ThreeMode Abstracts, Part I
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INDEX
Ia  Ib 
Ic  Id 
Ie  If 
Ig  Ih 
Ii  Ij 
Ik  Il 
Im  In 
Io  Ip 
Iq  Ir 
Is  It 
Iu  Iv 
Iw  Ix 
Iy  Iz 


Iacobucci, D. (1989).
Modeling multivariate sequential dyadic interactions. Social
Networks 11, 315362.
This study explores two methods for analysing sociometric data measured on
several relations observed at several points in time. The multirelational, sequential
data may be represented in a four dimensional actors x partners x relations x time
points supersociomatrix. The first method proposed as an alternative to analyzing
such supersociomatrices is an application of a fourmode eigenvector model. The
second proposed alternative method is an analysis of variance applied to parameter
estimates from simple loglinear network models. These methods are described in
detail and then applied to two real data sets: the relations in a monastry (Sampson
1968), and the friendship ties among a set of college students (Newcomb 1963).

Iacobucci, D. (1990).
Derivation of subgroups from dyadic interactions.
Psychological Bulletin, 107, 114132.
This article presents a simulation study that compares several methods for deriving empirical subgroups
from sociometric data. The Monte Carlo study was used to investigate how well the methods
recovered the subgroup structure that had been built into the actors' and partners' modes. Fortyeight
sociomatrices were generated using a 24 × 3 factorial design. The factors included the number
of individuals in the network, the true number of subgroups into which the individuals were classified,
the proportion of individuals falling into each of the subgroups, the structure of the dyadic
interactions, and the clarity of the subgroup structure. On the basis of the simulation study's results,
subgroups were derived for two real data sets. The first data set described the relations in a monastery
(Sampson, 1968). The second data set described the referral network of a service provider (Reingen
& Kernan, 1986).

Ibraghimov, I. (2002).
Application of the threeway decomposition for matrix comprehenssion.
Numerical Linear Algebra with Applications, 1, 116.
We present a new method to compress and invert 3D integral operators
on rectangular nonregular grids. This method requires a small amount of memory to
store the compressed matrix and in most cases can provide a good preconditioner for
the solution of linear systems with this matrix. We demonstrate efficiency of this
method for the solution of some model discrete problems associated with integral(R)
(3) A((x) over bar, (y) over bar )f((x) over bar )d((x) over bar) = u((y) over bar),
(x) over bar, (y) over bar is an element of R3 where A((x) over bar, (y) over bar)
such as 1/\(x) over bar  (y) over bar vertical bar is considered on a nonregular
grid. The arithmetical complexity of matrixvector and preconditionervector
multiplications are about N4/3 operations and there are only about N2/3 words of
memory to store.

IdborgBjorkman, H., Edlund, P. O., Kvalheim, O. M., SchuppeKoistinen, I. &
Jacobsson, S. P. (2003).
Screening of biomarkers in rat urine using LC/electrospray ionizationMS and
twoway data analysis.
Analytical Chemistry, 75, 47844792.
Biofluids, like urine, form very complex matrixes containing a large
number of potential biomarkers, that is, changes of endogenous metabolites in response to
xenobiotic exposure. This paper describes a fast and sensitive method of screening
biomarkers in rat urine. Biomarkers for phospholipidosis, induced by an antidepressant
drug, were studied. Urine samples from rats exposed to citalopram were analyzed using
solidphase extraction (SPE) and liquid chromatography mass spectrometry (LC/MS) analysis
detecting negative ions. A fast iterative method, called Gentle, was used for the
automatic curve resolution, and metabolic fingerprints were obtained. After peak alignment
principal component analysis (PCA) was performed for pattern recognition, PCA loadings
were studied as a means of discovering potential biomarkers. In this study a number of
potential biomarkers of phospholipidosis in rats are discussed. They are reported by
their retention time and base peak, as their identification is not within the scope of
the study. In addition to the fact that it was possible to differentiate control samples
from dosed samples, the data were very easy to interpret, and signals from
xenobioticrelated substances were easily removed without affecting the endogenous
compounds. The proposed method is a complement or an alternative to NMR for metabolomic
applications.

Idborg, H., Edlund, P. O., & Jacobsson, S. P. (2004).
Multivariate approaches for efficient detection of potential metabolites from
liquid chromatography/mass spectrometry data.
Rapid Communications in Mass Spectrometry, 18, 944954.
This work describes a novel method for rapid screening of unknown metabolites
in urine samples that narrows down the list of potential metabolites. Prior to analysis
by liquid chromatography/electrospray ionization mass spectrometry (LC/ESIMS), urine
samples were prepared using solidphase extraction (SPE). Automatic curve resolution was
used for deconvolution of the LC/MS data, followed by peak alignment. Preprocessed data
were then used for metabolite pattern recognition using principal component analysis
(PCA), parallel factor analysis (PARAFAC), and multilinear partial least squares (NPLS).
This approach enabled the rapid detection of metabolites of citalopram in urine by
maximizing the information extracted. The metabolites thus identified were compared with
earlier studies on the metabolism of citalopram. In addition, new, unreported metabolites
were found and characterized by LC/MS/MS and accurate mass measurements. A combination of
data from positive and negative ionization enhanced the identification of metabolites.

Iizuka, K., & Aishima, T. (1999).
Starch Gelation Process Observed by FTIR/ATR Spectrometry with Multivariate Data Analysis.
Journal of Food Science, 64, 653658.
For directly observing changes related to the gelation process of starch, IR spectra
of starch in water while heating were obtained using FTIR/ATR spectrometry.
Relationships between gelation and spectral changes were examined using factor
analysis, evolving factor analysis (EFA) and threeway principal component
analysis (PCA). Absorption at 3300 and 1610 cm1 decreased with temperature
but absorption at 1000 cm1 increased. The factor score plot patterns of amylose,
amylopectin and rice starches were similar but those of potato and corn starches
were unique. EFA indicated variances relating to changes caused in starch and
water as different factors. Loadings of the starch component 2 in threeway PCA
correlated with starch granule sizes.

Imada, A.S. & London, M. (1979).
Relationships between subjects, scales
and stimuli in research on social perception. Perceptual and Motor Skills,
48, 691697.
260 college students of varying ethnic backgrounds rated 6
ethnic stimuli on 24 bipolar semantic scales T3. Varimax on
factors for stimuli and subjects, but not on those for scales.
The core matrix was difficult to evaluate.

Inn, A., Hulin, C.L., & Tucker, L. (1972).
Three sources of criterion
variance: Static dimensionality, dynamic dimensionality, and individual
dimensionality. Organizational Behavior and Human Performance,
8, 5883.
11 performance measures were collected from 184 airline
reservation agents for each of 5 consecutive months.
Discussion of input scaling. Detailed analysis of solution
(timemode components are overall level, trend,
'acceleration'). 'Idealized subjects' were used to
characterize the subject dimensions. The computations for and
the results of this procedure are shown in great numerical
detail.

Inukai, Y. (1981).
Analysis of perceptual dimensions of schematic facial expressions
via threeway multidimensional scaling. Behaviormetrika,
9, 120.
In order to investigate perceptual dimensions of facial expressions, threeway
multidimensional scaling methods were applied to the analysis of two types of judgment data.
That is, dissimilarity judgments among facial expressions and rating judgments of each face
on 20 emotionterm scales were obtained in experiments, and analyzed by the scaling methods
which yielded uniquely oriented configurations. The faces used in the experiments consisted
of seventeen schematic facial expressions constructed by combinations of different
curvatures of the mouth and eyes. The results successfully exposed two perceptual
dimensions, which were interpreted as friendlinessunfriendliness and high activation  low
activation. And it was clarified that these dimensions were fairly consistent over the
different data types and scaling methods used in the present study.

Inukai, Y., Saito, S., & Mishima, I. (1980).
A vector model analysis of individual differences in sensory
measurement of surface roughness. Human Factors, 22,
2536.
In order to investigate the structure of individual differences in sensory measurement of
surface roughness, pairedcomparisons data of judged roughness on metal surfaces were
subjected to vector model analysis. Both of the derived most parsimonious configurations of
test pieces for the data from tactual and visual experiments were twodimensional and
wellpredicted by the physical variables of root mean square deviations in profile (Rrms)
and mean spacing of profile irregularities (pitch). Individual differences were observed in
the wide variety of weighted combinations of the two physical variables. The effects of
training of inspectors on their structures of sensory measurement were clarified in the
observed group differences. On the basis of these findings, some guidelines for instructing
and training inspectors were discussed.

Inukai, Y., Taya, H., Miyano, H., & Kuriyama, H. (1985).
Multidimensional evaluation method for psychological effects
of pure tones at low and infrasonic frequencies. Paper
presented at the 3rd International Conference on Low Frequency
Noise and Vibration, London, UK. Sept. 12  13.
Subjective ratings of pure tones at low and infrasonic frequencies (340 Hz) were obtained on
a set of semanticdifferentialtype scales and were analysed by factor analytic methods. As
the results, it was concluded that there were three main factors of the human responses to
the stimulus sound, that is: 1) the factor of pressure, 2) the factor of vibration, 3) the
factor of loudness. Then, in order to predict the human responses from the physical variables
of the sound stimuli, prediction equations were derived for each of the three factors. Also,
equal sensation contours for the factors were obtained. From these results, a new evaluation
method for the psychological effects was proposed, which considers the multidimensional
aspects of human perception of low and infrasonic frequencies.

Inukai Y. (1996).
Some applications of PARAFAC and INDSCAL to the analysis of
perceptual judgement data.
Japanese Psychological Review, 39, 476500. (in Japanese
with English abstract)
Applications of PARAFAC and INDSCAL to the analysis of perceptual
judgement are presented, in particular similarity judgements and
rating scale data on schematic facial expressions, and rating
scale data on low frequency noise. Reliability of the analyses and
problems in their applications are discussed.

Islam, F. M. A., Basford, K. E., Redden, R. J., Gonzalez, A. V.,
Kroonenberg, P. M., & Beebe, S. (2002).
Genetic variability in cultivated common bean beyond the two major gene pools.
Genetic Roesources and Crop Evolution, 49, 271283.
It is generally accepted that two major gene pools exist in cultivated common bean (Phaseolus vulgaris L.), a
Middle American and an Andean one. Some evidence, based on unique phaseolin morphotypes and AFLP
analysis, suggests that at least one more gene pool exists in cultivated common bean. To investigate this
hypothesis, 1072 accessions from a common bean core collection from the primary centres of origin, held at CIAT,
were investigated. Various agronomic and morphological attributes (14 categorical and 11 quantitative) were
measured. Multivariate analyses, consisting of homogeneity analysis and clustering for categorical data, clustering
and ordination techniques for quantitative data and nonlinear principal component analysis for mixed data, were
undertaken. The results of most analyses supported the existence of the two major gene pools. However, the
analysis of categorical data of protein types showed an additional minor gene pool. The minor gene pool is
designated North Andean and includes phaseolin types CH, S and T; lectin types 312, Pr, B and K; and mostly A5,
A6 and A4 types a amylase inhibitor. Analysis of the combined categorical data of protein types and some plant
categorical data also suggested that some other germplasm with C type phaseolin are distinguished from the major
gene pools.

Israelsson, A. (1969).
Threeway (or second order) component analysis.
In H. Wold & E. Lyttkens (Eds.), Nonlinear iterative partial least
squares (NIPALS) estimation procedures. Bulletin of the
International Statistical Institute, 43, 2951.
Proposal of T2, and a short discussion of its estimation
within the NIPALS framework.

Itakura, H., Nishikawa, Y., & Yamauchi, T. (1982).
An iterative solution procedure for individual differences
multidimensional scaling with weighted innerproduct model.
Behaviormetrika, 11, 115.
The weighted innerproduct model is discussed for a class of techniques of
multidmensional scaling incorporating individual differences. Data to be analyzed
are sets of arbitrary ones, from some individuals, expressing similarity between
objects. The model discussed is such that an inner product of position vectors, inn
a space, corresponding to the objects represents given similarity between the
objects. A set of parameters called weights is utilized for indicating individual
differences. In order to determine the vectors and the parameters, a leastsquares
criterion to be minimized is defined. For minimization of the criterion, an iterative
computation procedure is proposed considering quantitative data. The model and
the procedure are further extended to treat ordinal data. Illustrative examples are
attached with using artificial data and real survey data.

Iwatsubo, S. (1974).
Two classification techniques of 3way discrete data: Quantification
by means of correlation ratio and threedimensional correlation
coefficient. Kodokeiryogaku (Japanese Journal of Behaviormetrics),
2, 5465; English abstract, p. 79.
Two new classification methods are proposed to find out clusters from 3way
discrete data. They are quantification methods using the criteria maximizing
correlation ratio and threedimensional correlation coefficient, which lead to
solving eigenequations. Threedimensional correlation coefficient is defined by an
equation, which is convenient to estimate the degree of joint relation among three
variables of 3way data. Some properties of threedimensional correlation
coefficient are given. Results of applying the methods to small data are also
presented.

IzquierdoRidorsa, A., Saurina, J., HernándezCassou, S., &
Tauler, R. (1997).
Secondorder multivariate curve resolution applied
to rankdeficient data obtained from acidbase
spectrophotometric titrations of mixtures of
nucleic bases.
Chemometrics and Intelligent Laboratory Systems, 38, 183196.
Rankdeficient data matrices, obtained from
simulated spectrophotometric acidbase titrations
of mixtures of up to four nucleic bases (adenine,
cytosine, hypoxanthine and uracil), were analyzed
by secondorder multivariate curve resolution. The
analysis of these individual mixture data matrices
gives a rank value of n + 1, where n is the number
of nucleic bases present in the system. This
number is, however, lower than 2n, the number of
spectrometrically active species theoretically
present in the systems under study, since each
nucleic base is expected to give two species, a
protonated and a deprotonated species. This rank
deficiency is solved when more than one titration
is simultaneously analyzed by secondorder
multivariate curve resolution. Full rank recovery
is achieved when the titration of the mixture of
rt nucleic bases and other n: 1 titrations, each
one corresponding to a different base, are
simultaneously analyzed. Results obtained by
secondorder multivariate curve resolution
indicate that for a total resolution of the system
full rank is necessary. However, resolution and
quantitative determinations of individual nucleic
bases in mixtures in the presence of interferences
can be achieved (with a prediction error lower
than 2% in most cases) even in the case of rank
deficiency.
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 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;