ThreeMode Abstracts, Part O
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INDEX
Oa  Ob 
Oc  Od 
Oe  Of 
Og  Oh 
Oi  Oj 
Ok  Ol 
Om  On 
Oo  Op 
Oq  Or 
Os  Ot 
Ou  Ov 
Ow  Ox 
Oy  Oz 


Okada, A. (1990).
A generalization of asymmetric multidimensional scaling.
In M. Schader & W. Gaul (Eds.), Knowledge, data and
computerassisted decisions (pp. 127138). Berlin: Springer.
An asymmetric multidimensional scaling model, which is derived by
generalizing the predecessor, and the nonmetric algorithm to fit the present model to an
asymmetric proximity matrix is presented. In the present model asymmetries in proximities are
accounted for not only by the term related with stimuli or with dimensions but by the term
related with stimuli and dimensions. Geometrically each stimulus is represented as a point and
an ellipse (ellipsoid, hyperellipsoid) in a multidimensional Euclidean space. The
present model is applied to car switching data among 12 car segments. The obtained two
dimensional solution is compatible with the previous analyses. And it seems that the length of the
semiaxes of the ellipse might represent the relative dominance or attractiveness on the
two dimensions respectively.

Okada, A., & Imaizumi, T. (1980).
Nonmetric method for extended INDSCAL model.
Behaviormetrika, 7, 1322.
A new method is introduced which can explain individual
differences in dissimilarity judgments by N subjects. The method
is based on a weighted distance model which is a generalization
of DeLeeuw and Pruzansky's model to Minowski r metric. A set of N
dissimilarity matrices is analyzed nonmetrically to derive a
group stimulus configuration and a subject configuration just as
INDSCAL. The method optimizes the goodness of fit measure which
is based on the stress formula two by the method of steepest
descent. This optimizing measure makes the computing process
independent of the Minowski constant. The method was applied to
schematic face data, and gave satisfactory results.

Okada, A. (2002).
A review of cluster analysis and Multidimensional Scaling research in sociology.
Sociological Theory and Methods, 17, 167181.
An overview of studies is presented which utilize cluster analysis and MDS
(MultiDimensional Scaling) in sociology. Before focusing our attention onto studies in
sociology, questionable ways of applying these two procedures are discussed which can be seen
not only in studies in sociology but also commonly in many other areas. Then several aspects
of applying these two procedures in sociology, which seem to be interesting and to be
problematic, are focused upon. Discussions follow on how to cope with the problematic aspects
and how to apply these procedures more appropriately. Procedures of cluster analysis and MDS,
which have been developed with relation to sociological studies, are referred to, and
procedures of applying cluster analysis and MDS, which also have been introduced in sociological
studies, are presented. Several new aspects of applying cluster analysis and MDS in future
sociological studies are stated.

Okada, A., & Imaizumi, T. (1986).
How to use nonmetric Euclidean/nonEuclidean weighted
multidimensional scaling program (NNEWMDS version 1.1).
Journal of Applied Sociology, 3, 181.
This manual explains how to use a computer program which performs fitting
weighted Euclidean/nonEuclidean model of Okada and Imaizumi (1980) to do
individual difference multidimensional scaling. The model itself and the algorithm to fit the
model was introduced and described by the authors in that paper. But the present computational
algorithm is an improvement on the originally published one.

Okada A. & Imaizumi, T. (1996).
Analyzing friendship ties by using twomode threeway asymmetric
multidimensional scaling.
Japanese Psychological Review, 39,459475 (in Japanese
with English abstract).
Friendship tie data collected by Kumbasar et al. (1994) from 25
employees of a department of a computer company were analysed with
twomode threeway asymmetric mds in dimensions. Differnces in
asymmetry of different groups could be observed.

Okada A. & Imaizumi, T. (1997).
Asymmetric multidimensional scaling of twomode threeway
proximities.
Journal of Classification, 14,195224.
An asymmetric multidimensional scaling model and an associated
nonmetric algorithm to analyse twomode threeway asymmetric
proximites are introduced. The model consists of a common object
configuration and weights for symmetry and asymmetry. In the common
object configuration each object is represented by a point and a
circle in a Euclidean space. The common object configuration
represents pairwise proximity relationships between pairs of objects
for the 'group' of all sources. Each source has its own symmetry
weight and a set of asymmetry weights. Symmetry weights represent
individual differences among sources in asymmetric proximity
relationships. The associated nonmetric algorithm is an extension of
the algorithm developed earlier (Okada and Imaizumi, 1987). As an
illustrative example, intergenerational occupational mobility in
Japan among eight occupational categories is analysed.

Okada, A., & Imaizumi, T. (1999).
Twomode threeway asymmetric multidimensional scaling with constraints
on asymmetry. In R. Decker & W. Gaul (Eds.) Classification and
Information Processing at the Turn of the Millennium: Proceedings of the
23rd annual conference of the Gesellschaft für Klassifikation
(pp. 5259). Bielefield: 1012 March.
A model and an accompanying algorithm for twomode threeway asymmetric
multidimensional scaling is presented. The present model has a constraint
on asymmetry, compared with the model of
Okada, Imaizumi (1997)
where each source has a different magnitude of asymmetry, but all sources are
constrained so that the relative importance of the asymmetry along dimensions
is constant for all sources. The accompanying nonmetric algorithm was
developed from similar work in Okada, Imaizumi (1997). An application to
interpersonal attraction data among university students is presented.

Okada, A., & Marumo, J. (1993).
Utilizing MDPREF to disclose between and within group differences. Sociological
Theory and Methods, 8, 127141.
A procedure of using MDPREF to analyze paired comparison or dominance data on
items and to disclose between and within group differences when subjects consist
of several different groups is presented. The procedure consists of four phases.
(a) To cluster subjects of each group by applying some of cluster analysis methods.
(b) To derive an inner product matrix among items for each cluster. (c) To analyze
these inner product matrices by INDSCAL, and (d) To derive subject configuration
(subject vectors) of MDPREF by an external MDPREF analysis based on the common object
(item) configuration given by the INDSCAL analysis. The procedure inherited the
uniquely oriented dimensions of the object (item) configuration from INDSCAL. The
procedure is applied to the survey data comparing eating habits among three cities.

Olivieri, A. C., & Faber, N. K. M. (2004a).
Standard error of prediction in parallel factor analysis of threeway data.
Chemometrics en Intelligent Laboratory Systems, 70, 7582.
A simple approach is described to calculate samplespecific standard errors for
the concentrations predicted by a threeway parallel factor (PARAFAC) analysis
model. It involves a firstorder error propagation equation in which the correct
sensitivity and leverage values are introduced. A comparison is made with a related
unidimensional partial leastsquares (PLS) model, specifically as regards the
required leverage values. Monte Carlo simulation results obtained by adding random
noise to both concentrations and instrumental signals for theoretical binary mixtures
are in good agreement with the proposed approach. An experimental multicomponent
example was studied by a similar Monte Carlo approach, and the obtained standard
errors are also in agreement with the calculated values. Implications concerning
the limit of detection are discussed.

Olivieri, A. C., Arancibia, J. A., De La Pena, A. M., DuranMeras, I., & Mansilla, A. E. (2004b).
Secondorder advantage achieved with fourway fluorescence excitationemissionkinetic
data processed by parallel factor analysis and trilinear leastsquares. Determination
of methotrexate and leucovorin in human urine.
Analytical Chemistry, 76, 56575666.
Fourway fluorescence data recorded by following the kinetic evolution of
excitationemission fluorescence matrices (EEMs) have been analyzed by parallel factor
analysis and trilinear leastsquares algorithms. These methodologies exploit the
secondorder advantage of the studied data, allowing analyte concentrations to be
estimated even in the presence of an uncalibrated fluorescent background. They were
applied to the simultaneous determination of the components of the anticancer combination
of methotrexate and leucovorin in human urine samples. Both analytes were converted into
highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics
of the reaction was continuously monitored by recording full EEM of the samples at
different reaction times. A commercial fast scanning spectrofluorometer has been used
for the first time to measure the fourway EEM kinetic data. The rapid scanning
instrument allows the acquisition of a complete EEM in 12 s at a wavelength scanning
speed of 24 000 nm/min. The emission spectra were recorded from 335 to 490 nm at 5nm
intervals, exciting from 255 to 315 nm at 6nm intervals. Ten successive EEMs were
measured at 72s intervals, to follow the fluorescence kinetic evolution of the mixture
components. Good recoveries were obtained in synthetic binary samples and also in spiked
urine samples. The excitation, emission, and kinetic time profiles recovered by both
chemometric techniques are in good agreement with experimental observations.

Olivieri, A. C., Faber, N. K. M., Ferre, J., Boque, R. Kalivas, J. H., & Mark, H. (2006).
Uncertainty estimation and figures of merit for multivariate calibration.
International Union of Pure and Applied Chemistry, 78, 633661.
This paper gives an introduction to multivariate calibration from a
chemometrics perspective and reviews the various proposals to
generalize the wellestablished univariate methodology to the
multivariate domain. Univariate calibration leads to relatively simple
models with a sound statistical underpinning The associated uncertainty
estimation and figures of merit are thoroughly covered in several
official documents. However, univariate model predictions for unknown
samples are only reliable if the signal is sufficiently selective for
the analyte of interest. By contrast, multivariate calibration methods
may produce valid predictions also from highly unselective data. A case
in point is quantification from nearinfrared (NIR) spectra. With the
everincreasing sophistication of analytical instruments inevitably
comes a suite of multivariate calibration methods, each with its own
underlying assumptions and statistical properties. As a result,
uncertainty estimation and figures of merit for multivariate
calibration methods has become a subject of active research, especially
in the field of chemometrics.

Oort, F.J. (1999).
Stochastic threemode models for mean and
covariance structures.
British Journal of Mathematical & Statistical
Psychology, 52, 243272.
With threemode models, the three modes are
analysed simultaneously. Examples are the
analysis of multitraitmultimethod data where the
modes are traits, methods and subjects, and the
analysis of multivariate longitudinal data where
the modes are variables, occasions and subjects.
If we consider the subjects mode as random, and
the other modes as fixed, such data can be
analysed using stochastic threemode models.
Threemode factor analysis models and composite
direct product models are special cases, but they
are models for the covariance structure only.
Stochastic threemode models for mean and
covariance structures are presented, and the
identification, estimation and interpretation of
the model parameters are discussed.
Interpretation is facilitated by introducing a
new terminology and by considering various
special cases. Analyses of real data from the
field of economic psychology serve as an
illustration.

Oort, F.J. (2001).
Threemode models for multivariate longitudinal data. British Journal of Mathematical
and Statistical Psychology, 54, 4978.
Multivariate longitudinal data are characterized by three modes: variables,
occasions and subjects. Threemode models are described as special cases of a
linear latent variable model. The assumption of measurement invariance across
occasions yields threemade models that are suited for the analysis of
multivariate longitudinal data. These socalled longitudinal threemode models
include autoregressive models and latent curve models as special cases.
Empirical data from the held of industrial psychology are used in an example
of how to test substantive hypotheses with the longitudinal, autoregressive and
latent curve threemode models.

Orekhov, V.Y., Ibraghimov, I.V., & Billeter, M. (2001).
MUNIN: A new approach to multidimensional NMR spectra interpretation.
Journal of Biomolecular NMR, 20, 4960.
A new method, MUNIN (Multidimensional NMR spectra interpretation), is
introduced for the automated interpretation of threedimensional
NMR spectra. It is based on a mathematical concept referred to as threeway
decomposition. An NMR spectrum is decomposed into a sum of
components, with each component corresponding to one or a group of peaks.
Each component is defined as the direct product of three
onedimensional shapes. A consequence is reduction in dimensionality of the
spectral data used in further analysis. The decomposition may be
applied to frequencydomain or timedomain data, or to a mixture of these.
Features of MUNIN include good resolution in crowded regions and
the absence of assumptions about line shapes. Uniform sampling of timedomain
data, a prerequisite for discrete Fourier transform, is not
required. This opens an avenue for the processing of NMR data that do not
follow oscillating behaviour, e.g. from relaxation measurements.
The application of MUNIN is illustrated for a H1N15NOESYHSQC, where each
component is defined as the set of all NOE peaks formed by
a given amide group. As a result, the extraction of structural information
simply consists of onedimensional peak picking of the shape along
the NOEaxis obtained for each amide group.

Orekhov, V. Y., Ibraghimov, I., & Billeter, M. (2003).
Optimizing resolution in multidimensional NMR by threeway decomposition.
Journal of Biomolecular NMR, 27, 165173.
Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important
determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the
following timesaving scheme for threedimensional spectra. An extensive grid of discrete t1 and t2values is used,
which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the
recording of t3FIDs for selected pairs of t1 andt2; typically the recording is omitted for about 75% of the (1,2)
combinations. These data sets are referred to as sparse, and postexperimental processing making optimal use of
spectral redundancy provides the missing, nonrecorded data. We have previously shown that threeway decomposition
(TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a
novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl. 9, 551–565] is used to complement a
sparsely recorded timedomain data set by providing the missing FIDs for all (1,2) combinations omitted in the
experiment. A necessary condition is that for each t1value at least a few FIDs are recorded, and similar for each
t2value. The method is demonstrated on nonuniformly sampled 15 NNOESYHSQC data sets recorded for the
14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequencydomain
are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a
corresponding reference spectrum, for which all (1,2) combinations were recorded.

Orlik, P. (1980).
Das SummaxModell der dreimodalen Faktorenanalyse mit
interpretierbarer Kernmatrix. Archiv für die
Psychologie, 133, 189218.
O. proposes a completely symmetric threemode model (called
Summax) with a threemode identity matrix. The appearance of
the model is identical to that of Carroll & Chang (1970),
however, the 'factor' loadings are determined in a different
way. A leadingsign pattern matrix is sought for each of the
modes such that the sum of all elements with their 'best'
leadingsign is maximal. From these pattern matrices for the
data matrix the 'factor' loadings are derived. If these
'loading' matrices are rotated, the counterrotated core
matrix will contain the direction cosines of the derived
'factors'. Illustrated by an experiment in wich 4 coloured
disks are judged on 10 rating scales by 8 subjects.

Orlik, P. (1981).
Das SummaxModell der dreimodalen multiplen Prädiktion,
gezeigt an einem Demonstrationsexperiment [The Summaxmodel of threemode
multiple prediction, illustrated with a demonstration experiment]. In W.
Janke (Ed.),
Beiträge zur Methodik in der differentiellen,
diagnostischen und klinischen Psychologie  Festschrift zum 60.
Geburtstag von G.A. Lienert (pp. 280296).
Königstein/Ts.: Hain.
The Summaxmodel of threemode factor analysis is applied to three
dimensional data matrices
to widen the concept of multiple prediction and regression. Possible
strategies of data
analysis are demonstrated by an experiment.

Ossenkopp,K.P., & Mazmanian, D.S. (1985)
The measurement and integration of behavioral variables:
aggregation and complexity as important issues. Neurobehavior
Toxicology and Teratology, 7, 95100.
The measurement of motor activity in animals is central to the
description of animal behavior in general. Application of factor
analytic procedures to multivariate motor activity data is
suggested to be a useful method of reducing many variables into
fewer, more complex variables, which have greater phenomenon
realism. Examples of the application of such factor analytic
approaches are provided, both for the traditional twoway factor
analytic methods as well as a more recent procedure (PARAFAC
model) developed for analysis of threeway longitudinal data sets.
It is suggested that multivariate analytic procedures are
appropriate for data reduction and description in the area of
behavioral neuroscience.

Ossenkopp, K.P., Sorenson, L., & Mazmanian, D. S. (1994).
Factor analysis of openfield behavior in the rat (Rattus norvegicus):
Application of the threeway PARAFAC model to a longitudinal data set.
Behavioural Processes, 31, 129144.
Examined the multivariate nature of openfield behavior in 26
adult male rats. A longitudinal data set, obtained during 4
openfield test sessions, was subjected to a 3way PARAFAC
analysis, which allowed for the direct factor analysis of
3dimensional arrays and provided a unique factor solution to the
longitudinal data set. Analysis extracted 2 factors: emotional
reactivity and exploratory behavior. These factors changed in
temporal prominence, with animals showing greater emotional
reactivity on the 1st test session, and greater levels of
exploration on the 3rd and 4th test sessions. Findings indicate
that multivariate procedures, such as the PARAFAC analysis, can
be helpful in the quantitative characterization of behavioral
phenomena in a more realistic manner.

Ozzetti, R. A., De Oliveira, A. P., Schuchardt, U., & Mandelli, D. (2002).
Determination of tacticity in polypropylene by FTIR with multivariate calibration.
Journal of Applied Polymer Science, 85, 734745.
A method for determination of tacticity in polypropylene (PP) using FTIR
associated with multivariate analysis is presented. Blends of PP with known tacticity were
prepared with isotactic, syndiotactic, and atactic polymer and analyzed by C13NMR. The FTIR
spectra were recorded and processed through principal components regression (PCR) and partial
leastsquares regression (PLS), using information from several different portions of the
spectra. The method was compared with the classical methods of tacticity determination by FTIR
based on the intensities of the bands at 998 cm(1) (isotactic), 868 cm(1) (syndiotactic),
and 975 cm(1) (internal standard), which are known to be dependent on the crystallinity of
the polymer and, thus, affected by temperature and sample preparation. The models obtained
with multivariate calibration, both with PCR and PLS, gave prediction errors up to fivefold
smaller than that of the classical methods, and were also shown not to be heavily dependent
on the bands that are affected by the crystallinity of the polymer, but rather on the methyl
and methylene bendings at 1375 and 1462 cm(1).
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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:
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First version : 12/02/1997;