Three-Mode Abstracts, Part O

INDEX

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• Okada, A. (1990).
  A generalization of asymmetric multidimensional scaling. In M. Schader & W. Gaul (Eds.), Knowledge, data and computer-assisted decisions (pp. 127-138). Berlin: Springer.
  An asymmetric multidimensional scaling model, which is derived by generalizing the predecessor, and the nonmetric algorithm to fit the present model to an asymmetric proximity matrix is presented. In the present model asymmetries in proximities are accounted for not only by the term related with stimuli or with dimensions but by the term related with stimuli and dimensions. Geometrically each stimulus is represented as a point and an ellipse (ellipsoid, hyperellipsoid) in a multidimensional Euclidean space. The present model is applied to car switching data among 12 car segments. The obtained two- dimensional solution is compatible with the previous analyses. And it seems that the length of the semiaxes of the ellipse might represent the relative dominance or attractiveness on the two dimensions respectively.

• Okada, A., & Imaizumi, T. (1980).
  Nonmetric method for extended INDSCAL model. Behaviormetrika, 7, 13-22.
  A new method is introduced which can explain individual differences in dissimilarity judgments by N subjects. The method is based on a weighted distance model which is a generalization of DeLeeuw and Pruzansky's model to Minowski r metric. A set of N dissimilarity matrices is analyzed nonmetrically to derive a group stimulus configuration and a subject configuration just as INDSCAL. The method optimizes the goodness of fit measure which is based on the stress formula two by the method of steepest descent. This optimizing measure makes the computing process independent of the Minowski constant. The method was applied to schematic face data, and gave satisfactory results.

  

• Okada, A. (2002).
  A review of cluster analysis and Multidimensional Scaling research in sociology. Sociological Theory and Methods, 17, 167-181.
  An overview of studies is presented which utilize cluster analysis and MDS (MultiDimensional Scaling) in sociology. Before focusing our attention onto studies in sociology, questionable ways of applying these two procedures are discussed which can be seen not only in studies in sociology but also commonly in many other areas. Then several aspects of applying these two procedures in sociology, which seem to be interesting and to be problematic, are focused upon. Discussions follow on how to cope with the problematic aspects and how to apply these procedures more appropriately. Procedures of cluster analysis and MDS, which have been developed with relation to sociological studies, are referred to, and procedures of applying cluster analysis and MDS, which also have been introduced in sociological studies, are presented. Several new aspects of applying cluster analysis and MDS in future sociological studies are stated.

• Okada, A., & Imaizumi, T. (1986).
  How to use nonmetric Euclidean/non-Euclidean weighted multidimensional scaling program (N-NEWMDS version 1.1).
  Journal of Applied Sociology, 3, 1-81.
  This manual explains how to use a computer program which performs fitting weighted Euclidean/non-Euclidean model of Okada and Imaizumi (1980) to do individual difference multidimensional scaling. The model itself and the algorithm to fit the model was introduced and described by the authors in that paper. But the present computational algorithm is an improvement on the originally published one.

• Okada A. & Imaizumi, T. (1996).
  Analyzing friendship ties by using two-mode three-way asymmetric multidimensional scaling. Japanese Psychological Review, 39,459-475 (in Japanese with English abstract).
  Friendship tie data collected by Kumbasar et al. (1994) from 25 employees of a department of a computer company were analysed with two-mode three-way asymmetric mds in dimensions. Differnces in asymmetry of different groups could be observed.

• Okada A. & Imaizumi, T. (1997).
  Asymmetric multidimensional scaling of two-mode three-way proximities. Journal of Classification, 14,195-224.
  An asymmetric multidimensional scaling model and an associated nonmetric algorithm to analyse two-mode three-way asymmetric proximites are introduced. The model consists of a common object configuration and weights for symmetry and asymmetry. In the common object configuration each object is represented by a point and a circle in a Euclidean space. The common object configuration represents pairwise proximity relationships between pairs of objects for the 'group' of all sources. Each source has its own symmetry weight and a set of asymmetry weights. Symmetry weights represent individual differences among sources in asymmetric proximity relationships. The associated nonmetric algorithm is an extension of the algorithm developed earlier (Okada and Imaizumi, 1987). As an illustrative example, intergenerational occupational mobility in Japan among eight occupational categories is analysed.

• Okada, A., & Imaizumi, T. (1999).
  Two-mode three-way asymmetric multidimensional scaling with constraints on asymmetry. In R. Decker & W. Gaul (Eds.) Classification and Information Processing at the Turn of the Millennium: Proceedings of the 23rd annual conference of the Gesellschaft für Klassifikation (pp. 52-59). Bielefield: 10-12 March.
  A model and an accompanying algorithm for two-mode three-way asymmetric multidimensional scaling is presented. The present model has a constraint on asymmetry, compared with the model of Okada, Imaizumi (1997) where each source has a different magnitude of asymmetry, but all sources are constrained so that the relative importance of the asymmetry along dimensions is constant for all sources. The accompanying nonmetric algorithm was developed from similar work in Okada, Imaizumi (1997). An application to interpersonal attraction data among university students is presented.

• Okada, A., & Marumo, J. (1993).
  Utilizing MDPREF to disclose between and within group differences. Sociological Theory and Methods, 8, 127-141.
  A procedure of using MDPREF to analyze paired comparison or dominance data on items and to disclose between and within group differences when subjects consist of several different groups is presented. The procedure consists of four phases. (a) To cluster subjects of each group by applying some of cluster analysis methods. (b) To derive an inner product matrix among items for each cluster. (c) To analyze these inner product matrices by INDSCAL, and (d) To derive subject configuration (subject vectors) of MDPREF by an external MDPREF analysis based on the common object (item) configuration given by the INDSCAL analysis. The procedure inherited the uniquely oriented dimensions of the object (item) configuration from INDSCAL. The procedure is applied to the survey data comparing eating habits among three cities.

  
   

• Olivieri, A. C., & Faber, N. K. M. (2004a).
  Standard error of prediction in parallel factor analysis of three-way data. Chemometrics en Intelligent Laboratory Systems, 70, 75-82.
  A simple approach is described to calculate sample-specific standard errors for the concentrations predicted by a three-way parallel factor (PARAFAC) analysis model. It involves a first-order error propagation equation in which the correct sensitivity and leverage values are introduced. A comparison is made with a related unidimensional partial least-squares (PLS) model, specifically as regards the required leverage values. Monte Carlo simulation results obtained by adding random noise to both concentrations and instrumental signals for theoretical binary mixtures are in good agreement with the proposed approach. An experimental multicomponent example was studied by a similar Monte Carlo approach, and the obtained standard errors are also in agreement with the calculated values. Implications concerning the limit of detection are discussed.

• Olivieri, A. C., Arancibia, J. A., De La Pena, A. M., Duran-Meras, I., & Mansilla, A. E. (2004b).
  Second-order advantage achieved with four-way fluorescence excitation-emission-kinetic data processed by parallel factor analysis and trilinear least-squares. Determination of methotrexate and leucovorin in human urine. Analytical Chemistry, 76, 5657-5666.
  Four-way fluorescence data recorded by following the kinetic evolution of excitation-emission fluorescence matrices (EEMs) have been analyzed by parallel factor analysis and trilinear least-squares algorithms. These methodologies exploit the second-order advantage of the studied data, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. They were applied to the simultaneous determination of the components of the anticancer combination of methotrexate and leucovorin in human urine samples. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording full EEM of the samples at different reaction times. A commercial fast scanning spectrofluorometer has been used for the first time to measure the four-way EEM kinetic data. The rapid scanning instrument allows the acquisition of a complete EEM in 12 s at a wavelength scanning speed of 24 000 nm/min. The emission spectra were recorded from 335 to 490 nm at 5-nm intervals, exciting from 255 to 315 nm at 6-nm intervals. Ten successive EEMs were measured at 72-s intervals, to follow the fluorescence kinetic evolution of the mixture components. Good recoveries were obtained in synthetic binary samples and also in spiked urine samples. The excitation, emission, and kinetic time profiles recovered by both chemometric techniques are in good agreement with experimental observations.

• Olivieri, A. C., Faber, N. K. M., Ferre, J., Boque, R. Kalivas, J. H., & Mark, H. (2006).
  Uncertainty estimation and figures of merit for multivariate calibration. International Union of Pure and Applied Chemistry, 78, 633-661.
  This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.

       

• Oort, F.J. (1999).
  Stochastic three-mode models for mean and covariance structures. British Journal of Mathematical & Statistical Psychology, 52, 243-272.
  With three-mode models, the three modes are analysed simultaneously. Examples are the analysis of multitrait-multimethod data where the modes are traits, methods and subjects, and the analysis of multivariate longitudinal data where the modes are variables, occasions and subjects. If we consider the subjects mode as random, and the other modes as fixed, such data can be analysed using stochastic three-mode models. Three-mode factor analysis models and composite direct product models are special cases, but they are models for the covariance structure only. Stochastic three-mode models for mean and covariance structures are presented, and the identification, estimation and interpretation of the model parameters are discussed. Interpretation is facilitated by introducing a new terminology and by considering various special cases. Analyses of real data from the field of economic psychology serve as an illustration.

• Oort, F.J. (2001).
  Three-mode models for multivariate longitudinal data. British Journal of Mathematical and Statistical Psychology, 54, 49-78.
  Multivariate longitudinal data are characterized by three modes: variables, occasions and subjects. Three-mode models are described as special cases of a linear latent variable model. The assumption of measurement invariance across occasions yields three-made models that are suited for the analysis of multivariate longitudinal data. These so-called longitudinal three-mode models include autoregressive models and latent curve models as special cases. Empirical data from the held of industrial psychology are used in an example of how to test substantive hypotheses with the longitudinal, autoregressive and latent curve three-mode models.

       

• Orekhov, V.Y., Ibraghimov, I.V., & Billeter, M. (2001).
  MUNIN: A new approach to multi-dimensional NMR spectra interpretation. Journal of Biomolecular NMR, 20, 49-60.
  A new method, MUNIN (Multi-dimensional NMR spectra interpretation), is introduced for the automated interpretation of three-dimensional NMR spectra. It is based on a mathematical concept referred to as three-way decomposition. An NMR spectrum is decomposed into a sum of components, with each component corresponding to one or a group of peaks. Each component is defined as the direct product of three one-dimensional shapes. A consequence is reduction in dimensionality of the spectral data used in further analysis. The decomposition may be applied to frequency-domain or time-domain data, or to a mixture of these. Features of MUNIN include good resolution in crowded regions and the absence of assumptions about line shapes. Uniform sampling of time-domain data, a prerequisite for discrete Fourier transform, is not required. This opens an avenue for the processing of NMR data that do not follow oscillating behaviour, e.g. from relaxation measurements. The application of MUNIN is illustrated for a H-1-N-15-NOESY-HSQC, where each component is defined as the set of all NOE peaks formed by a given amide group. As a result, the extraction of structural information simply consists of one-dimensional peak picking of the shape along the NOE-axis obtained for each amide group.

• Orekhov, V. Y., Ibraghimov, I., & Billeter, M. (2003).
  Optimizing resolution in multidimensional NMR by three-way decomposition. Journal of Biomolecular NMR, 27, 165-173.
  Resolution depends on the number of points sampled in a FID; in indirectly detected dimensions it is an important determinant of the total experiment time. Based on the high redundancy present in NMR data, we propose the following timesaving scheme for three-dimensional spectra. An extensive grid of discrete t1- and t2-values is used, which increases resolution while preserving the spectral width. Total experiment time is reduced by avoiding the recording of t3-FIDs for selected pairs of t1 andt2; typically the recording is omitted for about 75% of the (1,2) combinations. These data sets are referred to as sparse, and post-experimental processing making optimal use of spectral redundancy provides the missing, non-recorded data. We have previously shown that three-way decom-position (TWD) within the MUNIN approach provides a practical way to process dense NMR data sets. Here, a novel TWD algorithm [Ibraghimov, (2002) Numer. Linear Algebra Appl. 9, 551–565] is used to complement a sparsely recorded time-domain data set by providing the missing FIDs for all (1,2) combinations omitted in the experiment. A necessary condition is that for each t1-value at least a few FIDs are recorded, and similar for each t2-value. The method is demonstrated on non-uniformly sampled 15 N-NOESY-HSQC data sets recorded for the 14 kD protein azurin. The spectra obtained by TWD, reconstruction and ordinary transform to frequency-domain are, in spite of the large number of signals and the high dynamic range typical for NOESYs, highly similar to a corresponding reference spectrum, for which all (1,2) combinations were recorded.

• Orlik, P. (1980).
  Das Summax-Modell der dreimodalen Faktorenanalyse mit interpretierbarer Kernmatrix. Archiv für die Psychologie, 133, 189-218.
  O. proposes a completely symmetric three-mode model (called Summax) with a three-mode identity matrix. The appearance of the model is identical to that of Carroll & Chang (1970), however, the 'factor' loadings are determined in a different way. A leading-sign pattern matrix is sought for each of the modes such that the sum of all elements with their 'best' leading-sign is maximal. From these pattern matrices for the data matrix the 'factor' loadings are derived. If these 'loading' matrices are rotated, the counter-rotated core matrix will contain the direction cosines of the derived 'factors'. Illustrated by an experiment in wich 4 coloured disks are judged on 10 rating scales by 8 subjects.

• Orlik, P. (1981).
  Das Summax-Modell der dreimodalen multiplen Prädiktion, gezeigt an einem Demonstrationsexperiment [The Summax-model of three-mode multiple prediction, illustrated with a demonstration experiment]. In W. Janke (Ed.), Beiträge zur Methodik in der differentiellen, diagnostischen und klinischen Psychologie - Festschrift zum 60. Geburtstag von G.A. Lienert (pp. 280-296). Königstein/Ts.: Hain.
  The Summax-model of three-mode factor analysis is applied to three dimensional data matrices to widen the concept of multiple prediction and regression. Possible strategies of data analysis are demonstrated by an experiment.

  
   

• Ossenkopp,K.P., & Mazmanian, D.S. (1985)
  The measurement and integration of behavioral variables: aggregation and complexity as important issues. Neurobehavior Toxicology and Teratology, 7, 95-100.
  The measurement of motor activity in animals is central to the description of animal behavior in general. Application of factor analytic procedures to multivariate motor activity data is suggested to be a useful method of reducing many variables into fewer, more complex variables, which have greater phenomenon realism. Examples of the application of such factor analytic approaches are provided, both for the traditional two-way factor analytic methods as well as a more recent procedure (PARAFAC model) developed for analysis of three-way longitudinal data sets. It is suggested that multivariate analytic procedures are appropriate for data reduction and description in the area of behavioral neuroscience.

• Ossenkopp, K.P., Sorenson, L., & Mazmanian, D. S. (1994).
  Factor analysis of open-field behavior in the rat (Rattus norvegicus): Application of the three-way PARAFAC model to a longitudinal data set. Behavioural Processes, 31, 129-144.
  Examined the multivariate nature of open-field behavior in 26 adult male rats. A longitudinal data set, obtained during 4 open-field test sessions, was subjected to a 3-way PARAFAC analysis, which allowed for the direct factor analysis of 3-dimensional arrays and provided a unique factor solution to the longitudinal data set. Analysis extracted 2 factors: emotional reactivity and exploratory behavior. These factors changed in temporal prominence, with animals showing greater emotional reactivity on the 1st test session, and greater levels of exploration on the 3rd and 4th test sessions. Findings indicate that multivariate procedures, such as the PARAFAC analysis, can be helpful in the quantitative characterization of behavioral phenomena in a more realistic manner.

               

• Ozzetti, R. A., De Oliveira, A. P., Schuchardt, U., & Mandelli, D. (2002).
  Determination of tacticity in polypropylene by FTIR with multivariate calibration. Journal of Applied Polymer Science, 85, 734-745.
  A method for determination of tacticity in polypropylene (PP) using FTIR associated with multivariate analysis is presented. Blends of PP with known tacticity were prepared with isotactic, syndiotactic, and atactic polymer and analyzed by C-13-NMR. The FTIR spectra were recorded and processed through principal components regression (PCR) and partial least-squares regression (PLS), using information from several different portions of the spectra. The method was compared with the classical methods of tacticity determination by FTIR based on the intensities of the bands at 998 cm(-1) (isotactic), 868 cm(-1) (syndiotactic), and 975 cm(-1) (internal standard), which are known to be dependent on the crystallinity of the polymer and, thus, affected by temperature and sample preparation. The models obtained with multivariate calibration, both with PCR and PLS, gave prediction errors up to fivefold smaller than that of the classical methods, and were also shown not to be heavily dependent on the bands that are affected by the crystallinity of the polymer, but rather on the methyl and methylene bendings at 1375 and 1462 cm(-1).

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