value
sumtab
Summary table
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(glass)
require(som)
Xs <- scale(glass)
Xn <- Xs/sqrt(apply(Xs^2,1,sum))
X_SOM <- som(Xn,xdim=4,ydim=4) # 4x4 fields
data(glass.grp)
res <- plotsom(X_SOM,glass.grp,type="bar")
PLS1 by NIPALS
Description
NIPALS algorithm for PLS1 regression (y is univariate)
Usage
pls1_nipals(X, y, a, it = 50, tol = 1e-08, scale = FALSE)
Arguments
X
original X data matrix
y
original y-data
a
number of PLS components
it
number of iterations
tol
tolerance for convergence
scale
if TRUE the X and y data will be scaled in addition to centering, if FALSE only mean centering is performed
Details
The NIPALS algorithm is the originally proposed algorithm for PLS. Here, the y-data are only allowed to be univariate. This simplifies the algorithm.
Value
P
matrix with loadings for X
T
matrix with scores for X
W
weights for X
C
weights for Y
b
final regression coefficients
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(PAC)
res <- pls1_nipals(PAC$X,PAC$y,a=5)
PLS2 by NIPALS
Description
NIPALS algorithm for PLS2 regression (y is multivariate)
Usage
pls2_nipals(X, Y, a, it = 50, tol = 1e-08, scale = FALSE)
Arguments
X
original X data matrix
Y
original Y-data matrix
a
number of PLS components
it
number of iterations
tol
tolerance for convergence
scale
if TRUE the X and y data will be scaled in addition to centering, if FALSE only mean centering is performed
Details
The NIPALS algorithm is the originally proposed algorithm for PLS. Here, the Y-data matrix is multivariate.
Value
P
matrix with loadings for X
T
matrix with scores for X
Q
matrix with loadings for Y
U
matrix with scores for Y
D
D-matrix within the algorithm
W
weights for X
C
weights for Y
B
final regression coefficients
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(cereal)
res <- pls2_nipals(cereal$X,cereal$Y,a=5)
Eigenvector algorithm for PLS
Description
Computes the PLS solution by eigenvector decompositions.
Usage
pls_eigen(X, Y, a)
Arguments
X
X input data, centered (and scaled)
Y
Y input data, centered (and scaled)
a
number of PLS components
Details
The X loadings (P) and scores (T) are found by the eigendecomposition of X'YY'X. The Y loadings (Q) and scores (U) come from the eigendecomposition of Y'XX'Y. The resulting P and Q are orthogonal. The first score vectors are the same as for standard PLS, subsequent score vectors different.
Value
P
matrix with loadings for X
T
matrix with scores for X
Q
matrix with loadings for Y
U
matrix with scores for Y
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(cereal)
res <- pls_eigen(cereal$X,cereal$Y,a=5)
Robust PLS
Description
Robust PLS by partial robust M-regression.
Usage
prm(X, y, a, fairct = 4, opt = "l1m",usesvd=FALSE)
Arguments
X
predictor matrix
y
response variable
a
number of PLS components
fairct
tuning constant, by default fairct=4
opt
if "l1m" the mean centering is done by the l1-median, otherwise if "median" the coordinate-wise median is taken
usesvd
if TRUE, SVD will be used if X has more columns than rows
Details
M-regression is used to robustify PLS, with initial weights based on the FAIR weight function.
Value
coef
vector with regression coefficients
intercept
coefficient for intercept
wy
vector of length(y) with residual weights
wt
vector of length(y) with weights for leverage
w
overall weights
scores
matrix with PLS X-scores
loadings
matrix with PLS X-loadings
fitted.values
vector with fitted y-values
mx
column means of X
my
mean of y
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
S. Serneels, C. Croux, P. Filzmoser, and P.J. Van Espen. Partial robust M-regression. Chemometrics and Intelligent Laboratory Systems, Vol. 79(1-2), pp. 55-64, 2005.
See Also
Examples
data(PAC)
res <- prm(PAC$X,PAC$y,a=5)
Cross-validation for robust PLS
Description
Cross-validation (CV) is carried out with robust PLS based on partial robust M-regression. A plot with the choice for the optimal number of components is generated. This only works for univariate y-data.
Usage
prm_cv(X, y, a, fairct = 4, opt = "median", subset = NULL, segments = 10,
segment.type = "random", trim = 0.2, sdfact = 2, plot.opt = TRUE)
Arguments
X
predictor matrix
y
response variable
a
number of PLS components
fairct
tuning constant, by default fairct=4
opt
if "l1m" the mean centering is done by the l1-median, otherwise by the coordinate-wise median
subset
optional vector defining a subset of objects
segments
the number of segments to use or a list with segments (see
mvrCv )
segment.type
the type of segments to use. Ignored if 'segments' is a list
trim
trimming percentage for the computation of the SEP
sdfact
factor for the multiplication of the standard deviation for
the determination of the optimal number of components, see
mvr_dcv
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, see
mvr_dcv
Details
A function for robust PLS based on partial robust M-regression is available at
prm . The optimal number of robust PLS components is chosen according
to the following criterion: Within the CV scheme, the mean of the trimmed SEPs
SEPtrimave is computed for each number of components, as well as their standard
errors SEPtrimse. Then one searches for the minimum of the SEPtrimave values and
adds sdfact*SEPtrimse. The optimal number of components is the most parsimonious
model that is below this bound.
Value
predicted
matrix with length(y) rows and a columns with predicted values
SEPall
vector of length a with SEP values for each number of components
SEPtrim
vector of length a with trimmed SEP values for each number of components
SEPj
matrix with segments rows and a columns with SEP values within the CV for each number of components
SEPtrimj
matrix with segments rows and a columns with trimmed SEP values within the CV for each number of components
optcomp
final optimal number of PLS components
SEPopt
trimmed SEP value for final optimal number of PLS components
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(cereal)
set.seed(123)
res <- prm_cv(cereal$X,cereal$Y[,1],a=5,segments=4,plot.opt=TRUE)
Repeated double-cross-validation for robust PLS
Description
Performs a careful evaluation by repeated double-CV for robust PLS, called PRM (partial robust M-estimation).
Usage
prm_dcv(X,Y,a=10,repl=10,segments0=4,segments=7,segment0.type="random",
segment.type="random",sdfact=2,fairct=4,trim=0.2,opt="median",plot.opt=FALSE, ...)
Arguments
X
predictor matrix
Y
response variable
a
number of PLS components
repl
Number of replicattion for the double-CV
segments0
the number of segments to use for splitting into training and
test data, or a list with segments (see mvrCv )
segments
the number of segments to use for selecting the optimal number if
components, or a list with segments (see mvrCv )
segment0.type
the type of segments to use. Ignored if 'segments0' is a list
segment.type
the type of segments to use. Ignored if 'segments' is a list
sdfact
factor for the multiplication of the standard deviation for
the determination of the optimal number of components, see
mvr_dcv
fairct
tuning constant, by default fairct=4
trim
trimming percentage for the computation of the SEP
opt
if "l1m" the mean centering is done by the l1-median, otherwise if "median", by the coordinate-wise median
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
...
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. 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.
Value
b
estimated regression coefficients
intercept
estimated regression intercept
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
residcomp
array [nrow(Y) x ncomp x repl] with residuals using optimum number of components
pred
array [nrow(Y) x ncol(Y) x ncomp x repl] with predicted Y for all numbers of components
SEPall
matrix [ncomp x repl] with SEP values
SEPtrim
matrix [ncomp x repl] with trimmed SEP values
SEPcomp
vector of length ncomp with trimmed SEP values; use the element afinal for the optimal trimmed SEP
afinal
final optimal number of components
SEPopt
trimmed SEP over all residuals using optimal number of components
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
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 <- prm_dcv(X,y,a=3,repl=2)
Repeated CV for Ridge regression
Description
Performs repeated cross-validation (CV) to evaluate the result of Ridge regression where the optimal Ridge parameter lambda was chosen on a fast evaluation scheme.
Usage
ridgeCV(formula, data, lambdaopt, repl = 5, segments = 10,
segment.type = c("random", "consecutive", "interleaved"), length.seg,
trace = FALSE, plot.opt = TRUE, ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data frame to be analyzed
lambdaopt
optimal Ridge parameter lambda
repl
number of replications for the CV
segments
the number of segments to use for CV,
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 predicted versus the observed y-values
...
additional plot arguments
Details
Generalized Cross Validation (GCV) is used by the function
lm.ridge to get a quick answer for the optimal Ridge parameter.
This function should make a careful evaluation once the optimal parameter lambda has
been selected. Measures for the prediction quality are computed and optionally plots
are shown.
Value
residuals
matrix of size length(y) x repl with residuals
predicted
matrix of size length(y) x repl with predicted values
SEP
Standard Error of Prediction computed for each column of "residuals"
SEPm
mean SEP value
sMAD
MAD of Prediction computed for each column of "residuals"
sMADm
mean of MAD values
RMSEP
Root MSEP value computed for each column of "residuals"
RMSEPm
mean RMSEP value
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(PAC)
res=ridgeCV(y~X,data=PAC,lambdaopt=4.3,repl=5,segments=5)
Trimmed standard deviation
Description
The trimmed standard deviation as a robust estimator of scale is computed.
Usage
sd_trim(x,trim=0.2,const=TRUE)
Arguments
x
numeric vector, data frame or matrix
trim
trimming proportion; should be between 0 and 0.5
const
if TRUE, the appropriate consistency correction is done
Details
The trimmed standard deviation is defined as the average trimmed sum of squared deviations around the trimmed mean. A consistency factor for normal distribution is included. However, this factor is only available now for trim equal to 0.1 or 0.2. For different trimming percentages the appropriate constant needs to be used. If the input is a data matrix, the trimmed standard deviation of the columns is computed.
Value
Returns the trimmed standard deviations of the vector x, or in case of a matrix, of the columns of x.
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
x <- c(rnorm(100),100) # outlier 100 is included
sd(x) # classical standard deviation
sd_trim(x) # trimmed standard deviation
Stepwise regression
Description
Stepwise regression, starting from the empty model, with scope to the full model
Usage
stepwise(formula, data, k, startM, maxTime = 1800, direction = "both",
writeFile = FALSE, maxsteps = 500, ...)
Arguments
formula
formula, like y~X, i.e., dependent~response variables
data
data frame to be analyzed
k
sensible values are log(nrow(x)) for BIC or 2 for AIC; if not provided -> BIC
startM
optional, the starting model; provide a binary vector
maxTime
maximal time to be used for algorithm
direction
either "forward" or "backward" or "both"
writeFile
if TRUE results are shown on the screen
maxsteps
maximum number of steps
...
additional plot arguments
Details
This function is similar to the function step for stepwise
regression. It is especially designed for cases where the number of regressor
variables is much higher than the number of objects. The formula for the full model
(scope) is automatically generated.
Value
usedTime
time that has been used for algorithm
bic
BIC values for different models
models
matrix with no. of models rows and no. of variables columns, and 0/1 entries defining the models
Author(s)
Leonhard Seyfang and (marginally) Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(NIR)
X <- NIR$xNIR[1:30,] # first 30 observations - for illustration
y <- NIR$yGlcEtOH[1:30,1] # only variable Glucose
NIR.Glc <- data.frame(X=X, y=y)
res <- stepwise(y~.,data=NIR.Glc,maxsteps=2)
Support Vector Machine evaluation by CV
Description
Evaluation for Support Vector Machines (SVM) by cross-validation
Usage
svmEval(X, grp, train, kfold = 10, gamvec = seq(0, 10, by = 1), kernel = "radial",
degree = 3, plotit = TRUE, legend = TRUE, legpos = "bottomright", ...)
Arguments
X
standardized complete X data matrix (training and test data)
grp
factor with groups for complete data (training and test data)
train
row indices of X indicating training data objects
kfold
number of folds for cross-validation
gamvec
range for gamma-values, see svm
kernel
kernel to be used for SVM, should be one of "radial", "linear",
"polynomial", "sigmoid", default to "radial", see svm
degree
degree of polynome if kernel is "polynomial", default to 3, see
svm
plotit
if TRUE a plot will be generated
legend
if TRUE a legend will be added to the plot
legpos
positioning of the legend in the plot
...
additional plot arguments
Details
The data are split into a calibration and a test data set (provided by "train"). Within the calibration set "kfold"-fold CV is performed by applying the classification method to "kfold"-1 parts and evaluation for the last part. The misclassification error is then computed for the training data, for the CV test data (CV error) and for the test data.
Value
trainerr
training error rate
testerr
test error rate
cvMean
mean of CV errors
cvSe
standard error of CV errors
cverr
all errors from CV
gamvec
range for gamma-values, taken from input
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(fgl,package="MASS")
grp=fgl$type
X=scale(fgl[,1:9])
k=length(unique(grp))
dat=data.frame(grp,X)
n=nrow(X)
ntrain=round(n*2/3)
require(e1071)
set.seed(143)
train=sample(1:n,ntrain)
ressvm=svmEval(X,grp,train,gamvec=c(0,0.05,0.1,0.2,0.3,0.5,1,2,5),
legpos="topright")
title("Support vector machines")
Classification tree evaluation by CV
Description
Evaluation for classification trees by cross-validation
Usage
treeEval(X, grp, train, kfold = 10, cp = seq(0.01, 0.1, by = 0.01), plotit = TRUE,
legend = TRUE, legpos = "bottomright", ...)
Arguments
X
standardized complete X data matrix (training and test data)
grp
factor with groups for complete data (training and test data)
train
row indices of X indicating training data objects
kfold
number of folds for cross-validation
cp
range for tree complexity parameter, see rpart
plotit
if TRUE a plot will be generated
legend
if TRUE a legend will be added to the plot
legpos
positioning of the legend in the plot
...
additional plot arguments
Details
The data are split into a calibration and a test data set (provided by "train"). Within the calibration set "kfold"-fold CV is performed by applying the classification method to "kfold"-1 parts and evaluation for the last part. The misclassification error is then computed for the training data, for the CV test data (CV error) and for the test data.
Value
trainerr
training error rate
testerr
test error rate
cvMean
mean of CV errors
cvSe
standard error of CV errors
cverr
all errors from CV
cp
range for tree complexity parameter, taken from input
Author(s)
Peter Filzmoser <P.Filzmoser@tuwien.ac.at>
References
K. Varmuza and P. Filzmoser: Introduction to Multivariate Statistical Analysis in Chemometrics. CRC Press, Boca Raton, FL, 2009.
See Also
Examples
data(fgl,package="MASS")
grp=fgl$type
X=scale(fgl[,1:9])
k=length(unique(grp))
dat=data.frame(grp,X)
n=nrow(X)
ntrain=round(n*2/3)
require(rpart)
set.seed(123)
train=sample(1:n,ntrain)
par(mar=c(4,4,3,1))
restree=treeEval(X,grp,train,cp=c(0.01,0.02:0.05,0.1,0.15,0.2:0.5,1))
title("Classification trees")