ThreeMode Abstracts, Part F
With one can go to the index of
this part of the Abstracts, with
one can go to other
parts (letters) of the Abstracts.
INDEX
Fa  Fb 
Fc  Fd 
Fe  Ff 
Fg  Fh 
Fi  Fj 
Fk  Fl 
Fm  Fn 
Fo  Fp 
Fq  Fr 
Fs  Ft 
Fu  Fv 
Fw  Fx 
Fy  Fz 


Faber, N. M. (1999b).
Note on the error analysis of the generalized rank annihilation method.
Analytical Letters, 32, 28992906.
The generalized rank annihilation method (gram) is a method for curve
resolution and quantitation that uses two data matrices simultaneously, i.E., one for the
unknown and one for the calibration sample. Requirements have been derived that ensure the
unique resolution of the analyte of interest in the presence of unknown interferences if the
data matrices are free from experimental error. In this paper, it is shown that the same
requirements allow for correct determination of bias and variance in the quantitative results
obtained by gram if the data matrices are not free from experimental error.

Faber, N.M. (2000).
Exact presentation of multivariate calibration
model as univariate calibration graph.
Chemometrics and Intelligent Laboratory Systems, 50, 107
114.
A proof is given that a recently introduced
univariate presentation of a multivariate
calibration model is exact, i.e., there are no
approximations involved. The proof is based on:
(1) previously proposed definitions of
multivariate net analyte signal and multivariate
calibration factors (sensitivity in classical
model and inverse sensitivity in inverse model)
and (2) the geometrical property of the true
regression vector in inverse multivariate
calibration that it must be proportional to the
true multivariate net analyte signal vector of a
particular sample. The extension of the proof to
multiway calibration is briefly discussed. a
practical example from nearinfrared (NIR)
spectroscopy is used to illustrate that the
proposed univariate presentation may give more
meaning to the term 'spectral overlap'.

Faber, N.M. (2001).
Comment on a recently proposed resampling method.
Journal of Chemometrics, 15, 169188.
A recently introduced resampling method for determining the contribution of
measurement errors to the standard error in bilinear and trilinear model estimates
is critically examined. Using Monte Carlo simulations, it is shown that this
method does not work as intended. A noise addition method is proposed as a
generally applicable alternative. The principles involved in applied work are
illustrated on real UVvis data taken from the literature.

Faber, N.M. (2001).
The price paid for the secondorder advantage when using the generalized rank
annihilation method. Journal of Chemometrics, 15, 743748.
In a groundbreaking paper, Linder and Sundberg developed a statistical
framework for the calibration of bilinear data (Chemometrics Intell. Lab.
Syst. 1998; 42: 159178). Within this framework they formulated three
different predictor construction methods (J. Chemometrics accepted), namely
a socalled naive method, a least squares (LS) method and a refined version
of the latter that takes account of the calibration uncertainty. They
showed that the naive method is statistically less efficient than the others
under the assumption of white noise. In the current work a close relationship
is established between the generalized rank annihilation method (GRAM) and
the naive method by comparing expressions for prediction variance. The main
conclusion is that the relatively poor efficiency of GRAM is the price one
pays for obtaining the secondorder advantage with a single calibration
sample.

Faber, N. M. (2002).
Towards a rehabilitation of the generalized rank annihilation method (GRAM)
Analytical and Bioanalytical Chemistry, 372, 683687.
The trilinear PARAFAC model occupies a central place in multiway analysis, because
the components of a data array can often be uniquely resolved. This paper compares
the resolution for a large variety of methods, namely the generalized rank annihilation
method (GRAM), alternating least squares (ALS), alternating trilinear decomposition
(ATLD), alternating coupled vectors resolution (ACOVER), alternating slicewise
diagonalization (ASD), alternating coupled matrices resolution (ACOMAR), selfweighted
alternating trilinear decomposition (SWATLD), and pseudo alternating least squares
(PALS). The comparison was conducted using Monte Carlo simulations. It was shown
that GRAM performs well for moderately and highly overlapped data. These results
argue strongly against the previously claimed superiority of the alternatives listed
above.

Faber, N.M., & Bro, R. (2002).
Standard error of prediction for multiway PLS: 1. Background and a simulation
study. Chemometrics and Intelligent Laboratory Systems, 60, 133149.
While a multitude of expressions has been proposed for calculating samplespecific
standard errors of prediction when using partial least squares (PLS) regression
for the calibration of firstorder data, potential generalisations to multiway
data are lacking to date. We have examined the adequacy of two approximate
expressions when using unfold or triPLS for the calibration of secondorder
data. The first expression is derived under the assumption that the errors in
the predictor variables are homoscedastic, i.e., of constant variance. In
contrast, the second expression is designed to also work in the heteroscedastic case.
The adequacy of the approximations is tested using extensive Monte Carlo simulations
while the practical utility is demonstrated in Part 2 of this series.

Faber, N.M., Bro, R. & Hopke P.K. (2003)
Recent developments in CANDECOMP/PARAFAC algorithms: a critical review.
Chemometrics and Intelligent Laboratory Systems65 119137.
Several recently proposed algorithms for fitting the PARAFAC model are investigated
and compared to more established alternatives. Alternating least squares (ALS),
direct trilinear decomposition (DTLD), alternating trilinear decomposition (ATLD),
selfweighted alternating trilinear decomposition (SWATLD), pseudo alternating
least squares (PALS), alternating coupled vectors resolution (ACOVER), alternating
slicewise diagonalization (ASD) and alternating coupled matrices resolution
(ACOMAR) are compared on both simulated and real data. For the recent algorithms,
only unconstrained threeway models can be fitted. In contrast, for example, ALS
allows modeling of higherorder data, as well as incorporating constraints on the
parameters and handling of missing data. Nevertheless, for threeway data, the
newer algorithms are interesting alternatives. It is found that the ALS estimated
models are generally of a better quality than any of the alternatives even when
overfactoring the model, but it is also found that ALS is significantly slower.
Based on the results (in particular the poor performance of DTLD), it is advised
that (a slightly modified) ASD may be a good alternative to ALS when a faster
algorithm is desired. (C) 2002 Elsevier Science B.V. All rights reserved.

Faber, N.M., Buydens, L.M.C., & Kateman, G. (1993).
Standard errors in the eigenvalues of a
crossproduct matrix: Theory and applications.
Journal of Chemometrics, 7, 495526.
New expressions are derived for the standard
errors in the eigenvalues of a crossproduct
matrix by the method of error propagation.
Crossproduct matrices frequently arise in
multivariate data analysis, especially in
principal component analysis (PCA). The derived
standard errors account for the variability in the
data as a result of measurement noise and are
therefore essentially different from the standard
errors developed in multivariate statistics. Those
standard errors were derived in order to account
for the finite number of observations on a fixed
number of variables, the socalled sampling error.
They can be used for making inferences about the
population eigenvalues. Making inferences about
the population eigenvalues is often not the
purposes of PCA in physical sciences. This is
particularly true if the measurements are
performed on an analytical instrument that
produces twodimensional arrays for one chemical
sample: The rows and columns of such a data matrix
cannot be identified with observations on
variables at all. However, PCA can still be used
as a general data reduction technique, but now the
effect of measurement noise on the standard errors
in the eigenvalues has to be considered. The
consequences for significance testing of the
eigenvalues as well as the usefulness for error
estimates for scores and loadings of PCA, multiple
linear regression (MLR) and the generalized rank
annihilation method (GRAM) are discussed. The
adequacy of the derived expressions is tested by
Monte Carlo simulations.

Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994a).
Generalized rank annihilation method. I:
Derivation of eigenvalue problems.
Journal of Chemometrics, 8, 147154.
Rank annihilation factor analysis (RAFA) is a
method for multicomponent calibration using two
data matrices simultaneously, one for the unknown
and one for the calibration sample. In its most
general form, the generalized rank annihilation
method (GRAM), an eigenvalue problem has to be
solved. In this first paper different formulations
of gram are compared and a slightly different
eigenvalue problem will be derived. The
eigenvectors of this specific eigenvalue problem
constitute the transformation matrix that rotates
the abstract factors from principal component
analysis (PCA) into their physical counterparts.
This reformulation of GRAM facilitates a
comparison with other PCAbased methods for curve
resolution and calibration. Furthermore, we will
discuss two characteristics common to all
formulations of gram, i.e. The distinct
possibility of a complex and degenerate solution.
It will be shown that a complex solutioncontrary
to degeneracyshould not arise for components
present in both samples for model data.

Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994b).
Generalized rank annihilation method. II: Bias and
variance in the estimated eigenvalues.
Journal of Chemometrics, 8, 181203.
Rank annihilation factor analysis (RAFA) is a
method for multicomponent calibration using two
data matrices simultaneously, one for the unknown
and one for the calibration sample. In its most
general form, the generalized rank annihilation
method (GRAM), an eigenvalue problem has to be
solved. In this second paper expressions are
derived for predicting the bias and variance in
the eigenvalues of GRAM. These expressions are
built on the analogies between a reformulation of
the eigenvalue problem and the prediction
equations of univariate and multivariate
calibration. The error analysis will also be
performed for Lorber's formulation of RAFA. It
will be demonstrated that, depending on the size
of the eigenvalue, large differences in
performance must be expected. A bias correction
technique is proposed that effectively eliminates
the bias if the error in the bias estimate is not
too large. The derived expressions are evaluated
by Monte Carlo simulations. It is shown that the
predictions are satisfactory up to the limit of
detection. The results are not sensitive to an
incorrect choice of the dimension of the factor
space.

Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994c).
Generalized rank annihilation method. III: Practical
implementation.
Journal of Chemometrics, 8, 273285.
In this paper we discuss the practical
implementation of the generalized rank
annihilation method (GRAM). The practical
implementation comes down to developing a computer
program where two critical steps can be
distinguished: The construction of the factor
space and the oblique rotation of the factors. The
construction of the factor space is a
leastsquares (LS) problem solved by singular
value decomposition (SVD), whereas the rotation of
the factors is brought about by solving an
eigenvalue problem. In the past several
formulations for GRAM have been published. The
differences essentially come down to solving
either a standard eigenvalue problem or a
generalized eigenvalue problem. The first
objective of this paper is to discuss the
numerical stability of the algorithms resulting
from these formulations. It is found that the
generalized eigenvalue problem is only to be
preferred if the construction of the factor space
is not performed with maximum precision. This is
demonstrated for the case where the dominant
factors are calculated by the nonlinear iterative
partial leastsquares (NIPALS) algorithm. Several
performance measures are proposed to investigate
the numerical accuracy of the computed solution.
The previously derived bias and variance are
proposed to estimate the number of physically
significant digits in the computed solution. The
second objective of this paper is to discuss the
relevance of theoretical considerations for
application of gram in the presence of model
errors.

Faber, N.M., Ferreé, J., & Boqué, R. (2001).
Iteratively reweighted generalized rank annihilation method 1. Improved
handling of prediction bias.
Chemometrics and Intelligent Laboratory Systems, 55, 6790.
The generalized rank annihilation method (CRAM) is a method for curve
resolution and calibration that uses two bilinear matrices simultaneously,
i.e., one for the unknown and one for the calibration sample. A GRAM
calculation amounts to solving an eigenvalue problem for which the eigenvalues
are related to the predicted analyte concentrations. Previous studies have
shown that random measurement errors bring about a bias in the eigenvalues,
which directly translates into prediction bias. In this paper, accurate
formulas are derived that enable removing most of this bias. Two bias
correction methods are investigated. While the first method directly subtracts
bias from the eigenvalues obtained by the original GRAM, the second method
first applies a weight to the data matrices to reduce bias. These weights
are specific for the analyte of interest and must be determined iteratively
from the data. Consequently, the proposed modification is called iteratively
reweighted GRAM (IRGRAM). The results of Monte Carlo simulations show that
both methods are effective in the sense that the standard error in the bias
corrected prediction compares favourably with the root mean squared error
(RMSE) that accompanies the original quantity. However, IRGRAM is found to
perform best because the increase of variance caused by subtracting bias is
minimised, In the original formulation of GRAM only a single calibration
sample is exploited. The error analysis is extended to cope with multiple
calibration samples. (C) 2001 Elsevier Science B.V. All rights reserved.

Faber, N.M., Ferreé, J., Boqué, R. & Kalivas, J. H. (2002).
Secondorder bilinear calibration: the effects of vectorising the data
matrices of the calibration set.
Chemometrics and Intelligent Laboratory Systems, 63, 107116.
In a groundbreaking paper, Linder and Sundberg [Chemometr. Intell. Lab. Syst.
42 (1998) 159] developed a statistical framework for the calibration of
secondorder bilinear data. Within this framework, they formulated three
different predictor construction methods [J. Chemom. 16 (2002) 12], namely
the socalled naive method, the bilinear least squares (BLLS) method, and a
refined version of the latter that takes account of the calibration
uncertainty. Elsewhere [J. Chemom. 15 (2001) 743], a close relationship is
established between the naive method and the generalized rank annihilation
method (GRAM) by comparing expressions for prediction variance. Here it is
proved that the BLLS method can be interpreted to work with vectorised data
matrices, which establishes an algebraic relationship with socalled unfold
partial least squares (PLS) and unfold principal component regression (PCR).
It is detailed how these results enable quantifying the effects of vectorising
bilinear secondorder data matrices on analytical figures of merit and variance
inflation factors. (C) 2002 Elsevier Science B.V. All rights reserved.

Faber, N.M., Ferreé, J., Boqué, R. & Kalivas, J. H. (2003).
Quantifying selectivity in spectrophotometric multicomponent analysis.
Tractrends in Analytical Chemistry, 22, 352361.
According to the latest recommendation of the International Union of Pure
and Applied Chemistry, "selectivity refers to the extent to which the method
can be used to determine particular analytes in mixtures or matrices without
interferences from other components of similar behavior". Because of the
prime importance of selectivity as an analytical figure of merit, numerous
proposals have been published on how to quantify it in spectrophotometric
multicomponent analysis. We show that the criterion independently developed
by Lorber [11,12] and Bergmann, von Oepen and Zinn [13] is the most suitable,
because it directly relates to prediction uncertainty and allows for a
consistent generalization to more complex systems of chemical analysis.
(C) 2003 Published by Elsevier Science B.V.

Faber, N.M., Lorber, A., & Kowalski, B.R. (1997a).
Analytical figures of merit for tensorial
calibration.
Journal of Chemometrics, 11, 419461.
The subject of analytical figures of merit for
tensorial calibration is critically reviewed.
Tensorial calibration derives its name from tensor
algebra, which provides a classification of
calibration methods depending on the complexity of
the data obtained for one chemical sample.
Expressions for net analyte signal, sensitivity
(classical model formulation), 'inverse
sensitivity' (inverse model formulation),
selectivity, signaltonoise ratio and limit of
detection (in signal space) are proposed for
Nthorder data (N greater than or equal to 2) that
are consistent with the accepted zerothorder
definitions and previously proposed definitions
for firstorder data. Useful relationships between
the proposed figures of merit and prediction error
variance are described. A selectivitybased rule
of thumb is derived to compare data analysis
across orders. Central to the currently proposed
framework for analytical figures of merit is the
reduction of a complex data structure to the
scalar net analyte signal. This allows for the
construction of a univariate calibration graph
(classical or inverse model), independent of the
complexity of the data. Enhanced visualization and
interpretation are obtained that may help to
bridge the gap between Nthorder calibration and
the intuitive understanding of zerothorder data.
(c) 1997 John Wiley & Sons, Ltd.

Faber, N.M., Lorber, A., & Kowalski, B.R. (1997b).
Generalized rank annihilation method: Standard
errors in the estimated eigenvalues if the
instrumental errors are heteroscedastic and
correlated.
Journal of Chemometrics, 11, 95109.
The generalized rank annihilation method (GRAM) is
a method for curve resolution and calibration that
uses two data matrices simultaneously, i.e. One
for the unknown and one for the calibration
sample. The method is known to become an
eigenvalue problem for which the eigenvalues are
the ratios of the concentrations for the samples
under scrutiny. Previously derived standard errors
in the estimated eigenvalues of GRAM have very
recently been shown to be based on unrealistic
assumptions about the measurement errors. In this
paper a systematic notation is introduced that
enables the propagation of errors that are based
on realistic assumptions concerning the
datagenerating process. The error propagation
will be performed in detail for the case that one
data order modulates the second one. Extensions to
more complicated error models are indicated. (c)
1997 by John Wiley & Sons, Ltd.

Faber, N.M., Meinders, M.J., Geladi, P., Sjöström, M.,
Buydens, L.M.C., & Kateman, G. (1995).
Random error bias in principal component analysis.
Part II. Application of theoretical predictions to
multivariate problems.
Analytica Chimica Acta, 304, 273283.
In the first part of this paper expressions were
derived for the prediction of random error bias in
the eigenvalues of principal component analysis
(PCA) and the singular values of singular value
decomposition (SVD). The main issues of Part I
were to investigate the question whether adequate
prediction of this bias is possible and to discuss
how the validation and evaluation of these
predictions could proceed for a specific
application in practice. The main issue of this
second part is to investigate how random error
bias should be taken into account. This question
will be treated for a number of seemingly
disparate multivariate problems. For example, the
construction of confidence intervals for the
biascorrected quantities will be discussed with
respect to the estimation of the number of
significant principal components. The consequences
of random error bias for calibration and
prediction with ordinary least squares (OLS),
principal component regression (PCR), partial
least squares (PLS) and the generalized rank
annihilation method (GRAM) will also be outlined.
Finally, the derived bias expressions will be
compared in detail with the corresponding results
for OLS and GRAM.

Fabricius, W. V., Nagoshi, C. T., & Mackinnon, D. P. (1997).
Concepts of drugs: differences in conceptual structure across groups with different
levels of drug expercience.
Addiction, 92, 847858.
Seventy seven college students varying in degree of drug use experience
rated the perceived similarities of all possible combinations of 16 drug classes
(cigarettes, other tobacco, alcohol, marijuana, barbiturates, minor and major
tranquilizers, amphetamines, amphetamine derivatives, cocaine, heroin, opiates,
hallucinogens, inhalants, PCP, anti depressants). Multi dimensional scaling (INDSCAL)
and network models (PFNET) indicated that abstainers had only one pharmacological
category involving sedatives/depressants, and that they attached more importance to
whether drugs were licit vs. illicit than to whether they were depressants vs. stimulants.
Conceptions became more coherent, differentiated and based on pharmacological properties
for more experienced drug users. In line with previous work, groups with greater
experience with drugs had more sophisticated conceptions not only about the drugs they
had used, but also about drugs they had not used These findings suggest that early on in
drug behavior sophisticated and interrelated concepts are developing that should be taken
into account when designing interventions and information campaigns.

Fabrizius, M.A., Cooper, M., & Basford, K.E. (1997).
Genetic analysis of variation for grain yield and
protein concentration in two wheat crosses.
Australian Journal of Agricultural Research, 48, 605
614.**
Grain yield and protein concentration are two of
the more important criteria for wheat breeding in
Queensland. Three aspects of the inheritance of
both of these traits can have an impact on
achieving genetic progress: (i) the magnitude and
form of the genetic correlation between the
traits, (ii) the magnitude of genetic variation
and genotype × environment interactions, and (iii)
the importance of epistasis in genetic variation.
These 3 factors were examined for 2 crosses in a
multienvironment trial conducted in Queensland in
1989. Negative genetic correlations were found
between. Grain yield and protein concentration in
both crosses. Genetic variation and genotype ×
environment interactions were found to be
important for both traits. There was little
evidence for the existence of significant additive
× additive epistasis for either trait and the
genotype × environment interactions were
predominantly additive × environment in nature.
From both crosses, progeny combining the high
yield and high protein levels of the parents were
identified. This suggests that there was a degree
of independent segregation of the genes
controlling grain yield and protein concentration
in both crosses. Therefore, simultaneous genetic
progress for yield and protein concentration is
possible in Queensland environments.

Fachin, S., Shea, D. G., & Vichi, M. (2002).
Exploring 3D datasets: a factorial matrices analysis of the US industry in the 1980s.
Applied Economics, 34, 295304.
In this paper a Factorial Matrices technique suitable for exploratory
analysis of multivariate, disaggregated time series is presented and applied to a data
set covering 19 US manufacturing industries over the years 1979 to 1990. The empirical
analysis confirms that the technique is a powerful tool, allowing otherwise difficult
extraction of stylized facts from multidimensional datasets. In this case: (i) there are
no signs of deindustrialization induced by growing import penetration, and, (ii),
employment decline has generally not been associated to substitution of capital to
labour.

Fah, D., & Koch, K. (2002).
Discrimination between earthquakes and, chemical explosions by multivariate
statistical analysis: A case study for Switzerland.
Bulletin of the Seismological Society of America, 92, 17951805.
A data set of 43 confirmed earthquakes and 42 explosions (1.3 +/ ML less
than or equal to 3.8) is analyzed by multivariate statistical analysis. The explosion events
include quarry blasts and explosions detonated for seismic experiments as well as an explosion
of an ammunition storage site. The events of this training data set are mainly located in the
Alpine mountains and Central Switzerland, with the seismic sources having excellent distance
(R < 300 km) and azimuthal coverage for the recording stations. Multivariate statistical
analysis is used to derive general discriminant functions based on regional waveform data for
the training set. The discriminant functions are then tested for consistency on the events of
the training data set, with the result that 97% of these events are correctly identified by
the multivariate discriminant functions. Of the total training data set, 17% is classified as
ambiguous cases, based on marginal discriminant functions. The method is subsequently applied
to an extended data set including nighttime events from 19921996, which are hence regarded as
earthquakes, and a set of presumed explosions from the years 19841997. For Central Switzerland,
the events of the extended data set can clearly be identified with the discriminant functions
derived from the training data set. The identification rate is lower for other regions in
Switzerland, which can be related to tectonic units. For these regions, considered to have a
laterally homogeneous crust, a linear correction term in the discriminant function providing
for station corrections can be found that significantly decreases the misidentification rate.

Ferreira, M. M. C. (2003).
Multivariate QSAR.
Journal of the Brazilian Chemical Society, 13, 742753.
In this work, the chemometric techniques most frequently used in QSAR
(quantitative structureactivity relationships) studies are reviewed. They are introduced
in chronological order, beginning with Hansch analysis and the exploratory data analysis
methods of principal components and hierarchical clustering (PCA and HCA). Principal
component regression and partial least squares regression methods (PCR and PLS) are
discussed, followed by the pattern recognition methods (KNN and SIMCA). Different
applications are presented to illustrate these chemometric techniques. The methodology
used for regression in 3DQSAR is presented ( unfolding PLS). Finally, the higher order
method called Multilinear PLS, already used in analytical chemistry but not yet explored
by the QSAR community, is introduced. This method maintains the multiway structure of the
data and has several advantages over bilinear PLS including speed in calculation,
simplicity and stability, since the number of parameters to be estimated can be greatly
reduced.

Ferreira, M.M.C., Brandes, M.L., Ferreira, I.M.C., Booksh, K.S.,
Dolowy, W.C., Gouterman, M., & Kowalski, B.R. (1995).
Chemometric study of the fluorescence of dental calculus by
trilinear decomposition. Applied Spectroscopy, 49,
13171325.
Chemometric techniques have been applied to the unresolved secondorder
porphyrinic
emissionexcitation fluorescent spectra of several animal dental calculus
deposits dissolved
in HCl. A singular value decomposition (SVD) procedure was used for
preliminary indication of
the number of fluorescent species present in the samples. The trilinear
decomposition (TLD)
method was applied to resolve component spectra, resulting in three
porphyrinic spectral
profiles for both canines and felines.

Ferrer, R., Beltrán, J. L., & Guiteras, J. (1999).
Multivariate calibration applied to synchronous fluorescence spectrometry. Simultaneous
determination of polycyclic aromatic hydrocarbons in water samples.
Talanta, 45, 10731080.
Synchronous fluorescence spectra of mixtures containing ten polycyclic aromatic
hydrocarbons (anthracene, benz[a]anthracene, benzo[a]pyrene, chrysene, fluoranthene, fluorene,
naphthalene, perylene, phenanthrene and pyrene) have been used for the determination of these
compounds by Partial Least Squares Regression (PLSR), using both PLS1 and PLS2. Different
procedures have been used for the pretreatment of the data in order to obtain better models, and
the size of the calibration matrix has also been studied. The best models have been used for the
determination of the above mentioned PAHs in spiked natural water samples at concentration levels
between 4 and 20 ng ml(1). Recoveries ranged from 80 to 120% in most cases, although fluorene gave
significantly lower results.

Ferrer, R., Guiteras, J. & Beltrán, J.L. (1999).
Artificial neural networks (ANNs) in the analysis
of polycyclic aromatic hydrocarbons in water
samples by synchronous fluorescence.
Analytica Chimica Acta, 384, 261269.
Backpropagation artificial neural networks,
principal component regression and partial least
squares have been compared in order to establish
the best multivariate calibration models for the
analysis of mixtures of polycyclic aromatic
hydrocarbons containing 10 of these compounds
(anthracene, benz[a]anthracene, benzo[a]pyrene,
chrysene, fluoranthene, fluorene, naphthalene,
perylene, phenanthrene and pyrene). The
synchronous fluorescence spectra (recorded at
wavelength increments of 50 and 100 nm) of 85
standards, with concentrations ranging from 0 to
20 ng ml^{1}, have been used for this purpose.

Fillipan, N., Bezemer, E., Burke, J., & Rutan, S. C. (2004).
Studies of liquidphase complexes in acetonitrile/water solutions by attenuated total
reflection infrared spectroscopy with acetaldehyde as a model solute.
Applied Spectroscopy, 58, 11871194.
Chemometric methods combined with infrared (IR) spectroscopy, using
attenuated total reflectance (ATR) sampling, are employed here to characterize the
stoichiometry of complexes of solvent molecules in the liquid phase. The spectral
information provides insight into the liquid microstructure present in liquid
chromatographic mobile phases. This information should make it easier to understand
and predict the effects of changes in mobile phase composition on the results of
chromatographic separations. In this paper, mobile phases consisting of 0 mol % to
100 mol % acetonitrile in water were studied, with the addition of acetaldehyde as
a model solute at concentrations ranging from 3 to 8 mol %. Using threeway multivariate
curve resolution by the alternating least squares method (MCRALS) it was possible to
resolve eight unique spectra: four mobile phase components, and four unique spectra of
acetaldehyde solvated in different environments. The directions of the shifts of the
important acetaldehyde infrared bands show good correlation with those predicted by
gasphase ab initio calculations of small solvated clusters.

Field, A.S, & Graupe, D. (1991)
Topographic component
(parallel factor) analysis of multichannel evoked potentials:
practical issues in trilinear spatiotemporal decomposition.
Brain Topography, 3, 407423.
An application of PARAFAC (called the trilinear
topographic components model (after Möcks 19**) to the
decomposition of multichannel evoked potentials (MEP's).
Practical guidelines and procedures for applying PARAFAC to MEP
decomposition are provided. Preprocessing, orthogonality
constraints, and validation of solutions in a complete PARAFAC
analysis were used for the first time using actual MEP data. The
PARAFAC model is shown to be superior to the traditional bilinear
principal components model in terms of data reduction, confirming
the advantage of PARAFAC added assumptions. The model is then
shown to provide a unique spatiotemporal decomposition that is
reproducible in different subject groups. The components are
shown to be consistent with spatial/temporal features evident in
the data, except for an artificial component resulting from
latency jitter. Subject scores on this component are shown to
reflect peak latencies in the data, suggesting a new aspect to
statistical analyses based on subject scores. In general, the
results support the conclusion that the PARAFAC model is a
promising alternative to principal components for data reduction
and analysis of MEP's.

Firth, P.M. & Snyder Jr, C.W. (1979).
Threemode factor
analysis of
selfreported difficulty in assertiveness. Australian Journal of
Psychology,
31, 125135.
Difficulty in Assertiveness Inventory (Leah et al., 1979).
Tucker's Method III (1966) with image factor analysis is used.
Replication of Leah's results on students and hospital
workers. Referent and response class factors similar,
individual differences and core matrix far less so.

Fischel, J.E. (1982).
The organization of human newborn sucking and movement during
auditory stimulation. Infant Behavior and Development,
5, 4561.
Many of the newborn human's earliest interactions occur during episodes
of sucking, but there
is little understanding of how sucking may interact with responsiveness
to other social and
physical stimuli. In the present study, levels of body movement, or
activity, and
characteristics of nonnutritive sucking were evaluated for two groups of
newborns; one
receiving brief presentations of a complex sound as they initiated
sucking bursts, and a
second group receiving the same sound during pauses between their suking
bursts. A control
group for comparison received no sound stimulation. Infants stimulated
during pausing showed
significantly higher activity levels and more rapid habituation of
movement than those
stimulated during bursting. Sound during bursting was less likely to
cause a shift to pausing
than sound during pausing was to cause a shift to sucking. These
differences suggested that
bursting and pausing were not similar contexts for responding to sound
stimulation. Potential
mechanisms underlying differential responsiveness during sucking are
suggested.

Flaten, G. R., Grung, B., & Kvalheim, O. M. (2004).
Quantification of pollution levels by multiway modelling.
Journal of Chemometrics,18, 173182.
Environmental surveys are performed regularly in environmental monitoring of possible industrial
pollution. The seabed pollution from industry in or near water, e.g. offshore oil production, can be
biologically monitored as benthic species, and their diversity can be used as indicators of pollution.
The community disturbance index (CDI) was recently proposed as a quantitative measure of
pollution calculated from the benthic data. However, the CDI and other measurements are not
optimal for quantifying the changes in level of environmental stress over several years. In this work
it is suggested that the total environmental stress over several monitoring surveys can be determined
by modelling the natural variation for a set of nonpolluted sites. The suggested approach uses a
multiway method (Tucker3) to describe the natural variation, and the threeway extension of CDI to
quantify the pollution. Implicitly, the traditional soft independent modelling of class analogies
(SIMCA) classification is extended to its threeway counterpart. The proposed method is tested on
the data from four subsequent surveys performed at the North Sea oil field Embla.

FloresCerrillo, J., & MacGregor, J.F. (2004).
Multivariate monitoring of batch processes using batchtobatch information.
Aiche Journal, 50, 12191228.
Multiway principal component analysis (MPCA) and multiway partialleast
squares (MPLS) are wellestablished methods for the analysis of historical data from batch
processes, and for monitoring the progress of new batches. Direct measurements made on prior
batches can also be incorporated into the analysis by monitoring with multiblock methods. An
extension of the multiblock MPCA/MPLS approach is introduced to explicitly incorporate
batchtobatch trajectory information summarized by the scores of previous batches, while
keeping all the advantages and monitoring statistics of the traditional MPCA/MPLS. However,
it is shown that the advantages of using information on prior batches for analysis and
monitoring are often small. Its main advantage is that it can be useful for detecting
problems when monitoring new batches in the early stages of their operation., the approach
and benefits are illustrated with condensation polymerization and emulsion polymerization
systems, as examples.

Flôres Jr, R.G. (1988b).
Classical approaches to cubic tables. Cahiers du Centre
d'Etudes et de Recherche Opérationelle,
30, 3946.
This paper presents two methods for the exploratory analysis of cubic
tables. Emphasis is
given to the modelling stages involved in these and similar techniques,
what motivates the
concept of symmetric and asymmetric procedures. The information losses at
each stage are
evaluated, for both methods, in terms of chisquare differences. A
discussion with other
existing viewpoints and a brief example are also included.

Flury, B.N. (1984).
Common principle components in k groups.
Journal of the American Statistical Association, 79,892898.
This article generalizes the method of principal components to socalled
"common principal components" as follows: Consider the hypothesis that the covariance
matrices sigma_{i} for k populations are simultaneously
diagonalizable. That is, there is an orthogonal matrix beta such that
beta'sigma_{i}beta is diagonal for i = 1,..., k. I derive the
normaltheory maximum likelihood estimates of the common component sigma_{i}
matrices and the loglikelihoodratio statistics for testing this hypothesis. The
solution has some favorable properties that do not depend on normality assumptions. Numerical
examples illustrate the method. Applications to data reduction, multiple regression, and
nonlinear discriminant analysis are sketched.

Flury, B. (1990).
Principal points.
Biometrika, 77, 3341.
The k principal points of a pvariate random variable X are
defined as those points Ea,....,Ek wich minimize the espected squared distance of X from the
hearest of the Ej. This paper presents result on the principal points of univariate symmetric
distributions, the univariate and bivariate normal distribution, multivariate elliptical distributions,
and multivariate distributions in general. In the cases of normal and elliptical distributions, the
relationship between principal points and principal components is studied.

Foss, M.A., Fabiani, M., Mane, A.M., & Donchin, E. (1989).
Unsupervised practice: The performance of the control group.
Acta Psychologica, 71, 2351.
40 male university students practiced the Space Fortress game, a task used
to
examine acquisition of complex skills previously described by Mane and
Donchin, for 10 1hr sessions. Performance data
were evaluated using threemode principal component analysis. Ss showed a
general improvement in performance throughout training; however,
individual
differences were found in the Ss' initial capacity, in their rate of
learning, and
in the strategies they adopted to achieve their final performance.

Foucart, Th. (1985a).
Application de l'analyse factorielle des correspondances.
[Application of correspondence factor analysis].
Statistique et Analyse de Données, 10, 5464.
The method used here to describe a sequence of boards is based upon
Correspondence Factor
Analysis. First we will explain particular procedures we have had to
use, and second we will
present the result obtained with this method in the analysis of the
common data.

Foucart, Th. (1985b).
Application de la méthode RAS. [Application of the RAS method]
Statistique et Analyse de Données, 10, 6582.
The algorithm RAS is a classical method to adjust a table to fixed
margins. We generalize it
to describe a sequence of boards, each of them being adjusted to the
margins of the next one
and use this approach to study common data.

Franc, A. (1989).
Multiway arrays: Some algebraic remarks. In R. Coppi & S. Bolasco
(Eds.), Multiway data analysis (pp. 1929). Amsterdam: Elsevier.
This paper is divided into three parts: * First, the main good
properties that
underly PCA are recalled. * Second, some PCA techniques for threeway
arrays
are looked on as PCA of linear maps nested on a particaular lattice
structure on
the tensor algebra. This is easily extended to nway arrays. * Third:
some of the
choices to be done to keep some good properties of PCA for its extension
to three
way arrays are sketched out on examples.

Frederiksen, N. (1972).
Toward a taxonomy of situations.
American Psychologist, 27, 114123.
F. cites in some detail T3 research of Levin (1965), Tucker
(1964) and Frederikson et al. (1972).

Frederiksen, N., Jensen, O. & Beaton, A.E. (1972).Prediction of
organizational
behavior. Elmsford N.Y.: Pergamon Press.
As part of a project to study the performance of managers in
various work situations, the performance of 118 subjects was
scored on 11 composite performance variables for each of 37
'inbasket' items. Although an indepth discussion is given of
the substantive results (after equimax rotations to simple
structure of the factor matrices). The methodological informa
tion is rather scanty.

Frenich, A. G., Galera, M. M., Vidal, J. L. M., Massart, D. L., TorresLapasio, J. R.,
De Braekeleer, K., Wang, J. H., & Hopke, P. K. (2000).
Resolution of multicomponent peaks by orthogonal projection approach, positive matrix
factorization and alternating least squares.
Analytica Chimica Acta, 411, 145155.
The application of orthogonal projection approach (OPA), alternating least squares
(ALS), and positive matrix factorization (PMF) to resolve HPLCDAD data into individual concentration
profiles and spectra is discussed. OPA was initially described as a purity method but the inclusion
of an ALS procedure allows its application as a curve resolution method. PMF is a least square
approach to factor analysis that in this study has been used as a tool to tackle the problem of curve
resolution. OPA, ALS and PMF have been applied using a single matrix (twoway data) or an augmented
matrix containing several data matrices simultaneously. The results obtained with the different
resolution methods are compared and evaluated using measures of dissimilarity between the real and
the estimated spectra. The study is performed in three data subsets, obtained by segmentation of the
original data matrix. Within each data subset, there is a reduced number of species present which
makes the resolution easier.

Frenich, A. G., Galera, M. M., Garcia, M. D. G., Vidal, J. L. M., Catasus,
M., Marti, L., & Mederos, M. V.(2001).
Resolution of HPLCDAD highly overlapping analytical signals for quantitation of
pesticide mixtures in groundwater and soil using multicomponent analysis and
neural networks.
Journal of Liquid Chromatography & Related Technologies, 24, 651668.
Along with the development of hyphenated chromatography techniques,
such as high performance liquid chromatography (HPLC) with diode array detection
(DAD), threedimensional data matrix for each sample can be easily obtained. In this
paper, a comparative study of three methods using this type of data is presented.
The capabilities of inverse calibration through ordinary least squares (OLS), partial
least squares (PLS), and an artificial neural network (ANN) model, have been
investigated for the simultaneous multicomponent analysis of synthetic mixtures of
iprodione, procymidone, chlorothalonil, folpet, and triazophos when highly overlapping
analytical signals are present.
Also, the methods have been satisfactorily applied to the determination of the
pesticides in groundwater and soil samples, although the ANN gave the best results.

Frenich, A.G., Zamora, D.P. Galera, M.M. & Vidal, J.L.M.
Application of GRAM and TLD to the resolution and quantitation of real complex
multicomponent mixtures by fluorescence spectroscopy
Analytical and Bioanalytical Chemistry, 375, 974980.
The application of the generalised rank annihilation method (GRAM) and the
trilinear decomposition (TLD) method to the resolution and quantitation of
fluorescence excitationemission matrices of a ternary mixture of pesticides,
carbendazim, fuberidazole, and thiabendazole, with overlapped spectra is described.
The results obtained with both methods are compared and evaluated using measures
of similarity (correlation coefficients) between the real and estimated spectra.
Both approaches have been tested using augmented data matrices containing only
two samples, but none of these methods succeeded completely in resolution of the
system. When TLD was applied to augmented data matrices containing more than two
samples better performance was achieved. To illustrate the application of both
algorithms to real samples, they were used in the analysis of water samples containing
the target pesticides. Again, TLD had an advantage over GRAM because the ability
to analyse data from multiple (more than two) samples simultaneously allowed the
resolution of the mixtures.

Frenich, A. G., Vidal, J. L. M., & Galera, M. M.(1999).
Use of the crosssection technique linked with multivariate calibration methods to
resolve complex pesticide mixtures.
Analytical Chemistry, 71, 48444850.
The potential of the crosssection (CS) approach in combination with the
partial least squares (PLS) and principal component regression (PCR)was assessed in the
resolution of a complex pesticide mixture showing twelve overlapped components in High
Performance Liquid Chromatography with Diode Array Detection (HPLCDAD). Careful selection
of the CS through the threedimensional (3D) (A, lambda, t) data matrix gave twodimensional
(2D) signals with the best sensitivity for the determination of each pesticide. In all
cases, the application of the PLS method demonstrated a better quantitative prediction
ability than that of the PCR method. The CSPLS approach is a powerful analytical tool.
Ten pesticides were wellresolved, while for the other two pesticides of the mixture
prediction ability was poor, and they could not be determined, probably due to their low
net analytical signal. The CSPLS model was evaluated by predicting the concentrations of
independent test set samples. Finally, the proposed model was successfully applied for
the determination of these pesticides in groundwater.

Frisvad, J. C. (1994).
Correspondence, principal coordinate and redundancy analysis used on mixed
chemotaxonomical qualitative and quantitave data.
Chenometrics and Intelligent Laboratory Systems, 23, 213229.
A mixed type data matrix consisting of 11 quantitative carbohydrate variables and 23 binary
secondary metabolites data measured in 58 isolates of 7 species of Penicillium was analyzed
using different multivariate statistical methods. This kind of data matrix is common in numerical
taxonomy and has formerly been analyzed by consensus methods based on the separate analysis
of the quantitative and qualitative data matrix, by using Gower's general similarity coefficient
for mixed data or by location models. For the initial data treatment the chi2, BrayCurtis and
Canberra distance coefficients were useful for cluster analysis and minimum spanning trees (MSTs)
combined with principal coordinate analysis (PCO). The multivariate ordination methods hitherto
recommended for chemotaxonomic data, principal component analysis (PCA) and its constrained
ordination equivalent partial least squares (PLS) analysis (using dummy variables for each species)
gave seven quite diffuse clusters with some overlap in twodimensional ordination plots, while
correspondence analysis (CA) gave seven very clear clusters. The results indicate that qualitative
data strongly dominate quantitative data and that these qualitative data are best represented in
plots by correspondence analysis. However, in physiological studies the quantitative data may be
considered the most important, PCA and CA are preferred for the analysis of mixed data. Dummy
constrained PLS may be used to select quantitative variables that are species specific rather than
related to climatic conditions. In classification studies at the species level it is recommended to
use correspondence analysis on mixed chemotaxonomical data. In the latter studies
variables based on differentiation, such as the biosynthetic families of secondary metabolites
used here, give clear species separations, and can be used for further cladistic analyses.

Fruchter, B. (1969).
A comparison of twomode and threemode factor
analysis of
psychomotor learning performance. In H. R. Wijngaarden (Pres.),
Proceedings of the XVIth
International Congress of Applied Psychology, (pp. 600607).
Amsterdam: Swets &
Zeitlinger.
Go to other sections of the Abstracts
 A  B 
C  D 
E  F 
G  H 
I  J 
K  L 
M  N 
O  P 
Q  R 
S  T 
U  V 
W  X 
Y  Z 
Top 
Algemene en Gezinspedagogiek  Datatheorie

Centre for Child and
Family Studies 
Department of Education 
The ThreeMode Company 
ThreeMode bibliography

P.M. Kroonenberg
Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *31715273446/5273434 (secr.); fax *31715273945
Email:
kroonenb@fsw.leidenuniv.nl
First version : 12/02/1997;