Three-Mode Abstracts, Part M
one can go to the index of
this part of the bibliography, with
one can go to other
parts (letters) of the bibliography.
|Ma | Mb |
Mc | Md |
Me | Mf |
Mg | Mh |
Mi | Mj |
Mk | Ml |
Mm | Mn |
Mo | Mp |
Mq | Mr |
Ms | Mt |
Mu | Mv |
Mw | Mx |
My | Mz |
Ma, B., Gemperline, P. J., Cash, E., Bosserman, M., & Comas, E. (2003).
Characterizing batch reactions with in situ spectroscopic measurements, calorimetry
and dynamic modeling.
Journal of Chemometrics, 17, 470-479.
A method for fully characterizing consecutive batch reactions using
self-modeling curve resolution of in situ spectroscopic measurements and reaction energy
profiles is reported. Simultaneous measurement of reaction temperature, reactor jacket
temperature, reactor heater power and UV/visible spectra was made with a laboratory
(50 ml capacity) batch reactor equipped with a UV/visible spectrometer and a fiber optic
attenuated total reflectance (ATR) probe. Composition profiles and pure component spectra
of reactants and products were estimated without the aid of reference measurements or
standards from the in situ U-V/visible spectra using non-negative alternating least
squares (ALS), a type of self-modeling curve resolution (SMCR). Multiway SMCR analysis of
consecutive batches permitted standardless comparisons of consecutive batches to
determine which batch produced more or less product and which batch proceeded faster or
slower. Dynamic modeling of batch energy profiles permitted mathematical resolution of
the reaction dose heat and reaction heat. Kinetic fitting of the in situ reaction spectra
was used to determine reaction rate constants. These three complementary approaches
permitted simple and rapid characterization of the reaction's rate of reaction, energy
balance and mass balance.
MacCallum, R.C. (1974).
A comparison of two individual differences
for multidimensional scaling: Carrol and Chang's INDSCAL and
Tucker's three-mode factor analysis. Unpublished doctoral
thesis, University of Illinois, Urbana, Illinois.
(Dissertation Abstracts International, 1975, 35 (7-B),
(See MacCallum, 1976a, 1976b.)
MacCallum, R.C. (1974b).
Relations between factor analysis and
multidimensional scaling. Psychogical Bulletin,
Treats the differences between factor analysis and scaling in
general. Discusses shortly the relation between INDSCAL and
Tucker's three-mode scaling.
MacCallum, R.C. (1976).
Effects on INDSCAL of non-orthogonal
perceptions of object space dimensions. Psychometrika,
Investigation into the effect of violations of assumptions of
the INDSCAL model. Relation between INDSCAL and Tucker (1972)
model is discussed; the latter is recommended when violation
of assumptions in the former are suspected.
MacCallum, R.C. (1976b).
Transformation of a three-mode
multidimensional scaling solution to INDSCAL form. Psychometrika, 41,
Relations between Tucker (1972) and INDSCAL are discussed. A
gradient procedure is developed which seeks to diagonalize the
core matrix in all its frontal planes. A necessary condition
for the extended core matrix to be diagonal is that the core
matrix is diagonal. The developed procedure can be seen as a
first step towards checking the assumptions of the INDSCAL
model, as the latter is defined to have a diagonal extended
core matrix. It is also shown that a core matrix consisting of
two frontal planes can always be diagonalised. The
transformation procedure is applied to the Tucker (1972) data,
and to Jones & Young data consisting of judgments of 19
respondents about the similarities of 17 stimulus persons (see
also De Leeuw & Pruzansky, 1978).
MacCallum, R.C. (1978).
TRINFORM: A computer program to transform a three-mode
multidimensional scaling solution to INDSCAL form. Applied
Psychological Measurement, 2, 62.
TRINFORM is a program which transforms a three-mode
multidimensional scaling solution (Tucker, 1972) to the form, as
nearly as possible, of an INDSCAL solution (Carroll and Chang,
1970). Using a method suggested by MacCallum (1976), this is
achieved by transforming the three-mode core matrix, a matrix
consisting of as many sections as person dimensions with each
section specifying how each person dimension is related to
perception of the stimulus dimensions.
MacGregor, J.F., & Kourti, T. (1995).
Statistical process control of multivariate
Control Engineering Practice, 3, 403-414.
With process computers routinely collecting measurements on large
numbers of process variables, multivariate statistical methods
for the analysis, monitoring and diagnosis of process operating
performance have received increasing attention. Extensions of
traditional univariate Shewhart, CUSUM and EWMA control charts to
multivariate quality control situations are based on Hotelling's
T² statistic. Recent approaches to multivariate statistical
process control which utilize not only product quality data (Y),
but also all of the available process variable data (X) are based
on multivariate statistical projection methods (Principal
Component Analysis (PCA) and partial least squares (PLS)). This
paper gives an overview of these methods, and their use for the
statistical process control of both continuous and batch
multivariate processes. Examples are provided of their use for
analysing the operations of a mineral processing plant, for
on-line monitoring and fault diagnosis of a continuous
polymerization process and for the on-line monitoring of an
industrial batch polymerization reactor.
Maeda, S. (1992).
Articulatory modeling of the vocal-tract.
Journal de physique iv, 2, 307-314.**
Recently, there is some renewed interest in the representation of
speech at the articulatory level. For such a representation, it
is essential to have a parsimonious model which is capable of
describing accurately and meaningfully the states of the vocal
tract during speech production. In this paper, first we briefly
review various types of models proposed in the past. Then we
focus our attention to a specific type of articulatory models,
which are derived from a factor analysis of sagittal x-ray film
data. The advantage of this type of model is that the vocal tract
profiles are specified by a small number of the model parameters,
less than 10, and their values can be directly calculated, not
estimated, from data. Second, we describe the particular
relationships between the model parameters and acoustics
parameters (formant frequencies) that suggest acoustic
compensation between different articulators as the lower jaw and
tongue-body. Our analysis of x-ray data shows that such
compensation is actually used in speech production, and that the
larger variability in articulatory "targets" than in acoustic
ones is, in part, due to compensation.
Maeder, M., Neuhold, Y. M., Olsen, A., Puxty, G., Dyson, R., & Zilian, A. (2002).
Rank annihilation correction for the amendment of instrumental inconsistencies.
Analytica Chimica ActaIV, 464, 249-259.
The globalisation of the analysis of a series of individual measurements
often results in more robust and reliable outcomes. However, instrumental drifts that can
occur between individual measurements destroy the ideal data structure and thus the advantages.
A method based on rank annihilation factor analysis (RAFA) is introduced for the correction
of several types of instrumental inconsistencies. It can be applied to many series of bilinear
datasets. Experimental examples discussed in this paper comprise the successful correction of
non-uniform retention time drifts in chromatography due to temperature or pressure changes,
wavelength shifts in IR spectroscopy in an industrial control situation, and background
absorption shifts in UV-VIS spectroscopy applied to equilibrium investigations.
Mager, P. P. (1996).
A random number experiment to simulate resample model evaluations.
Journal of Chemometrics, 10, 221-240.
Gaussian distributed scores lying within the range
from +4 to -4 were calculated using a random generator. The random sample was divided
sequentially into three subsamples with equal and unequal sizes. This classification leads to
different internal correlation-regression structures depending on the subsample size. The
subsamples show also departures from multivariate normality. This is misleading for hypothesis
testing. Randomness of raw and vector-valued observations is unpredictable after subsampling.
Furthermore, the chance to get outlying observations must be taken into account.
Two sets of variables drawn from the subsamples did not show remarkable relationships. The
situation changed after omission of certain variables and subsample members. The formally
significant equations are artifacts and show the real danger of a selection of regressors extracted
from a variable pool of individual subsamples. Consequently, sequential resampling is unsuitable
for testing statistical hypotheses. There remains the big question in the daily practice of
chemometrics and in QSAR and 3D QSAR designs of how to select randomly the number of groups and
their sizes. However, sequential resampling may be useful for diagnostic statistics which prove the
assumptions of the underlying theory of hypothesis testing.
Manne, R., Shen, H., & Liang, Y. (1999).
Subwindow factor analysis.
Chemometrics and Intelligent Laboratory Systems, 45, 171-176.
The method of subwindow factor analysis (SFA) is introduced as a solution to the problem of directly
extracting component spectra from overlapping structures obtained from hyphenated chromatography without first
resolving concentration profiles. This is of advantage when a complete resolution cannot be obtained or is of less
interest in the analytical situation. The method is based upon comparisons of chromatographic regions (subwindows)
which have only one eluting component in common. The paper presents the theory and an application to a structure
with 4 overlapping components from a data set from a mixture of polyaromatic hydrocarbons recorded by
high-performance liquid chromatography diode array detection (HPLC-DAD).
Mansurov, H.H., Muratov, F.H., & Timerkaev, V.S. (1986).
Computational methods of the data-cube analysis in the chronic
hepatic lesion research. Paper presented at COMPSTAT
86, Rome, 1-5 September.
The paper discusses how information obtained from patients with chronic hepatic
lesions at several points in time can be shaped into a three-way array so that
it can be analyzed with three-way methods.
Marasinghe, M.G., & Boik, R.J. (1993).
A three-degree of freedom test of additivity in three-way
Computational Statistics & Data Analysis, 16, 47-61.
This article proposes a new interaction model for nonreplicated
three-way classifications. A simulation study is used to show
that a three-degree of freedom score test based on the new model
compares favorably with existing one-degree of freedom score and
likelihood ratio tests of additivity. The tests are illustrated
through an analysis of a data set where it is shown how the new
model may reveal a specific structure of three-factor
interaction. This structure may be exploited to suggest possible
explanations for the nonadditivity.
Marchand, B. (1984).
Urban growth models revisited: Cities as self-organizing
systems. Environment and Planning A, 16, 949-964.
Contains a summary of a three-mode analysis á la Tucker
(1966) presented in full in Marchand (1986) "The Emergence of
Los Angeles: Population and Housing in the City of Dreams,
1940-1970". Data from four censuses were arranged in a
parallelepiped that has been analyzed through three-way factor
analysis. The method, taken from Tucker (1966), is somewhat
complex, but essentially leads to a description of change over
Marcos, A., Foulkes, M., & Hill, S. J. (2001).
Application of a multi-way method to study long-term stability in ICP-AES.
Journal of Analytical Atomic Spectrometry,16, 105-114.
Although major advantages have been made in developing robust,
easy-to-use ICP-AES instruments offering sub mug g(-1) detection limits
and relative interference free operation, long-term drift of the
analytical signal continuous to be problematic and necessitates regular
re-calibration. The work presented here focuses on the effect of two
instrumental parameters, i.e. the rf power and the nebuliser gas flow
rate, on the robustness of the signals. The effects on the long-term
stability when varying these two factors was systematically studied using
an experimental design protocol. A "drift diagnosis" on thirty emission
lines was performed at 12 different sets of operating conditions by
repeated determination of a multi-element solution over several hours. The
results were studied using standard parameters, i.e., Mg ratio,
sensitivity, drift error, drift patterns and multi-way analysis. Parallel
factor analysis (PARAFAC) was employed to analyse the 3-way data array
generated: "emission lines x replicates x operating conditions". The
physical interpretation of the new PARAFAC-factors is shown to enable a
better understanding of the drift phenomenon by mathematically
characterising the causes of long-term instability. Finally, the
robustness of the technique using different operating conditions is
evaluated and the appropriate use of internal standards to correct for
drift is discussed.
Marengo, E., Leardi, R., Robotti, E., Righetti, P. G., Antonucci, F.
& Cecconi, D. (2003).
Application of three-way principal component analysis to the evaluation of
two-dimensional maps in proteomics Journal of Proteome Research,
Three-way PCA has been applied to proteomic pattern images to identify the
classes of samples present in the dataset. The developed method has been
applied to two different datasets: a rat sera dataset, constituted by five
samples of healthy Wistar rat sera and five samples of nicotine-treated
Wistar rat sera; a human lymph-node dataset constituted by four healthy
lymph-nodes and four lymph-nodes affected by a non-Hodgkin's lymphoma. The
method proved to be successful in the identification of the classes of
samples present in both of the groups of 2D-PAGE images, and it allowed us
to identify the regions of the two-dimensional maps responsible for the
differences occurring between the classes for both rat sera and human lymph-
Marsili, N. R., Lista, A., Band, B. S. F., Goicoechea, H. C., & Olivieri, A. C. (2004).
New method for the determination of benzoic and sorbic acids in commercial orange juices
based on second-order spectrophotometric data generated by a pH gradient flow injection
Journal of Agricultural and Food Chemistry, 52, 2479-2484.
Two widely employed antimicrobials, benzoic and sorbic acids, were simultaneously
determined in commercial orange juices employing a combination of a flow injection system
with pH gradient generation, diode array spectro photometric detection, and chemometric
processing of the recorded second-order data. Parallel factor analysis and multivariate
curve resolution-alternating least-squares were used for obtaining the spectral profiles
of sample components and concentration profiles as a function of pH, including provisions
for managing rank-deficient data sets. An appropriately designed calibration with a
nine-sample set of binary mixtures of standards, coupled to the use of the second-order
advantage offered by the applied chemometric techniques, allowed quantitation of the
analytes in synthetic test samples and also in commercial orange juices, even in the
presence of unmodeled interferents (with relative prediction errors of 8.7% for benzoic
acid and 2.5% for sorbic acid). No prior separation or sample pretreatment steps were
required. The comparison of results concerning commercial samples with a laborious
reference technique yielded satisfactory statistical indicators (recoveries were 99.0%
for benzoic acid and 101.4% for sorbic acid).
Martens, H. (1980).
On the calibration of a multivariate instrument for quantitative estimation of
individual components in a mixture. In A. Höskuldsson, K. Conradsen, B.S.
Jensen, & K. Esbensen (Eds.). Symposium I Anvendt Statistik
[Symposium on Applied Statistics] (pp. 393-414). Lyngby, Denmark: Technical
University of Denmark.
Within the context of indirect calibration based on extensions of Beer's law,
Martens discusses the potential use of three-way methods for calibration with
hyphenated instruments. In particular, the attractiveness of the PARAFAC model
(discussed within the context of Sands & Young's (1980, 1983) ALSCOMP3) is indicated for
spectometric data, emphasizing the uniqueness of the model.
Martínez-Montes, E., Valdés-Sosa, P. A., Miwakeichi, F.,
Goldman, R. I., & Cohen, M. S. (2004).
Concurrent EEG/fMRI analysis by multiway Partial Least Squares.
NeuroImage, 22, 1023-1034.
Data may now be recorded concurrently from EEG and functional
MRI, using the Simultaneous Imaging for Tomographic Electrophys-iology
(SITE) method. As yet, there is no established means to integrate
the analysis of the combined data set. Recognizing that the
hemodynamically convolved time-varying EEG spectrum, S, is
intrinsically multidimensional in space, frequency, and time motivated
us to use multiway Partial Least-Squares (N-PLS) analysis to
decompose EEG (independent variable) and fMRI (dependent
variable) data uniquely as a sum of ‘‘atoms’’. Each EEG atom is the
outer product of spatial, spectral, and temporal signatures and each
fMRI atom the product of spatial and temporal signatures. The
decomposition was constrained to maximize the covariance between
corresponding temporal signatures of the EEG and fMRI. On all data
sets, three components whose spectral peaks were in the theta, alpha,
and gamma bands appeared; only the alpha atom had a significant
temporal correlation with the fMRI signal. The spatial distribution of
the alpha-band atom included parieto-occipital cortex, thalamus, and
insula, and corresponded closely to that reported by Goldman et al.
[NeuroReport 13(18) (2002) 2487] using a more conventional analysis.
The source reconstruction from EEG spatial signature showed only the
parieto-occipital sources. We interpret these results to indicate that
some electrical sources may be intrinsically invisible to scalp EEG, yet
may be revealed through conjoint analysis of EEG and fMRI data.
These results may also expose brain regions that participate in the
control of brain rhythms but may not themselves be generators. As of
yet, no single neuroimaging method offers the optimal combination of
spatial and temporal resolution; fusing fMRI and EEG meaningfully
extends the spatio-temporal resolution and sensitivity of each method.
Martins, J.A., Sena, M.M., Poppi, R.J. & Pessine, F.B.T.
Fluorescence Piroxicam study in the presence of
cyclodextrins by using the PARAFAC method.
Applied Spectroscopy, 53, 510-522.
The nonsteroidal anti-inflammatory drug Piroxicam in solution
presents several equilibria that depend on its conformational
structure and the medium. It was studied by total fluorescence by
using parallel factor analysis (PARAFAC) to resolve its spectra.
It was possible to identify a correlation between some spectra
and the isomers and to reach some understanding of the
spectroscopic behaviour of the drug in cyclodextrin-containing
Mastandrea, S., Zani, A., Giuliani, M. V., & Bove, G. (1993).
Meaning of industrial-design objects - from designers to users.
Environment and Planning B-Planning & Design, 20, 307-319.
Structural features of everyday objects of industrial design
and expressive qualities possibly communicated by the same
objects are investigated. The objective may be defined in terms
of the following points: (1) communication between designers
and users; (2) differences in appraisal between groups of
experts and nonexperts; (3) systematic relationships between
structural characteristics and expressive qualities of the
objects considered. Three groups of subjects were interviewed:
four designers responsible for the design of six objects,
twenty advanced-level design students (experts), and twenty
nonexpert students. All subjects had to fill in a questionnaire
based on an open interview with the designers. The
questionnaire was divided into two parts: structural
characteristics and expressive characteristics. A
multifactorial analysis and t-test were performed on the data.
The results suggest that (1) communication between designers
and users exists in a large number of item appraisals and is
not the result of the ambiguity of the physical properties of
the objects; (2) specific training in design has a direct
influence upon object appraisal, indicating a certain
differentiation between the groups of experts and nonexperts;
(3) there are no systematic correlations between structural and
expressive characteristics except in one very specific case:
between the structural characteristic of shape and consistency
of material, on the one hand, and the expressive qualities of
dynamism, on the other.
Mayekawa, S. (1987).
Maximum likelihood solution to the PARAFAC model.
Behaviormetrika, 21, 45-63.
The traditional factor analytic view of the PARAFAC model and
its extension to a four mode situation with the derivation of
the maximum likelihood estimation procedure by the generalized
EM algorithm was presented. The four mode model was applied to
six ASVAB data matrices defined by three specialty (clerical,
mechanical, and electrical), times two services, (Air Force and
Marine Corps) and successfully recovered the usual four
dimensional structure without any rotation. The specialty and
service differences was expressed in terms of different
weighting of the common factor structure. A model which allows
us to compare the factor score means was also
McAdams, S., Winsberg, S., Donnadieu, S., De Soete, G., &
Krimphoff, J. (1995).
Perceptual scaling of synthesized musical timbres: Common
dimensions, specifities, and latent subject classes.
Psychological Research, 58, 177-192.
To study the perceptual structure of musical timbre and the
effects of musical training, timbral dissimilarities of
synthesized instrument sounds were rated by professional
musicians, amateur musicians, and nonmusicians. The data were
analyzed with an extended version of the multidimensional
scaling algorithm CLASCAL (Winsberg & De Soete, 1993), which
estimated the number of latent classes of subjects, the
coordinates of each timbre on common Euclidean di- mensions, a
specificity value of unique attributes for each timbre, and a
separate weight for each latent class on each of the common
dimensions and the set of specificities. Five latent classes
were found for a three-dimensional spatial model with
specificities. Weight patterns indicate that perceptual salience
of dimensions and specificities varied across classes. The model
with latent classes and specificities gave a better fit to the
data and made the acoustic correlates of the common dimensions
McArdle, J.J. (1984).
On the madness in his method: R.B. Cattell's contributions to structural
equation modeling. Multivariate Behavioral Research, 19,
This essay looks at the many methodological contributions of
R.B. Cattell from the vantage point of contemporary issues in
structural equation modeling. Cattell's factor analytical
approach is compared with current modeling practices. A
critical evaluation is offered which finds much of Cattell's
work still innovative, still technically advanced, and still of
great value to contemporary model builders.
McArdle, J. J. & Cattell, R. B. (1994).
Structural equation models of factorial invariance in parallel proportional profiles
and oblique confactor problems.
Multivariate Behavioral Research, 29, 63-113.
Some problems of multiple group factor rotation based on
Cattell's ''parallel proportional profiles'' and ''confactor rotation'' are
described (see Cattell, 1944, 1966, 1972). Some relations between these
classic ideas and contemporary practices in structural equation modeling
(e.g., LISREL) are explored. We show how the Confactor approach: (a) is
related to Meredith's (1964a) selection model, (b) can be a parsimonious
model for multiple group factor analyses, and (c) how this model can be
fitted using standard structural equation modeling techniques- We discuss
several alternative structural modeling solutions, including (d) selection
of a good reference variable solution, (e) rotation of the invariant
orthogonal structure by standard rotation routines, and (f) higher-order,
latent paths, and latent means structural model restrictions. Mathematical
and statistical properties of these models are examined using Meredith's
(1964b) four group problem fitted by Joreskog and Sorbom's (1979, 1985)
LISREL algorithm. The benefits and limitations of this structural modeling
approach to oblique Confactor resolution are examined and opportunities for
future research are discussed.
McCloskey, J. & Jackson, P.R. (1979).
FORTRAN IV program for three-mode factor analysis. Behavior
Research Methods & Instrumentation, 11,
A computer program for T3 (Tucker, 1966 - Method I) is
described without technical details.
McDonald, R.P. (1969).
A generalized common factor analysis based on residual covariance
matrices of prescribed structure. The British Journal of
Mathematical and Statistical Psychology, 22, 149-163.
An algorithm is described, the purpose of which is to express a
correlation matrix as the sum of two matrices, of which one is
of rank less than its order, and the other, the residual
matrix, is of prescribed structure. Applications are described
to approximate simplex and circumplex matrices, to the
factoring of groups of variables, and to a form of multi-mode
Medina, R., Losada, M.A., Losada, I.J., & Vidal, C. (1994).
Temporal and spatial relationship between sediment
grain-size and beach profile.
Marine Geology, 118, 195-206.**
Sediment samples and beach profile evolution data collected along
one profile line at ''El Puntal'' spit, Santander, Spain, are
used to analyze the spatial and temporal structure of the grain
size distribution variability and its relationship with the beach
profile changes. Standard principal component analysis (PCA) and
three-way PCA is applied to determine the temporal and spatial
scales of variability of the data. Results indicate that the
sediment grain size distribution varies markedly along the beach
profile both spatially and temporally. These variations are shown
to be strongly related to morphological changes in the beach
profile. The spatial eigenvectors determined from the profile
data and those from the sediment data exhibit similar patterns
with their maxima and minima located at the same position. Since
eigenvectors may be regarded as representative of uncorrelated
modes of variability it is concluded that the spatial variability
of both sediment and profile data are strongly related. In
particular, it is shown that the location of the highest
variability of grain size corresponds to that of the beach
profile. Also, different grain sizes are shown to exhibit a
distinct degree of variability which leads to the conclusion that
each sediment size responds to the same hydrodynamics
differently. The temporal eigenvectors determined from the
profile and the sediment data shown a seasonal dependency.
However, their maxima and minima are not located at the same
position. It is shown that this temporal shift is due to the
different response of each sediment size to the hydrodynamics,
and in particular, that the recovery of the profile starts with
fine material from the bar. It is inferred that models for beach
profile evolution which do not take into account the sorting
processes involved in the sediment transport cannot be fully
succesful. A "master" grain size sample, constructed by adding
all the grain samples taken over the profile, is used to further
examine the cross-shore redistribution of the sediment. The
following working hypothesis is suggested: "For a beach profile
within a physiographic unit the master grain size does not depend
Mendieta, J., Díaz-Cruz, M. S., Esteban, M., & Tauler, R. (1998).
Multivariate Curve Resolution: A Possible Tool in the Detection of Inermediate Structures
in Protein Folding. Biophysical Journal, 74, 2876-28888.
Different multivariate data analysis techniques based on factor analysis and multivariate curve resolution are
shown for the study of biochemical evolutionary processes like conformational changes and protein folding. Several
simulated CD spectral data sets describing different hypothetical protein folding pathways are analyzed and discussed in
relation to the feasibility of factor analysis techniques to detect and resolve the number of components needed to explain the
evolution of the CD spectra corresponding to the process (i.e., to detect the presence of intermediate forms). When more than
two components (the native and unordered forms) are needed to explain the evolution of the spectra, an iterative multivariate
curve resolution procedure based on an alternating least squares algorithm is proposed to estimate the CD spectrum
corresponding to the intermediate form.
Meijs, B.W.G.Ph. (1980).
Huis van bewaring en subkultuur: een
studie bij jeugdige gedetineerden naar het effekt van '102 dagen'
preventieve hechtenis op attitudes en andere indikatoren van
subkultuur. Unpublished master thesis, University of Leiden,
T3 (as implemented by Kroonenberg & De Leeuw, 1980) was one of
the analyses of semantic differential data from 37 juvenile
delinquents judging their surroundings, i.e. remand prison, home,
law enforcers, and the judiciary (26 aspects, 10 scales). The data
were collected at two time point (directly after intake and one
month later), and each time point was analysed separately.
Interesting shifts of opinions about aspects could be
Meng, X., Morris, A. J. & Martin, E. B. (2003).
On-line monitoring of batch processes using a PARAFAC representation
Journal of Chemometrics, 17, 65-81.
For assured through-batch process performance monitoring, a number of established
bilinear and trilinear modelling techniques require data to be available for the
entire duration of the batch to realize the on-line application of the nominal model.
Various strategies have been proposed for the in-filling of those yet unknown values.
A methodology is presented where the unknown observations are calculated as a weighted
combination of the, scores up to the current time. point in the new-batch and
those previously computed from a reference data set. This approach is investigated
for the trilinear technique of parallel factor analysis (PARAFAC). Modified
confidence limits are then proposed for the bivariate scores plot for on-line
monitoring with a PARAFAC model. The identification of those variables indicative
of causing changes in process operation has been accomplished through the application
of contribution plots. Based on such plots, a methodology, with associated confidence
limits, is proposed for the location of those variables whose behaviour differs
from that encapsulated within the reference data set. The approach is demonstrated
and compared with existing techniques on a benchmark simulation of a semi-batch
emulsion polymerization that has-been used in similar studies.
Meulders, M., De Boeck, P., Kuppens, P., & van Mechelen, I. (2002).
Constrained latent class analysis of three-way three-mode data.
Journal of Classification, 19, 277-302.
Meulman, J.J. (1989).
Distance analysis in reduced canonical spaces. In R. Coppi &
S. Bolasco (Eds.), Multiway data analysis (pp.233-244).
A particular form of generalized canonical analysis compares
p- dimensional linear combinations of M sets of
variables with a p-dimensional unknown matrix X.
This technique can be shown to have certain distance properties
in terms of the objects in the analysis. From this starting
point various modifications of the technique can be introduced
that optimize these distance properties. In this paper a quite
general approach is presented that has a previous generalization
(Meulman, 1986) as a special case.
Meulman, J.J., & Verboon, P. (1993).
Points of view analysis revisited: fitting multidimensional structures
to optimal distance components with cluster restrictions on the
variables. Psychometrika, 58, 7-35.
A procedure is proposed that can be viewed as a streamlined,
integrated version of the Tucker and Messick (1963)
Point-of-View analysis, which consisted of a number of separate
steps. At the same time, our procedure can be regarded as a
particularly constrained weighted Euclidean model. While fitting
the model, two types of nonlinear data transformations are
feasible, either for given dissimilarities, where the two types
of transformation can be mixed in the same analysis; a quadratic
assignment framework is used to evaluate the results.
Meuwese, W. (1970).
Een vergelijking van twee methoden van beoordeling
van verbale stimuli. Nederlands Tijdschrift voor de
Psychologie, 25, 594-603.
A selection of 15 university subjects were judged by 44 staff
and students of a technical university on 21 seven-point
rating scales. T3 was performed, and all modes were
interpreted but not the core matrix. The stimulus space was
compared with a MDS-solution obtained from paired comparison
Meyer, J.P. (1980).
Causal attribution for success and failure: A multivariate
investigation of dimensionality, formation, and
consequences.Journal of Personality and Social Psychology,
The dimensions underlying causal attributions for success and
failure, the influence of various informational cues on
attributions along the dimensions, and the consequences of such
attributions were investigated using PARAFAC (Harshman, 1976).
Hypothetical cases describing high school students' performance
on a university entrance exam and in high school, the performance
of others on the exam, and the importance of the exam were
presented to 193 male undergraduates in a within-Ss design.
Meyer, P., Wilhelms, R., & Strube, H. W. (1989).
A quasiarticulatory speech synthesizer for German language running in real-time.
Journal of the Acoustical Society of America, 86, 523-539.
A system for simple quasiarticulatory speech synthesis is described. It is based
on an articulatory model, which is controlled by seven parameters. The synthesizer employs a
stylized vocal tract model that is realized using wave digital filter techniques. It includes a
self-oscillating glottis model, voiceless excitation in the tract, damping, a nasal tract, and a
radiation load that allows the simulation of lip protrusion. The synthesizer runs in real time on
a signal processor. The described model was fit to natural speech using a Kalman filter
algorithm. Simple rules for the synthesis of unrestricted German speech are described.
Meyners, M. (2001).
Statistische Eigenschaften der STATIS-Methode -Propriétés statistiques de
la méthode STATIS.[Statistical properties of the STATIS method].
Various statistical properties of the STATIS-method were
investigate. Main issues are the difference with a true
underlying consensus solution and the asymptotic properties
whenever the number of products and / or assessors converges to
infinity. It was shown that STATIS overestimates dimensionality
of the consensus. Therefore, a correction to STATIS was
proposed in order to correct for this as much as possible. By
means of simulations, this corrected version of STATIS was
compared with the original version as well as with two
additional variants, one of which uses asymptotically optimal
weights for the assessors, the other one does not use weights.
It was found that the corrected versions outperformed all
others and, in an additional study, there were shown to be
comparable to Generalized Procrustes Analysis (GPA). A
disavantage of GPA is that it requires an iterative algorithm,
while the corrected STATIS does not. Graphical comparisons
supported the theoretical and empirical results, be it that,
with respect to the interpretation of the results, all methods
under consideration seemed to be comparable for the cases
Meyners, M. (2000).
Comparing generalized procrustes analysis and STATIS. Food Quality and Preference
We consider a model for sensory profiling data including translation, rotation
and scaling. We compare two methods to calculate an overall consensus from
several data matrices: Generalized Procrustes Analysis (GPA) and STATIS (Structuration
des Tableaux à Trois Indices de la Statistique). These methods are
briefly illustrated and explained under our model. A series of simulations
to compare their performance has been carried out. We found significant
differences in performance depending on the variance of random errors and
on the dimensionality of the true underlying consensus. Therefore, we investigated
on the dimensionality of the calculated group averages. We found both methods
gave too many dimensions compared to the true consensus. This finding is
supported by some theoretical considerations. Finally we propose a combined
approach which takes advantage of both methods and which gave better results
in the simulations.
Michailidis, G., & De Leeuw, J. (2000).
Multilevel homogeneity analysis with differential weighting. Computational
Statistics and Data Analysis, 32, 411-442.
A model is introduced for multilevel homogeneity analysis with fixed group
category quantification across groups with differential weights for each group.
The authors show this model to be a constrained form of the standard PARAFAC
Miettinen, T., Hurse, T. J., Connor, M. A., Reinikainen, S. P., & Minkkinen, P. (2004).
Multivariate monitoring of a biological wastewater treatment process: a case study at Melbourne
Water's Western Treatment Plant.
Chemometrics and Intelligent Laboratory Systems, 73, 131-138.
Biological wastewater treatment is a complex, multivariate process, in
which a number of physical and biological processes occur simultaneously. In this study,
principal component analysis (PCA) and parallel factor analysis (PARAFAC) were used to
profile and characterise Lagoon 115E, a multistage biological lagoon treatment system at
Melbourne Water's Western Treatment Plant (WTP) in Melbourne, Australia. In this study,
the objective was to increase our understanding of the multivariate processes taking
place in the lagoon. The data used in the study span a 7-year period during which samples
were collected as often as weekly from the ponds of Lagoon 115E and subjected to analysis.
The resulting database, involving 19 chemical and physical variables, was studied using
the multivariate data analysis methods PCA and PARAFAC. With these methods, alterations
in the state of the wastewater due to intrinsic and extrinsic factors could be discerned.
The methods were effective in illustrating and visually representing the complex
purification stages and cyclic changes occurring along the lagoon system. The two methods
proved complementary, with each having its own beneficial features.
Miller, K., & Gelman, R. (1983).
The child's representation of number: A multidimensional scaling
analysis. Child Development, 54, 1470-1479.
In order to describe developments in children's conceptions of
number, judgments of similarities between numbers were solicited
from children in grades kindergarten, 3, and 6 as well as from
adults. Analysis of the resulting data by clustering and
nonmetric multidimensional scaling techniques suggested that
children become sensitive to an expanding set of numerical
relations during this period, although even kindergartners
appear to understand the importance of magnitude as a basis for
judging similarity between numbers. This study is an application
Millican, D.W., & McGown, L.B. (1990).
Fluorescence lifetime resolution of spectra in the frequency
domain using multiway analysis. Analytical Chemistry,
Spectral resolution of two-component systems by multiway
analysis of excitation-emission-frequency arrays is compared
with single-matrix analysis of steady-state excitation-emission
matrices for both real and computer-simulated systems.
Fluorescence lifetime selectivity can improve resolution,
especially for the minor component in mixtures in which the two
components have unequal contributions to the total intensity.
However, in some cases the lifetime difference between two
fluorophores is insufficient to aid resolution.
Mills, D.H. & Tucker, L.R. (1966).
factor analysis of clinical judgment of schizophrenicity.
Journal of Clinical Psychology, 22, 136-139.
Schizophrenicity judgments of 23 persons (patients and
normals) on 20 items of the WAIS' vocabulary and comprehension
by 5 judges was subjected to T3. A nice, clearly interpretable
Millsap, R.E., & Meredith, W. (1991).
Some mathematical relationships between three-mode component
analysis and stationary component analysis. Multivariate
Behavioral Research, 26, 413-419.
One application of three-mode component analysis is in the
analysis of longitudinal multivariate data. Millsap and
Meredith (1988) have developed a component analysis method for
this application that uses stationary compositing weights. This
article presents theorems giving constraints which must be
satisfied for equivalency between the component representations
provided by three- mode component analysis and by methods
employing stationary compositing weights. In general, the two
approaches will provide mathematically distinct
Mirkin, B.G. (1987).
Additive clustering and qualitative factor analysis methods for
matrices. Journal of Classification, 4, 7-31.
This paper reviews methods of qualitative factor analysis
(QFA) developed by the author and his collaborators over the
last decade and discusses the use of QFA methods for the
additive clustering problem. The QFA method includes, first,
finding a square Boolean matrix in a fixed set of Boolean
matrices with "simple structure" to approximate a given
similarity matrix, and, second, repeating this process again
and again using residual similarity matrices. Convergence
properties for three versions of the method are presented,
"cluster" interpretations for results obtained from the
algorithms provided, and formulas for the evaluation of
"factor shares" of the initial similarities variance given.
Mitchell, B.C., & Burdick, D.S. (1993).
An empirical comparison of resolution methods for
Chemometrics and Intelligent Laboratory Systems, 20, 149-
In chemometrics applications it is common to
resolve a trilinear array by solving a generalized
eigenvalue problem, rather than by employing the
iterative parafac algorithm commonly used by
psychometricians. Although an eigenanalysis-based
procedure works perfectly in the absence of noise,
it is not guaranteed to yield least squares
resolutions when noise is present. The Parafac
algorithm on the other hand is guaranteed to
reduce the residual sum of squares at each
In this paper we propose synthesizing the two
methods by using the resolution generated by
eigenanalysis as starting values for the iterative
Parafac algorithm. We find for simulated
four-component data at moderate noise levels that
following an eigenanalysis resolution with Parafac
frequently leads to significant improvement in the
quality of the resolution.
Mitchell, B.C., & Burdick, D.S. (1994).
Slowly converging Parafac sequences: Swamps and
Journal of Chemometrics, 8, 155-168.
The alternating least squares Parafac algorithm is
a useful tool for resolving trilinear three-way
data arrays. Occasionally, however, it becomes
bogged down for many iterations in the vicinity of
a poor quality resolution before moving on to a
much superior optimum fit. We investigate this
behavior in a simulation study and suggest ways of
overcoming the obstacles it presents.
Miyano, H., & Inukai, Y. (1982).
Sequential estimation in multidimensional scaling. Psychometrika,
The concept of sequential estimation is introduced in
multidimensional scaling (MDS). The sequential estimation
method developed in this paper refers to continually updating
estimates of a configuration as new observations are added.
This method has a number of advantages, such as a locally
optimal design of the experiment can be easily constructed,
and dynamic experimentation is made possible. Using artificial
data, the performance of our sequential method is illustrated.
Miwakeichi, F., Martinez-Montes, E., Valdes-Sosa, P. A., Nishiyama, N., Mizuhara, H., & Yamaguchia, Y.(2004).
Decomposing EEG data into space-time-frequency components using Parallel Factor Analysis.
Neuroimage, 22, 1035-1045.
Finding the means to efficiently summarize electroencephalographic data
has been a long-standing problem in electrophysiology. A popular approach is identification
of component modes on the basis of the time-varying spectrum of multichannel EEG
recordings-in other words, a space/frequency/time atomic decomposition of the time-varying
EEG spectrum. Previous work has been limited to only two of these dimensions. Principal
Component Analysis (PCA) and Independent Component Analysis (ICA) have been used to
create space/time decompositions; suffering an inherent lack of uniqueness that is overcome
only by imposing constraints of orthogonality or independence of atoms. Conventional
frequency/time decompositions ignore the spatial aspects of the EEG. Framing of the data
being as a three-way array indexed by channel, frequency, and time allows the application
of a unique decomposition that is known as Parallel Factor Analysis (PARAFAC). Each atom
is the tri-linear decomposition into a spatial, spectral, and temporal signature. We
applied this decomposition to the EEG recordings of five subjects during the resting state
and during mental arithmetic. Common to all subjects were two atoms with spectra signatures
whose peaks were in the theta and alpha range. These signatures were modulated by
physiological state, increasing during the resting stage for alpha and during mental
arithmetic for theta. Furthermore, we describe a new method (Source Spectra Imaging or SSI)
to estimate the location of electric current sources from the EEG spectrum. The topography
of the theta atom is frontal and the maximum of the corresponding SSI solution is in the
anterior frontal cortex. The topography of the alpha atom is occipital with maximum of the
SSI solution in the visual cortex. We show that the proposed decomposition can be used to
search for activity with a given spectral and topographic profile in new recordings, and
that the method may be useful for artifact recognition and removal.
Three-way data analysis based on Tucker2 model: A method utilizing
a priori information on some model parameters.
Japanese Psychological Review, 39,429-438 (in Japanese
with English abstract).
It is well-known that each of the component matrices in the
Tucker2 model is only determined upto a nonsingular
transformation. This indeterminacy often makes it difficult to
derive substantive information present in the data. A new
algorithm is proposed for the Tucker2 model which utilises a
priori information on the model parameters. The efficiency of the
proposed algorith is confirmed by analysing both an artificial
data set and real data.
Mizère, D. (1981).
Analyse d'un cube de données: décomposition
tensorielle et liens entre procédures de comparaison de
tableaux rectangulaires de données. [Analysis of a
data cube: Tensorial decomposition and links with procedures to
compare rectangular data matrices]. Unpublished doctoral thesis,
The Scientific and Medical University of Grenoble, France.
I. Algebraic background.
Euclidian spaces: duality diagrams and metrics.
II. Analysis with second order tensors.
Treatment of three-way data with second order tensors.
III. Analysis with third order tensors.
Mathematical and statistical developments; Tensorial decomposition and
principal component analysis.
Matrices as a specification of three-way arrays; Procrustes rotation and
the search for a
intrametric; Comparison with other procedures.
Mizère, D. (1984).
L'Aspect choix de métrique dans l'analyse d'un cube de
contingence. Afrika Matematika, 6, 49-68.
In this paper research into three-dimensional matrices is extended to
specific contingency tables.
Moberg, L., Robertsson, G., & Karlberg, B. (2001).
Spectrofluorimetric determination of chlorophylls and pheopigments using
parallel factor analysis.
Talanta, 54, 161-170.
In this study, parallel factor analysis (PARAFAC) was applied to
fluorescence excitation emission matrices (EEM) of chlorophylls and pheopigments
dissolved in acetone:water (9:1). The excitation wavelength range was from 350 to 500
nm and the emission was recorded from 600 to 730 nm. Nine standards, comprising mixtures
of six analytes, were decomposed into a six-component PARAFAC model. Each component
resembled the corresponding EEM of the pure analyte, demonstrating the uniqueness
properties of PARAFAC. The score matrix obtained from the model was used for calibration
and prediction of an independent set of standards and for eleven samples collected in
the Baltic proper. The results obtained by the proposed method were compared to
classical least squares (CLS) and to predictions by reference methods (HPLC and visible
spectroscopy). For the independent set of standards the proposed method and CLS performed
equal well in terms of predictive ability. But fur the samples the proposed method
yielded results that were in good agreement to the reference methods, whereas CLS failed.
Also the so-called "second-order advantage" was examined, showing that not all
constituents must be included in the calibration set. The concentration range was for
chlorophyll a varied between 10 and 75 mug l(-1) and similar for the other analytes.
Moller, J. K. S., Parolari, G., Gabba, L., Christensen, J., & Skibsted, L. H. (2003).
Monitoring chemical changes of dry-cured parma ham during processing by surface
Journal of Agricultural and Food Chemistry, 51, 1224-1230.
Parma hams at various processing stages were investigated by surface
autofluorescence spectroscopy. Fluorescence "landscapes" of raw meat and salted (3 months),
matured (11 and 12 months), and aged (15 and 18 months) Parma hams were obtained, and a
three-dimensional data array (sample x emission x excitation) was used to develop a
PARAFAC model including five components, which all exhibited characteristics of pure
fluorophores regarding both excitation and emission spectra. The relative amount of each
component related strongly to the processing stage, and sample age showed good correlation
to fluorescence data (R = 0.98), with a relative error of prediction of approximately 1
month. Fluorescence measurements from samples of either semimembranosus or biceps femoris
were used to predict chemical or sensory reference data, yielding good correlation for
biceps femoris data, thereby enabling moisture content, sensory and instrumental color,
and proteolysis value to be fairly well predicted. Overall, surface autofluorescence of
Parma hams proved to hold relevant information, relating to major chemical/physical
changes during processing. It is concluded that fluorescence spectroscopy has potential
as an innovative method of quality control in dry-cured ham.
Möcks, J. (1988a).
Decomposing event-related potentials: A new topographic components
model. Biological Psychology, 26, 199-215.
"Component" notions inherently used with measurement
approaches, raw peak determination, PCA and generator approaches
are discussed. By combining aspects of them all, a new model of
ERP decomposition is established; quite profitable and surprising
mathematical properties are illutrated and discussed.
Möcks, J. (1988b).
Topographic components model for event-related potentials and
some biophysical considerations. IEEE Transactions on
Biomedical Engineering, 35, 482-484.
Models for decomposing averaged event-related potentials in component
functions are discussed. Biophysical considerations motivate a
new sample model, which is shown to lead to unique identifiable
components, thereby overcoming a major drawback of the customary
approach by principal components analysis.
Montanelli, D.S. (1972).
Multiple-cue learning in
children. Developmental Psychology, 7,
Response patterns of 144 children in a multiple-cue learning
experiment with 8 trial blocks and 3 cue weightings were ana-
lysed by T3 (or actually T2, as no components were determined
for the cue weightings). Very little numerical information was
presented and only a cursory interpretation given.
Montano,D. & Adamopoulos, J. (1984).
The perception of crowding in interpersonal situations: Affective and
behavioral responses.Environment and Behavior, 16,
Likelihood judgments of responses of 280 undergraduates to
crowded situations were subjected to three-mode factor analysis.
The dimensionality of the components are discussed, and behavior
patterns in different situational contexts are identified.
Mooijaart, A. (1992).
Three-factor interaction models by log-trilinear terms in three-way
contingency tables. Statistica Applicata, 4,
Association models are usually defined for two-way tables. In
this paper these models will be generalized to three-way tables,
where the three-factor interaction parameters are constrained to
be equal to one or more log-trililnear terms. The generalization
is analogous to the PARAFAC/CANDECOMP model for continuous data.
Parameters will be estimated by the maximum likelihood method. An
example with real data will illustrate the usefulness of our
Moonen, J. (1978).
Computergestuurd Onderwijs. Een
onderzoek naar de
mogelijkheden tot geïntegreerd gebruik van een
computergestuurd systeem in een statistiekkurrikulum (doctoral
thesis). Leiden, The Netherlands: author.
As part of a large scale investigation into the possibilities of
integrating computer aided instruction into a statistics course,
the data of 121 subjects rating 8 organisational approaches to
studying statistics on 8 aspects related to a statistics course
were analysed using TUCKALS2 (Kroonenberg & De Leeuw,
1977,1980, 1981c). The data were collected and analysed twice,
once after one third of the course was over, and once at the end
of the course. Rather straight forward interpretation; no
interpretation was attempted of the subjects.
Moreda-Pineiro, A., Marcos, A., Fisher, A., & Hill, S. J. (2001a).
Chemometrics approaches for the study of systematic error in inductively coupled
plasma atomic emission spectrometry and mass spectrometry.
Journal of Analytical Atomic Spectrometry, 16, 350-359.
Systematic errors observed when using inductively coupled plasma atomic
emission spectrometry (ICP-AES) and mass spectrometry (ICP-MS) for the multi-element
determination in acid digests of environmental samples (tea leaves) were evaluated. Two
chemometric approaches, experimental design and principal component analysis, were used
in order to establish the errors associated with each stage of the analytical method:
sample digestion (effect of the "number of acid digestions") and measurement step
(effect of the "number of replicates" and the "calibration"). The elements under study
were Co, Cr, Cs, Cu, Ni, Pb, Rb and Ti by ICP-MS, and Ba, Ca, Fe, Mg, Mn, Sr and Zn by
ICP-MS and ICP-AES. Flame atomic absorption spectrometry was used for comparative
purposes. A Chinese tea certified reference material with certified concentration for
most of the elements was employed as the sample matrix. Variance estimation was made
from ANOVA outputs from a full factorial design (FFD) 4(1) x 4(1) x 2(1).
Moreda-Pineiro, A., Marcos, A., Fisher, A., & Hill, S. J. (2001b).
Parallel factor analysis for the study of systematic error in inductively coupled
plasma atomic emission spectrometry and mass spectrometry.
Journal of Analytical Atomic Spectrometry, 16, 360-369.
This paper describes the application of a trilinear parallel factor
analysis (PARAFAC) to study systematic error during the multi-element determination of a
range of analytes in acid digests of solid samples (tea leaves) by ICP-AES and ICP-MS.
The three variables studied were the "number of digestions", in order to assess the
systematic error associated with the sample pre-treatment, and the "number of replicates"
and "calibration", to provide information on the systematic error associated with the
analytical determination itself. The elements under study were Co, Cr, Cu, Ni, Pb, Rb
and Ti by ICP-MS, and Ba, Ca, Fe, Mg, Mn, Sr and Zn by both ICP-MS and ICP-AES. For some
elements flame atomic absorption spectrometry was used for comparative purposes. A
Chinese tea certified reference material containing many of the metals above was used in
the study. The results obtained were compared to results from ANOVA. It was found that
the systematic error, expressed as the sum of squares after PARAFAC, was quite different
from the results obtained using ANOVA due to the very different way in which the models
are built. The PARAFAC approach is shown to be straightforward to implement and robust.
Morais, H., Ramos, C., Forgács, E., Cserháti, T., Oliviera, J., & Illés, T. (2001).
Three-dimensional principal component analysis employed for the study of the
beta-glucosidase prodution of Lentinus edodes strains.
Chemometrics and Intelligent Laboratory Systems, 57, 57-64.
The effect of cation type and concentration and fermentation time on the
beta-glucosidase of four strains of Lentinus edodes was determined.
Three-dimensional principal component analysis (3D-PCA) followed by nonlinear
mapping technique (NLMAP) was employed for the assessment of similarities and
dissimilarities between the enzymatic activities. The results proved that
3D_PCA followed by NLMAP is a valuable tool for the evaluation of three-dimensional
data matrices in biology and microbiology.
Morais, H., Ramos, C., Forgács, E., Jakab, A., Cserháti, T.,
Oliviera, J., Illés, T. & Illés, Z. (2003).
Comparison of principal analysis and the Tucker3 model - A case study.
QSAR & Combinatorial Science, 22, 449-455.
A three-ways array data matrix consisting of the activity data of laccase enzyme
has been evaluated by both principal component analyses (PCA) and Tucker3 model.
Activity data have been determined in 28 culture media, at 6 sampling times and
by four strains of Lentinus edodes. PCA has been carried out three times one of
the factors being always the variables and the other two factors being the observations.
The dimensionality of the matrices of loadings calculated by PCAs and those of
component matrices of Tucker3 model has been reduced to two by the nonlinear mapping
technique. It has been found that the dimensionality of component matrices for
Tucker3 model can be predicted from the results of PCAs. Linear regression analyses
indicated that the distribution of the original data points on the two-dimensional
nonlinear maps considerably depends on the fact that the data have been calculated
by PCA or by Tucker3 model.
Morais, H., Ramos, C., Forgacs, E., Jakab, A., & Cserhati, T. (2004).
Enzyme production of Pleurotus ostreatus evaluated by the three-way principal component analysis.
Engineering in Life Sciences, 4, 165-170.
The effect of the composition of culture media and fermentation time on
the production of beta-glucosidase, xylanase, laccase, manganese-dependent and independent
peroxidases by the edible fungus Pleurotus ostreatus was determined. Culture medium
separately containing potato, pepper, and tomato extracts and the enzyme activities were
assessed to 31.5 days of fermentation. Three-dimensional principal component analysis
(3D-PCA) followed.by the plots of the first two elements of component matrices was
employed for the elucidation of the similarities and dissimilarities between the
parameters. It was established that the dimensionality of the original 3D matrix (9, 5, 4)
could be reduced to 2, 1, 2 with 4.54 % loss of information. The plots demonstrated that
the culture media displayed large differences in their capacity to promote enzyme
production and that the presence of pepper and tomato extracts exerted the greatest
influence on the enzyme activities. The effect of the fermentation time was manifested
only after 1.4 d of fermentation and the highest differences were observed after 28
and 31.5 d of fermentation. Except laccase and manganese-dependent peroxidase, the enzyme
activities also differed considerably dependent on the composition of the fermentation
broth. 3D-PCA followed by the plots of component matrices is a valuable tool for the
simultaneous assessment of three dimensional data matrices in biotechnological
Munck, L., Nørgaard, L., Engelsen, S.B., Bro, R., &
Andersson, C.A. (1998). Chemometrics in food science - a
demonstration of the feasibility of a highly exploratory,
inductive evaluation strategy of fundamental scientific
significance. Chemometrics and Intelligent Laboratory
Systems, 44, 31-60.
At the roots of science lies observation and data collection from
the world as is and from which conclusions can be induced after
classification. This is far from the present theory-driven,
deductive, normative stage of science which depends heavily on
modelling discrete functional factors in laboratory experiments
and suppresses the aspect of interaction. In spite of its
successes, science today has great difficulty in adapting to the
changes which technology has created to cope with registering and
evaluating real data from the world, such as in food production
chains. This paper demonstrates that it is possible and
profitable with the help of new technology to reintroduce an
explorative, inductive strategy to investigate the chemistry of a
complex food process as is with a minimum of a priori
assumptions. The food process investigated is a sugar plant and
the tools necessary in this strategy include a multivariate
screening method (fluorescence spectroscopy), an arsenal of
chemometric models (PCA, PLS, principal variables), including
multiway models (Parafac, Tucker), and a computer. Not only can
chemical criteria and process parameters throughout the process
be validly predicted by the screening method, but process
irregularities as well as chemical species can also be detected
and validated by multiway chemometric techniques. Inspired by
examples from the food area, the paper further discusses the
nature of the exploration method in the selection of tools and
data. The aim is to study complex processes as a whole in order
to model interaction of the underlying latent functional factors
which may later be defined more precisely by deductive methods.
These methods in combination with an appropriate multivariate
screening method allow for unique identification of objects - a
significant prerequisite for a viable, exploratory, inductive
data strategy which is needed as a fundamental complement to
prevalent normative research in order to obtain a science on the
Murakami, T. (1979).
Inshi henka no kijutsu to jun3so inshi bunseki [Description of
factor change and quasi three-mode factor analysis]. Bulletin
of the Faculty of Education, Nagoya University, 26,
A simplified three-mode factor analysis model is investigated as
a procedure for factor analysis of data matrices obtained on
several occasion and for assessment of factor change. The model,
termed quasi three-mode factor analysis, approximates the raw
data with a Tucker model. In the quasi three-mode model the two
component matrices A and B are considered to be the criterion
for description of factor change by core matrices. The proposed
procedures do not yield the overall least squares solutions for
Eq. (1), but make the quasi three- mode model interpretable as
the summarized form of method I and method II. The core matrix
Gk has a useful interpretation that it
is the covariance matrix of factor scores in
Fk with factor scores in
A. Moreover, the core matrix can distinguish
factor loadings change from factor scores change. As a matter of
fact, Gk's are shown to exhibit the
characteristic patterns corresponding to the four types of
factor changes suggested by Baltes and Nesselroade
Murakami, T. (1981).
Saisho jijoho ni yoru jun3so inshi bunseki no algorithm [An
algorithm of quasi three-mode factor analysis by the least
squares methods]. Bulletin of the Faculty of Education, Nagoya
University, 28, 39-59.
Quasi three-mode factor analysis is a method for the factor
analytic treatment of a 3-way data matrix. In this paper, a
rationale of least squares algorithm for the model was
formulated in the manner of the alternating least squares
method and a practical computational procedure requiring only
the multitrait- multimethod type correlation matrix is
developed. This algorithm not only gave the least squares
solution of quasi three-mode factor analysis in the strict
sense, but also prompted the interpretation of the parameters.
A slightly modified model in which the core matrix is
transformed into the correlation matrix rather than the
covariance matrix is discussed. The core matrix in this revised
model can be regarded as a sort of higher order loading matrix,
for its elements are the correlations of the factor scores for
each occasion with the factor scores in common which might be,
so to speak, the factor of factors. Kelly and Fiske's
multitrait-multimethod matrix including five personality traits
(Assertive, Cheerful, Serious, Unshakable poise and Broad
interests) rated by three methods was reanalyzed in this
Murakami, T. (1983a).
3so data ni okeru inshi henka no kijutsu no tameno sho hoho
[Methods for description of factor change in three-mode data
(I): Factor analytical models]. Bulletin of the Faculty of
Education, Nagoya University, 30, 145-176.
This paper presents and compares several factor analytic models,
some of which are new, dealing with three-mode data, especially
longitudinal or multitrait- multimethod data. The main models
are: General model; Longitudinal factor analysis model
(Corballis, 1973); Multimethod factor analysis model (Jackson,
1975); Common factor loading model; Invariant factor loading
model (Hakstian, 1973); Quasi three-mode factor analysis;
Extended PARAFAC model; Common factor score model; Invariant
model. Analysis of Kelly ∧ Fiske's multitrait- multimethod
matrix is attached as a numerical example, and the type of the
factor change described by each model is discussed.
Murakami, T. (1983b).
Quasi three-mode principal component analysis - A method for
assessing the factor change. Behaviormetrika, 14,
Quasi three-mode factor analysis (= Tucker2 model) is described as
a procedure for assessing factor change and it is shown to be
applicable to longitudinal data and multitrait-multimethod
matrices. The standardised data matrix for each occasion is
decomposed as the product of three matrices, the factor score
matrix, a slice of the extended core matrix, and the factor
loading matrix. It is illustrated that the patterns to which core
matrices conform can distinguish the change in factor loadings
from the change in factor scores. A least squares algorithm for
the model is formulated, and a way of scaling the parameters for
easy interpretation and comparison with other factor analytic
methods is discussed. The procedure is illustrated with a
Murakami, T. (1985).
Tashugo data no tameno tansakuteki inshi bunseki [Exploratory
factor analysis of multiset data]. Bulletin of the Faculty of
Education, Nagoya University, 32, 75-93.
A new exploratory method, multiset factor analysis, which factor
analyzes data consisting of several sets of variables related to
different domains or levels was proposed. An alternating least
squares algorithm is formulated. This algorithm is a natural
extensions of the ordinary principal factor method. Questionnaire
data collected from housewives in Aichi prefecture was analyzed
by this method. It consists of four sets, - buying behavior,
attitude for buying, need for information and confidence in the
various media. A factor which could not be found by separate
factor analysis was derived in the first set and interesting
relations between the factor and factors of other sets were
Murakami, T. (1989).
Theory of psychological measurement and the concept of family
resemblances. Bulletin of the Faculty of Education, Nagoya
University, 36, 149-156. (in Japanese, English abstract)
The concept of unidimensionality is a central notion of
classical test theory. As is well known, there is a dilemma
between reliability and validity of a test because it is
impossible to maximize both the coefficient alpha, an increasing
function of variance of the test score, and the validity
coefficient, a decreasing function of it simultaneously. But the
dilemma is diminished if scores of all the items of the test are
explained by a single factor in the basic model of factor
analysis. Under the condition, it is demonstrated that both the
correlation of an item with another item in the test and the
correlation of the item with an external criterion are
proportional to the factor loading of the item. In a way, the
assumption of unidimensionality guarantees the legitimacy of
ordinary item analysis technique.##
Murakami, T. (1990).
On the principal component analysis of multigroup, multiset, and
multimode data. Kodokeiryugaku (Japanese Journal of
Behaviormetrics), 18, 28-40 (in Japanese)
This paper considers exploratory methods for investigating the
factor invariance or factor changes in multigroup, multiset, and
three-mode data, orthogonal rotations achieving the congruence
of loading matrices, canonical analysis of component scores, and
simultaneous principal component analytical methods with various
optimization criteria and constraints. Desirable properties
which should be shared by exploratory factor analytical methods
are discussed based on simple schematic models of differences of
factor loadings and factor scores as an extension of van de
Geer's Maxbet method for multiset data. The method is equivalent
to the slightly generalized Tuckals2 model (Kroonenberg and De
Leeuw) for three-mode data, and can be modified to be applicable
to multigroup data. It is demonstrated that these methods have
the desirable properties as exploratory analysis.
Murakami, T. (1991).
Hierarchical principal component analysis of multiset-multigroup
data. Bulletin of the Faculty of Education, Nagoya
University, 38, 155-166. (in Japanese).
Consider a data matrix Z, which is of the form:
variables × subjects, and it can be partitioned into
m sets of rows and g groups of columns.
Z can then be seen as a super matrix. Let us call
the data which can be arranged as Z
multiset-multigroup one. This paper proposes a method for
component analysis of multiset-multigroup data. The basic model
is a natural extension of Kroonenberg & De Leeuw (1977)'s
TUCKER 2 model for three-mode data. An alternating least squares
algorithm, which is also a slight modification of TUCKALS 2
solving TUCKER 2 problem, is derived and adapted to handle the
data with large Ns's. One of the most distinct
features of the output of this method is that the first order
loading matrices can be interpreted as correlation matrices
between variables and first order components. This hierarchical
component model is not only able to explain the data more
parsimoniously than individual analysis of each element matrix
but it is also more sensitive to the group differences of
loadings than analysis of all groups as a whole. An application
for the data with two sets - Peer and Self ratings, and two
groups - males and females is demonstrated as an illustrative
Murakami, T. (1996).
Three-mode factor models and the concept of individual
Japanese Psychological Review, 39, 408-428 (in
Japanese with English abstract).
Two kinds of individual differences are found in the history of
psychology, and distinguishing them is essential for the
appropriate use of factor analytic three-mode models. Each type of
individual difference correspondds to the specific way of
preprocessing data, especially the mode across which is centred
creates substantial differences in analytical results. There are
at least two models: (1) individual differences models
which embody differences in cognitive structures present in the
individuals' factor structures, and which require three-mode data
for their description; (2) condition differences models,
in which individual differ in their location on dimensions, for
instance, defined by test scores, and which can be described with
two-mode data sets. However, three-mode models can be used to
describe the variability and stability on the individual
differences on several dimensions.
Murakami, T. (1998).
Tucker2 as a second-order principal component analysis. In C. Hayashi,
N. Ohsumi, K. Yajima, Y. Tanaka, H.-H. Bock, & Y. Baba (Eds.),
Data science, classification, and related methods (pp. 575-586).
Statistical properties of the Tucker2 (T2) model, a simplified
version of three-mode principal component analysis (PCA), are
investigated aiming at applications to the study of factor
invariance. The T2 model is derived as a restricted form of
second-order PCA in the situation comparing component loadings
and component scores across occasions. Several statistical
interpretations of coefficients obtained from the least squares
algorithm of T2 are proposed, and several aspects of T2 are
shown to be natural extensions of characteristics of classical
PCA. A scale free formulation of T2 and a new derivation of the
algorithm for the large sample case are also shown. The
relationship with a generalized canonical correlation model is
Murakami, T. & Kroonenberg, P. M. (2003).
Three-mode models and individual differences in semantic differential data.
Multivariate Behavioral Research. 38 247-283.
This article investigates how individual differences in semantic differential
data can be modeled and assessed using three-mode models. Individual differences
are important because their existence may affect the generality of conclusions
based on such data. An overview is given how individual differences arise and
how they can be handled in the analysis. The results of the investigation will
be illustrated with semantic differential data on the characterization of Chopin's
Preludes by a group of Japanese university students.
Murakami, T., Ten Berge, J.M.F., & Kiers, H.A.L. (1998).
A case of extreme simplicity of the core matrix in three-mode principal
Psychometrika, 63, 255-261.
In three-mode Principle Components Analysis, the P
× Q × R core matrix G can be
transformed to simple structure before it is interpreted. It is
well-known that, when P = QR, G can be
transformed to the identity matrix, which implies that all
elements become equal to values specified a priori. In the
present paper it is shown that, when P = QR - 1,
G can be transformed to have nearly all elements equal
to values specified a priori. A closed- form solution for this
transformation is offered. Theoretical and practical
implications of this simple structure transformation of
G are discussed.
Murdoch, V.J., Snyder Jr, C.W., Law, H.G., Pamment, P.R.,
& Payne, P.V. (1985).
Environmental evaluations of a "hard hat" residential area in rural
Australia. Journal-of-Community-Psychology, 13,
244 construction workers and wives living in Nanango, a remote
Austalian community, provided survey self-report ratings of (a)
the availability of environmental features, (b) their importance
to overall life quality, and (c) the extent to which they bring
happiness and satisfaction. L. R. Tucker's (1966) 3-mode common
factor analysis method was used to explicate the individual
differences in environmental evaluations among these residents.
Results suggest that Tucker's 3-mode factor analysis method was a
useful way of partitioning individual differences' variance in
Muroski, A.R., Booksh, K.S., & Myrick, M.L. (1996).
Single-measurement excitation/emission matrix
spectrofluorometer for determination of
hydrocarbons in ocean water. 1. Instrumentation
and background correction.
Analytical Chemistry, 68, 3534-3538.
A spectrofluorometer capable of
dispersed-spectrum, simultaneous, multiwavelength
UV excitation and collection of luminescence has
been constructed for the purpose of qualitatively
and quantitatively determining aromatic
hydrocarbon pollutants dissolved in ocean water.
Hydrocarbon fluorescence data produced by this
instrument were in the form of excitation/emission
matrices, which provide more spectral information
about these complex mixtures than is available
from conventional excitation or emission
fluorescence profiles. Second-order statistical
methods were applied to these data to determine
low part-per-billion concentrations of two primary
fluorescent compounds, naphthalene and styrene,
found in ocean water exposed to gasoline despite
the presence of uncalibrated interference from
similar aromatic compounds, the ocean water
matrix, and the instrumental background.
Muthén, B., Olsson, U., Pettersson, T. & Stahlberg, G.
Measuring religious attitudes using the semantic differential
technique: An application of three-mode factor analysis.
Journal for the Scientific Study of
Religion, 16, 275-288.
120 theology students were presented with 6 religious concepts
to be scored on 60 semantic bipolar seven-point scales. These
data were subjected to T3. A straight forward application and
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Institute of Education and Child Studies |
The Three-Mode Company |
Department of Education , Leiden University
The Three-Mode Company, Leiden, The Netherlands
E-mail: kroonenb at fsw.leidenuniv.nl
First version: 12/02/1997;