ThreeMode Abstracts, Part V
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
Va  Vb 
Vc  Vd 
Ve  Vf 
Vg  Vh 
Vi  Vj 
Vk  Vl 
Vm  Vn 
Vo  Vp 
Vq  Vr 
Vs  Vt 
Vu  Vv 
Vw  Vx 
Vy  Vz 

Van Benthem, M. H., Keenan, M. R., & Haaland, D. M. (2002).
Application of equality constraints on variables during alternating least squares
procedures.
Journal of Chemometrics, 16, 613622.
We describe several methods of applying equality
constraints while performing procedures that employ alternating least
squares. Among these are mathematically rigorous methods of applying
equality constraints, as well as approximate methods, commonly used in
chemometrics, that are not mathematically rigorous. The rigorous methods
are extensions of the methods described in detail in Lawson and Hanson's
landmark text on solving least squares problems, which exhibit
wellbehaved least squares performance. The approximate methods tend to be
easy to use and code, but they exhibit poor least squares behaviors and
have properties that bare not well understood. This paper explains the
application of rigorous equalityconstrained least squares and
demonstrates the dangers of employing nonrigorous methods. We found that
in some cases, upon initiating multivariate curve resolution with the
exact basis vectors underlying synthetic data overlaid with noise, the
approximate method actually results in an increase in the magnitude of
residuals. This phenomenon indicates that the solutions for the
approximate methods May actually diverge from the least squares
solution.

Van Benthem, M. H., & Keenana, M. R. (2008).
Tucker1 model
algorithms for fast solutions to large PARAFAC problems. Journal of
Chemometrics, 22, 345354.
We describe a method of performing trilinear analysis on
large data sets using a modification of the PARAFACALS algorithm. Our
method iteratively decomposes the data matrix into a core matrix and three
loading matrices based on the Tucker1 model. The algorithm is particularly
useful for data sets that are too large to upload into a computer's main
memory. While the performance advantage in utilizing our algorithm is
dependent on the number of data elements and dimensions of the data array,
we have seen a significant performance improvement over operating
PARAFACALS on the full data set. In one case of data comprising
hyperspectral images from a confocal microscope, our method of analysis
was approximately 60 times faster than operating on the full data set,
while obtaining essentially equivalent results.


Van de Geer, J.P. (1974).
Toepassing van drieweganalyse voor de analyse van multiple
tijdreeksen. In C.J. Lammers, Groei en ontwikkeling van de
ziekenhuisorganisaties in Nederland. Interim rapport, Institute of
Sociology, University of Leiden, Leiden, The Netherlands.
The application of T3 for the analysis of multivariate time series is
illustrated with a mini
example. The data are a
subset from a study of the growth of 188 Dutch hospitals over
11 years as measured by 27 variables. The computational
procedures are shown step by step to aid the explanation of
the technique.

Van de Geer, J.P. (1975).
Drieweg komponenten analyse (Memo). Department of Data Theory,
University of Leiden, Leiden, The Netherlands.
A detailed and clear discussion of many technical aspects of
T3 making extensive use of sums of squares interpretations.
Ample discussion of scaling of the input data and the effects
of this on the analysis. Description of the use of an
interactive APL threemode program.

Van den Broek, W. H. A. M., Wienke, D., Melssen, W. J., Decrom, C. W. A., & Buydens, L. (1995).
Identification of plastics among nonplastics in mixed waste by remotesensing nearinfrared imaging spectroscopy .1.
Image inmprovement and analysis by singularvalue decomposition.
Analytical Cemistry, 67, 37533759.
A nearIR camera has been installed in an experimental setup for realtime plastic
identification. Singular value decomposition (SVD) has been used for qualitative analysis and substantial
improvement of the measured multivariate images. The obtained score plots provided spatial correlations between
different pixel structures caused by sample material on the one hand and image artifacts on the other. In this
way, the score plots have been used as a tool to optimize the experimental setup and image quality. The improved
images were offered to a new classification algorithm called multivariate image rank analysis, based on SVD, as
described in part 2 of this series of articles, which follows in this issue (Wienke, D.; et al. Anal. Chem. 1995,
67, 3760).

Van der Burg, E., De Leeuw, J., & Dijksterhuis, G. (1994).
OVERALS: Nonlinear canonical correlation with k sets of
variables. Computational Statistics & Data Analysis,
18, 141163.
OVERALS is a technique for canonical correlation analysis with
two or more sets of variables. Any three way table can be used as
input for the OVERALS program. In OVERALS terminology the ways
are called objects, variables and sets. Three measurement levels
of the data can be handled: numerical, ordinal and nominal. They
can be defined for each variable separately. Also the
conditionality of the data is defined variablewise. The OVERALS
technique searches for what is common between sets of variables
measured on the same objects. The mathematical model and the
algorithm are discussed. In addition an illustration of the
technique is given in the form of an application.

Van der Burg, E., De Leeuw, J., & Verdegaal, R. (1988).
Homogeneity analysis with k sets of variables: An alternating
least squares method with optimal scaling features.
Psychometrika, 53, 177197.
Homogeneity analysis, or multiple correspondence analysis, is usually applied to
k separate variables. In this paper it is applied to sets of variables by
using sums within sets. The resulting technique is called OVERALS. It uses the
notion of optimal scaling, with transformations that can be multiple or single.
The single transformations consists of three types: nominal, ordinal, and
numerical. The corresponding OVERALS computer program minimizes a least squares
loss function by using an alternating least squares algorithm. Many existing
linear and nonlinear multivariate analysis techniques are shown to be special
cases of OVERALS. An application to data from an epidemiological survey is
presented.

Van der Heijden, P. G. M., De Falguerolles, A., & De Leeuw, J. (1989).
A combined approach to contingency table analysis
using correspondenceanalysis and loglinear analysis (with discussion).
Applied Statistics, 38, 249292.
Correspondence analysis and one of its generalizations are presented as tools
that can be ised for the analysis of residuals from loglinear models. By
recognizing relations between correspondence analysis and loglinear analysis
a better understanding of correspondence analysis is obtained. Furthermore,
it is shown how these relations can be used to arrive at a combined approach
to contingency table analysis using both loglinear analysis and correspondence
analysis.

Vander Heyden, Y., Pravdova, V., Questier, F., Tallieu, L., Scott, A., & Massart, D. L. (1989).
Parallel coordinate geometry and principal component analysis for the interpretation
of large multiresponse experimental designs.
Analytica Chimica Acta, 458, 397415.
In the evaluation of large or complex data sets the use of
visualization methods can be of great benefit. In this paper, the use of parallel
coordinate geometry (PCG) plots, principal component analysis (PCA) and Nway
PCA as visualization procedures for large multiresponse experimental designs was
compared with the more traditional approach of calculating factor effects by
multiple linear regression. PCG plots are a recent addition to the visualization
tools and offer a possibility to visualize multidimensional data in two dimensions
while no calculations are required. It was found that PCA and PCG each have their
own benefits and disadvantages. Both methods can be used to some extent to select
optimal conditions. Moreover, it was possible to use the PCA score plot as a
Pareto optimality plot that allowed to select the experiments considered to be
Pareto optimal. Therefore, the examined visualization methods can be useful and
complementary aids in the interpretation of large multiresponse experimental d
esign data and they add a multivariate dimension to the more classical univariate
analysis of such data.

Van der Kloot, W.A. & Kroonenberg, P.M. (1982)
Group and individual implicit theories of personality: An
application of threemode principal component analysis.
Multivariate Behavioral Research,
17, 471492.
The data of 60 subjects who rated 31 stimulus persons on 11
personality trait rating scales were analysed with Kroonenberg
& De Leeuw's (1980) method of threemode principal component
analysis. The study showed the advantages of including data of
'artificial subjects', and of partitioning the residual sum of
squares (badness of fit) for the elements of each of the
modes.

Van der Kloot, W.A., & Kroonenberg, P.M. (1985).
External analysis with threemode principal component models.
Psychometrika, 50, 479494.
Through external analysis of twomode data one attempts to map the elements of
one mode (e.g., attributes) as vectors in a fixed space of the elements of the
other mode (e.g., stimuli). This type of analysis is extended to threemode
data, for instance, when the ratings are made by more individuals. It is
described how alternating least squares algorithms for threemode principal
component analysis (PCA) are adapted to enable external analysis, and it is
demonstrated that these techniques are useful for exploring differences in the
individuals' mappings of the attribute vectors in the fixed stimulus space.
Conditions are described under which individual differences may be ignored.
External threemode PCA is illustrated with data from a person perception
experiment designed after two studies by Rosenberg and his associates whose
results were used as external information.

Van der Kloot, W.A., Kroonenberg, P.M., & Bakker, D. (1985).
Implicit theories of personality: Further evidence of extreme
response style. Multivariate Behavioral Research, 20, 369
387.
Five groups of 19 subjects made ratings on 11 personality trait scales of
overlapping subsets of 59 artificial stimulus persons who were described by one
to five personality trait adjectives. The data were analyzed per group of
subjects (blockwise) and per type of stimulus person (questionnairewise) by
means of threemode principal component analyses. This yielded highly similar
structures for the scales, and in the blockwise analyses, for the stimulus
persons. This similarity was substantiated by external threemode analyses,
which showed that all stimulus persons can be mapped into one overall
configuration. In all analyses it was found that differences between subjects
consisted of differences in extremity of judgment, which suggests the operation
of response style.

Van der Ven, C., Muresan, S., Gruppen, H., De Bont, D. B. A., Merck, K. B., & Voragen, A. G. J. (2002).
FTIR spectra of whey and casein hydrolysates in relation to their functional properties.
Journal of Agricultural and Food Chemistry, 50, 69436950.
Midinfrared spectra of whey and casein hydrolysates were recorded
using Fourier transform infrared (FTIR) spectroscopy. Multivariate data analysis
techniques were used to investigate the capacity of FTIR spectra to classify
hydrolysates and to study the ability of the spectra to predict bitterness,
solubility, emulsifying, and foaming properties of hydrolysates. Principal
component analysis revealed that hydrolysates prepared from different protein
sources or with different classes of proteolytic enzymes are distinguished
effectively on basis of their FTIR spectra. Moreover, multivariate regression
analysis showed satisfactory to good prediction of functional parameters; the
coefficient of determination (R2) varied from 0.60 to 0.92. The accurate
prediction of bitterness and emulsion forming ability of hydrolysates by using
only one uncomplicated and rapid analytical method has not been reported before.
FTIR spectra in combination with multivariate data analysis proved to be valuable
in. protein hydrolysate fingerprinting and can be used as. an. alternative for
laborious functionality measurements.

Van Eeuwijk, F.A. (1992).
Multiplicative models for genotypeenvironment interaction in
plant breeding. Statistica Applicata, 4, 393406.
In this paper multiplicative models for the interaction between genotype and
environment are presented, which have not yet found broad application in plant
breeding. These models are compared to the popular regression on the
environmental mean model.

Van Eeuwijk, F.A., & Kroonenberg, P.M. (1995).
The simultaneous analysis of genotype by environment interaction
for a number [of] traits using threeway multiplicative modelling.
Biuletyn Oceny Odmian/Cultivar Testing Bulletin, 26/27,
8396.
For the description of genotype by environment interaction in individual trait
twoway multiplicative models have become a popular means of analysis. For the
simultaneous analysis of genotype by environment interaction in a number of
traits threeway multiplicative models are proposed. Theory for such models is
reviewed and illustrated by an application to sugar beet resistance
data.

Van Eeuwijk, F.A., & Kroonenberg, P.M. (1998).
Multiplicative models for interaction in threeway ANOVA, with applications to
plant
breeding. Biometrics, 54, 13151333.
[Also appeared in F.A. van Eeuwijk (1996), Beyond Additivity and Non
Additivity, Unpublished doctoral thesis, University of Groningen.]
In plant breeding, multiplicative models for twoway analysis of variance
interaction have become a general means of describing
genotypebyenvironment interaction. These models offer parsimonious
descriptions and facilitate interpretations in biological terms. A
disadvantage of the prevailing dominance of twoway multiplicative models is
that data with more complicated environmental structure are
often forced to fit the twoway framework. As a partial solution to this
problem, threeway multiplicative models are presented that can be used
in addition to the more familiar twoway multiplicative models. Most
importantly, a threeway generalization is given of the twoway
singularvalue decomposition that can be applied for closer inspection of three
way analysis of variance interaction, much in the same way as
its twoway counterpart is used for twoway interaction. Two real data sets are
analyzed to illustrate how two and threeway multiplicative
models for interaction jointly provide parsimonious descriptions of various
types of genotypebyenvironment interaction. These parsimonious
descriptions are often open to meaningful biological interpretations as well.

Van Espen, P., Janssens, G., Van Hoolst, W., & Geladi, P.(1992).
Imaging and imageprocessing in analytical/chemistry.
Analusis, 20, 8190.
The concepts of acquisition and analysis of digital images obtained from spatially resolved
chemical analysis are introduced. Classical image processing techniques can be used to study these "chemical
images". However, chemical images are often multivariate in nature and require specific methods for improving
the chemical interpretation. Multivariate image analysis is introduced and explained. An example with 8
different images generated by secondary ion microscopy and electron microscopy is given.

Van IJzendoorn, M. H., & Kroonenberg, P. M. (1990).
Crosscultural consistency of doding in the strange situation.
Infant Behavior & Development, 13, 469485.
This study tested wether or not crosscultural differences in attachment classification
distributions result from systematic differences in coding practices. First, we investigated wether or not
the interactive scales have been scored consistently in several different crosscultural samples. Second,
the Richters, Waters and Vaughn (1988) functions were applied to address the question of wether or not
attachment classifications were consistently based upon the same pattern of interactive behaviors. Third,
crosscultural coding differences were described from a multivariate perspective. Data sets from seven
investigators in six countries were available for analysis. Analyses on this 'multinational data set'
revealed that except for distance interaction, the interactive scales in the two reunion episodes were
scored in accordance with the original coding rules. Furthermore, a good to reasonable agreement appeared
to exist between the original classifications and those computed by the functions, except for infants older
than 20 months of age. The multivariate principal compnent analysis showed that classification groups across
cultures were more alike than cultures across classification groups. Our data showed, therefore, that attachment
classifications have been consistently coded across cultures.

Van Mechelen, I., & Kiers, H. A. L. (1999).
Individual Differences in Anxiety Responses to Stressful Situations: A ThreeMode Component
Analysis Model.
European Journal of Personality, 13, 409428.
The threemode component analysis model is discussed as a tool for a contextualized
study of personality. When applied to person x situation x response data, the model
includes sets of latent dimensions for persons, situations, and responses as well as a so
called core array, which may be considered a summary description of the individual
di€erences in response profiles across situations. Underlying psychological processes
may be further revealed by relating the model to external data on cognitive±a€ective
personality system (CAPS) variables. The model as well as its validation in CAPS terms
is illustrated with selfreport data on anxiety responses displayed by several persons in a
sample of situations. Furthermore, the model is tested against recently formulated
criticisms regarding the use of (twomode) factor analysis in personality research, and
its relation to the triple typology model recently proposed by Vansteelandt and Van
Mechelen (1998) is briefly discussed.

Van Mispelaar, V. G., Tas, A. C., Smilde, A. K., Schoenmakers, P. J.
& van Asten, A. C. (2003).
Quantitative analysis of target components by comprehensive twodimensional
gas chromatography.
Journal of Chromatography A, 1019, 1529.
Quantitative analysis using comprehensive twodimensional (2D) gas chromatography
(GC) is still rarely reported. This is largely due to a lack of suitable software.
The objective of the present study is to generate quantitative results from a
large GC x GC data set, consisting of 32 chromatograms. In this data set, six
target components need to be quantified. We compare the results of conventional
integration with those obtained using socalled "multiway analysis methods". With
regard to accuracy and precision, integration performs slightly better than Parallel
Factor (PARAFAC) analysis. In terms of speed and possibilities for automation,
multiway methods in general are far superior to traditional integration.

Van Sprang, E. N. M., Ramaker, H. J., Westerhuis, J. A., Gurden, S. P, & Smilde, A. K. (2002).
Critical evaluation of approaches for online batch process monitoring.
Chemical Engineering Science, 57, 39793991.
Since the introduction of batch process monitoring using component
models in 1992, different approaches for statistical batch process monitoring have
been suggested in the literature. This is the first evaluation of five proposed
approaches so far. The differences and similarities between the approaches are
highlighted. The derivation of control charts for these approaches are discussed.
A control chart should give a fast and reliable detection of disturbances in the
process. These features are evaluated for each approach by means of two performance
indices. First, the action signal time for various disturbed batches is tested.
Secondly, the probability of a false warning in a control chart is computed. In
order to evaluate the five approaches, five different data sets are studied: one
simulation of a batch process, three batch processes obtained from industry and
one laboratory spectral data set. The obtained results for the performance indices
are summarised and discussed. Recommendations helpful for practical use are given.

Vansteelandt, K., & Van Mechelen, I. (1998).
Individual differences in situationbehaviour profiles: A triple typology model.
Journal of Personality and Social Psychology, 75, 751765.
A model is proposed to represent individual differences in situationbehaviour
profiles. The model consists of 3 components: a) Typologies of person,
situation, and behaviour classes; b) hierarchical relations between the classes
of each typology; and c) a characterization of the person types in terms of
different sets of if (situation class) then (behaviour class) rules by which the
3 typologies are linked to one another. A data analysis technique (INDCLAS) is
available to induce a triple typology model from empirical data. To reveal the
psychological mechanisms behind such a model, the classes of the model can be
related to situation, behaviour and person features. As a result, person types
can be interpreted in terms of systems of cognitiveaffective variables that
mediate between active situation features and behavioural manifestations. This
is illustrated with a study on selfreported hostile behaviour in frustrating
situations.

Van Stokkum, I. H. M., Larsen, D. S., & Van Grondelle, R. (2004).
Global and target analysis of timeresolved spectra.
Biochimica et Biophysica ActaBioenergetics, 1657, 82104.
In biological/bioenergetics research the response of a complex system to
an externally applied perturbation is often studied. Spectroscopic measurements at
multiple wavelengths are used to monitor the kinetics. These timeresolved spectra are
considered as an example of multiway data. In this paper, the methodology for global and
target analysis of timeresolved spectra is reviewed. To fully extract the information
from the overwhelming amount of data, a modelbased analysis is mandatory. This analysis
is based upon assumptions regarding the measurement process and upon a physicochemical
model for the complex system. This model is composed of building blocks representing
scientific knowledge and assumptions. Building blocks are the instrument response
function (IRF), the components of the system connected in a kinetic scheme, and
anisotropy properties of the components. The combination of a model for the kinetics and
for the spectra of the components results in a more powerful spectrotemporal model. The
model parameters, like rate constants and spectra, can be estimated from the data, thus
providing a concise description of the complex system dynamics. This spectrotemporal
modeling approach is illustrated with an elaborate case study of the ultrafast dynamics
of the photoactive yellow protein.

Van Zomeren, P. V., Hoogvorst, A., Coenegracht, P. M. J., & de Jong, G. J. (2004).
Optimisation of highperformance liquid chromatography with diode array detection
using an automatic peak tracking procedure based on augmented iterative target
transformation factor analysis.
Analyst, 129, 241248.
An automated method for the optimisation of highperformance liquid
chromatography is developed. First of all, the sample of interest is analysed with various
eluent compositions. All obtained data are combined into one augmented data matrix.
Subsequently, augmented iterative target transformation factor analysis performs the
integrated tasks of curve resolution and peak tracking. Since this type of curve resolution
processes all data at once, it can deal with strong peak overlap and reveal the
correspondence of compounds between runs, i.e. peak tracking. The retention time and peak
width at half height for each component of the sample are determined for every eluent
composition. Next, models are built for the retention time and the peak width at half height.
These models are used to predict the resolution and the analysis time for each point in
factor space. Finally, a multicriterion decisionmaking method, Pareto optimality, is used
to find the optimum. The method completes all calculations within a few minutes and without
user intervention. By means of this procedure, a mixture of three benzodiazepines is
successfully separated using a ternary mobile phase. There are two requirements for the
automated optimisation method to work correctly. Firstly, all components of the sample must
have sufficiently different spectra. Secondly, each compound should have the same spectrum
under all experimental conditions.

Vasilescu, M. A. O., & Terzopoulos, D. (2002).
Multilinear Analysis of Image Ensembles: TensorFaces.
In A. Heyden, G. Sparr, M. Nielsen, and P. Johansen (Eds.),
Computer Vision  ECCV 2002, Part II, (pp. 447460).
SpringerVerlag, Berlin.
Natural images are the composite consequence of multiple
factors related to scene structure, illumination, and imaging. Multilinear
algebra, the algebra of higherorder tensors, offers a potent mathematical
framework for analyzing the multifactor structure of image ensembles and
for addressing the difficult problem of disentangling the constituent
factors or modes. Our multilinear modeling technique employs a tensor
extension of the conventional matrix singular value decomposition (SVD),
known as the Nmode SVD. As a concrete example, we consider the
multilinear analysis of ensembles of facial images that combine several
modes, including different facial geometries (people), expressions, head
poses, and lighting conditions. Our resulting "TensorFaces" representation
has several advantages over conventional eigenfaces. More generally,
multilinear analysis shows promise as a unifying framework for a variety
of computer vision problems.

Vasilescu, M. A. O., & Terzopoulos, D. (2004).
TensorTextures: Multilinear Imagebased rendering.
ACM Transactions on Graphics, 23, 336342.
This paper introduces a tensor framework for imagebased rendering. In
particular, we develop an algorithm called TensorTextures that learns a parsimonious model
of the bidirectional texture function (BTF) from observational data. Given an ensemble of
images of a textured surface, our nonlinear, generative model explicitly represents the
multifactor interaction implicit in the detailed appearance of the surface under varying
photometric angles, including local (pertexel) reflectance, complex mesostructural
selfocclusion, interreflection and selfshadowing, and other BTFrelevant phenomena.
Mathematically, TensorTextures is based on multilinear algebra, the algebra of higherorder
tensors, hence its name. It is computed through a decomposition known as the Nmode SVD, an
extension to tensors of the conventional matrix singular value decomposition (SVD). We
demonstrate the application of TensorTextures to the imagebased rendering of natural and
synthetic textured surfaces under continuously varying viewpoint and illumination conditions.

Vavra, T.G. (1972).
An application of threemode factor analysis to product
perception. In F.D. Allvine (Ed.) Marketing in motion/Relevance in Marketing. Chicago: American
Marketing Association, Series no.33 (Pp. 578583).

Vavra, T.G. (1973).
A threemode factor analytic investigation into the effectiveness
of advertising. Unpublished doctoral thesis, University of
Illinois, UrbanaChampaign, IL. (Dissertation Ab
stracts International, 1974, 34 (12A), 7802.)
T3 is used to assess the effectiveness of various types of
commercials for specific groups of customers. The problem of
interpreting the solution is discussed, and two alternative
procedures are shown.

VegaMontoto, L. & Wentzell, P. D. (2003).
Maximum likelihood parallel factor analysis (MLPARAFAC) Journal of Chemometrics,
17, 237253.
Algorithms for carrying out maximum likelihood parallel
factor analysis (MLPARAFAC) for threeway data are described. These
algorithms are based on the principle of alternating least squares, but
differ from conventional PARAFAC algorithms in that they incorporate
measurement error information into the trilinear decomposition. This
information is represented in the form of an error covariance matrix. Four
algorithms are discussed for dealing with different error structures in
the threeway array. The simplest of these treats measurements with
nonuniform measurement noise which is uncorrelated. The most general
algorithm can analyze data with any type of noise correlation structure.
The other two algorithms are simplifications of the general algorithm
which can be applied with greater efficiency to cases where the noise is
correlated only along one mode of the threeway array. Simulation studies
carried out under a variety of measurement error conditions were used for
statistical validation of the maximum likelihood properties of the
algorithms. The MLPARAFAC methods are also shown to produce more accurate
results than PARAFAC under a variety of conditions.

VegaMontoto, L, & Wentzell, P. D. (2005).
Mathematical
improvements to maximum likelihood parallel factor analysis: experimental
studies. Journal of Chemometrics, 19, 236252.
In this paper, the application of a number of simplified
algorithms for maximum likelihood parallel factor analysis (MLPARAFAC) to
experimental data is explored. The algorithms, described in a companion
paper, allow the incorporation of a variety of correlated error structures
into the threeway analysis. In this work, three experimental data sets
involving fluorescence excitationemission spectra of synthetic
threecomponent mixtures of aromatic compounds are used to test these
algorithms. Different experimental designs were employed for the
acquisition of these data sets, resulting in measurement errors that were
correlated in either two or three modes. A number of dataanalysis methods
were applied to characterize the error structures of these data sets. In
all cases, the introduction of statistically meaningful information
translated to estimates of better quality than the conventional PARAFAC
estimates of concentrations and spectra. The use of the algorithms that
employ the error structure suggested by the analysis of the error
covariance matrix yielded the best results for each data set.

Veldscholte, C.M. (1994).
A threemode principal component analysis of perceptions of
economic activities: TUCKALS3 also compared with twomode PCA.
Master's Thesis, Department of Method and Technique, Leiden University.
Threedimensional data of four countries from a research
project on 'perceptions on economic activities', originally analysed with
the help of twomode principal component analyses (PCA), were reanalysed
with TUCKALS3, a program for three mode PCA. The objective of the
analysis was to trace the similarities and differences in perceptual
structure of the four countries, and to compare the results with those of
the twomode PCA's.

Veldscholte, C.M., Antonides, G., & Kroonenberg, P.M. (1995).
Converging perceptions of economic activities between East and
West: A threemode principal component analysis. (Research
Report R9519/A), Rotterdam Institute for Business Economic
Studies, Erasmus University, Rotterdam. (also: Tinbergen Institute
Research Report Nr. TI 195192).
The similarities and differences in perceptual structure of economic activities
in Hungary, Poland, the Netherlands and the United Kingdom are the focus of this
study. The threemode data consisted of economic activities (mode 1) scored on
rating scales (mode 2) by a number of individuals (mode 3). The data were
analysed with threemode principal component analysis (PCA) using the program
TUCKALS3. The primary result is that there is a perceptual space common to all
four nations. It is characterised by a contrast between economic and social
values in the first dimension, by immediate or delayed consequences of
activities in the second dimension, and finally by an occupationalprivate
dimension. The most striking difference between countries is that the British
have another view of the financial resources necessary for certain detail in
order to show how it can be applied to unravel structures in complicated three
mode data such as these, which frequently arise in the field of
perception.

Veldscholte, C. M., Kroonenberg, P. M., & Antonides, G. (1998).
Threemode analysis of perceptions of economic activities in Eastern and Western Europe.
Journal of Economic Psychology, 19, 321351.
Data on similarities and differences in perceptions of economic activities
in Hungary, Poland, the Netherlands and the United Kingdom were collected. The data set
is a threemode one consisting of economic activities (mode 1) scored on rating scales
(mode 2) by a number of individuals or judges (mode 3). The major thesis of this paper is
that such data should be analyzed by threemode analysis methods rather than twomode
methods. To demonstrate this, the data were analyzed with threemode principal component
analysis (PCA) using the program TUCKALS3. Both the decisions which precede the threemode
analysis, the threemode analysis itself, and its interpretation are illustrated and
explained. The paper treats threemode PCA in some detail in order to show how it can be
applied to unravel structures in complicated threemode data which frequently arise in the
field of economic perception. The substantive result is that there is a perceptual space
common to all four nations. It is characterized by contrasts between economic and social
values, by immediate or delayed consequences of activities, and by a difference between
occupational and private activities. The most striking difference between countries is that
the British have a different view of the financial resources necessary for certain activities
compared to inhabitants of the other three countries.

Venth, K., Danzer, K., Kundermann, G., & Blaufuss, K. H. (1996).
Multisignal evaluation in ICPMS  Determination of trace elements in MoZralloys.
Fresenius Journal of Analytical Chemistry, 354, 811817.
The existence of isobaric and polyatomic ion
interferences has been considered to be a
significant shortcoming of inductively coupled
plasma  mass spectrometry (ICPMS). In the
special case of MoZralloys problems caused by
polyatomic ions are substantial. The determination
of trace elements by using classical univariate
linear regression of single signals or any
correction equations presented by the instrumental
software is impossible. There are various
possibilities to overcome spectral interferences,
in principle. The application of highresolution
ICPMS, separation methods or alternative sample
introduction systems is limited by the high cost
and the apparative expenditure. In this report
methods of multisignal calibration, like partial
least squares (PLS) regression and canonical
correlation analysis (CCA), are used to overcome
isobaric or chemical interferences in ICPMS. It
is shown, that PLS and CCA are able to handle or
tolerate, respectively, spectral interferences
existing in a MoZrOHF system. The results of
quantitative analysis provided by PLS and CCA were
comparable.

Verhees, J. (1989).
Econometric analysis of multidimensional models.
Unpublished doctoral thesis, Department of Econometrics,
University of Groningen, the Netherlands.
Part 1. Matrix algebra.
1. Matrices and properties; 2. Kronecker product and vec operator; 3. (0,1)
matrices and their properties.
Part 2. Multidimensional data analysis models.
4. kmode principal component analysis; 5. kmode factor analysis;
6. kmode covariance structure analysis; 7. kmode interdependent
regression; 8. kmode Poisson regression; 9. From formulas to programs;
10. Conclusion.

Verhees, J., & Wansbeek, T.J. (1990).
A multimode direct product model for covariance structure analysis.
British Journal of Mathematical and Statistical Psychology,
43, 231240.
In psychometrc literature, there is evidence that the modes
(facets, dimensions, etc.) in multimode data interact
mutliplicatively. A basic expression of this idea is that a
covariance matrix may then be written as repeated Kronecker
product of k, say, parameter matrices, where k is the number of
modes. For such a 'factorial covariance structure' we give an
integrated treatment of ML, WLS, and ULS estimators. A
modification of the ULS estimator appears to be noniteratively
computable.

Vichi, M. (1988).
Twoway data matrix representative syntheses of a threeway data
matrix. Statistica, 48, 91106.
This paper deals with threeway data of individuals and variables observed on
r different occasions. We are interested 1) in defining properties which
have hold for twoway syntheses of threeway matrices; 2) in detecting matrices
that possess these properties. A twoway matrix X* is a representative
synthesis of a threeway data matrix if: a) it minimizes differences between
itself and the threeway matrix, over all possible twoway matrices, according
to a predefined distance between three and twoway matrices; b) it satisfies a
specific internality property. It turns out that the median matrix and the
arithmetic mean matrix possess properties a) and b). Also Rizzi's matrix (1987)
is a representative synthesis of the threeway transformed matrix, while the
matrix of Escoufier does not possess properties a) and b). We compute some
representative syntheses in order to compare different X*'s, and to give
intuitive reasons for the choice of one matrix instead of another in different
research situations.

Vichi, M. (1989).
La connessione e la correlazione tra due matrici dei dati
componenti una matrice a tre indici. [Association and regression
between data matrices in a threeway matrix]. Statistica,
49, 225243.
A systematic study and a critical examination is carried out on the connections
and correlations between all pairs of slices of a threeway matrix. Correlations
between two matrices have to reflect whether all variables of a matrix are more
frequently concordant or discordant with all variables of the other matrix. Two
such correlations are proposed which revert to appropriate correlation measures
if the matrices each contain one variable.

Vichi, M. (1990).
L'analisi in matrici fattoriali di una matrice a tre indici.
[Factorial matrix analysis for a threeway matrix]. Statistica,
50, 525546.
In this paper the FAMA model (FActorial Matrix Analysis) is proposed and
studied. FAMA is characterised by three steps. The analysis of
dependence, in which a suitable correlation index between matrices
Z_{h} and Z_{m} (frontal slices of
Z) is chosen. The index quantifies the statistical relationships between
couples of situations h and m. Different measures can be derived
by the generalised index of dependence between matrices (Vichi, 1989). Furthermore the matrices
Z_{h} are geometrically represented as points in an
appropriate Euclidean space in order to examine the trend of the phenomenon in
different occasions. The synthesis: The gth factorial matrix is
the normalised linear combination of Z_{h} (h= 1,
..., r), which summarises the gth largest amount of dependence
(according to generalised index of dependence) and it is independent of the
former factorial matrices (following the meaning of the generalised index).
The singular decomposition, which allows us to represent into a cartesian
reference system simultaneously the individuals and the variables of the three
way data matrix and the factorial matrix.

Vichi, M. (1991).
Le techniche che derivano dall'analisi in matrici fattoriali di
una matrice a tre indici. [Factorial matrices derived from a
threeway matrix]. Statistica, 51, 5377.
In this paper, after introducing the Factorial Matrices Analysis (FAMA) in order
to study a threeway matrix (Vichi, 1990),
the author examines techniques already known in literature, that can be derived
from FAMA, adding new tools of analysis. Furthermore, the author introduces new
methodologies from FAMA to overcome problems connected with some of the known
techniques.

Vichi, M. (1998).
Principal classifications analysis: a method for generating consensus dendograms and its
application to threeway data. Computational Statistics & Data Analysis, 27,
311331.
A threeway data set is the result of the observation of data characterized
by three modes: units, variables, and occasions. It is often useful to classify the elements
of one mode on the basis of the other two. This is referred to as One Mode Classification
(OMC) of a threeway data set and it can be seen as a synthesis of a set of hierarchical
classifications, each one defined by applying a hierarchical algorithm to a twomode matrix
of the threeway data set (after standardizing variables if necessary). For example, the OMC
of the units according to variables and occasions is a consensus of the set of hierarchical
classifications defined by clustering the same units according to variables for each different
occasion; i.e., the classification of the same multivariate units observed in different
occasions. This last case will be considered in this paper.
Many consensus methods can be used to achieve OMC of a threeway data set, however, often
the set of hierarchical classifications is wide and some of these are dissimilar, hence a
single synthesis, is generally not representative of the entire set. This might happen because
in the observed threeway data set there are several groups of similar hierarchical
classifications, i.e., formed by dendrograms that partially or completely repeat in different
occasions without systematic differences. Therefore a consensus classification for each subset
of similar classifications can be defined. Furthermore, when a single consensus is used for a
set of classifications relative to different time situations, a loss of meaningful information
on the evolution of the set of classifications is generally observed. To overcome these
difficulties we propose the PRINcipal CLassifications Analysis of a threeway data set. The
idea, in PRINCLA, is to find few nonobservable hierarchical classifications, called principal
classifications, each defined as a weighted mean hierarchical classification. No pairs of
principal classifications are computed with the contribution of a same original hierarchical
classification.

Vives, M., Gargallo, R., & Tauler, R. (2001).
Threeway multivariate curve resolution applied to speciation of
acidbase and thermal unfolding transitions of an alternating
polynucleotide.
Biopolymers, 59, 477488.
Analytical speciation of acidbase equilibria and
thermal unfolding transitions of an alternating random polynucleotide
containing cytosine and hypoxanthine, poly(C, I). is studied. The
results (ire compared with those obtained previously for singlestranded
polynucleotides, poly(I) and poly(C), and for the doublestranded poly(I).
poly(C), to examine the influence of the secondary structure on the
acidbase properties of bases. This study is based on monitoring
acidbase titrations and thermal unfolding experiments by molecular
absorption, CD, and molecular fluorescence spectroscopies. Experimental
data were analyzed by a novel chemometric approach based on a recently
developed threeway Multivariate Curve Resolution method, which allowed
the simultaneous analysis of data from several spectroscopies. This procedure
improves the resolution of the concentration profiles and pure spectra for
the species and conformations present in foldingunfolding and acidbase
equilibria.
The results from acidbase studies showed the existence of only three
species in the pH range 212 at 37 degreesC and 0.15M ionic strength.
No cooperative effects were detected front the resolved concentration
profiles, showing that equilibria concerning alternating polynucleotides
like poly(C, I) are simpler than those involving poly(I) . poly(C). T
hermal unfolding experiments at neutral pH confirmed the existence of
two transitions and one intermediate conformation. This intermediate
conformation could only be detected and resolved without ambiguities
when molecular absorption and CD spectral data were analyzed simultaneously.

Vivien, M., & Sabatier, R. (2001b).
Une extension multitableaux de la régression PLS.
Revue Statistique Appliquée, 49, 3154.
In this article, an extension for the PLS method, OMCIAPLS, is presented. It allows
a "global" modelling of K data sets measured on the same n individuals.
The optimization of the criterion that is proposed amounts to resolving usual PLS,
but gives extra objects and help to interpretation. An example based on real data
is processed.

Vivien, M., & Sabatier, R. (2003).
Generalized orthogonal multiple coinertia analysis(PLS): new multiblock component
and regression methods. Journal of Chemometrics, 17, 2873001.
The purpose of this paper is to develop new componentwise component and regression
multiblock methods that overcome some of the difficulties traditionally associated
with multiblocks, such as the stepbystep optimization and component orthogonalities.
Generalized orthogonal multiple coinertia analysis (GOMCIA) and generalized orthogonal
multiple coinertia analysispartial least squares (GOMCIAPLS) are proposed for
modelling two sets of blocks measured on the same observations. We especially emphasize
GOMCIAPLS methods in which we consider one of the sets as predictive. All these
methods are based on the stepbystep maximization of the same criterion under
normalization constraints and produce orthogonal components or supercomponents.
The solutions of the problem have to be computed with an iterative algorithm (which
we prove to be convergent). We also give some interesting special cases and discuss
the differences compared with a few other multiblock and/or multiway methods. Finally,
short examples of real data are processed to show how GOMCIAPLS can be used and its
properties.

Vivien, M., & Sabatier, R. (2004).
A generalization of STATISACT strategy: DOACT for two multiblocks tables.
Computational Statistics & Data Analysis, 46, 155171.
A new strategy is introduced for analyzing two multiblocks tables:DOACT.This method is
closely related to the STATIS (or ACT)methodology and the Tucker interbattery method.The
length of two multiblocks are not necessarily the same and the optimal solution obtained is that
of a global optimization problem.The advantage of using DOACT is that the rst step provides
a summary of the two multiblocks tables,in the second step two optimal representations (one for
each multiblock)of the observations can be plotted and in the third step a global description of
each table of each multiblock can be made.An example of DOACT performance is illustrated
with a real data set.The program implementing the method has been developed using the SPlus
6 :0 J (2000)language.
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Algemene en Gezinspedagogiek  Datatheorie

Centre for Child and
Family Studies 
Department of Educational
Sciences 
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;