Three-Mode Abstracts, Part I

INDEX

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• Iacobucci, D. (1989).
  Modeling multivariate sequential dyadic interactions. Social Networks 11, 315-362.
  This study explores two methods for analysing sociometric data measured on several relations observed at several points in time. The multirelational, sequential data may be represented in a four dimensional actors x partners x relations x time points super-sociomatrix. The first method proposed as an alternative to analyzing such super-sociomatrices is an application of a four-mode eigenvector model. The second proposed alternative method is an analysis of variance applied to parameter estimates from simple log-linear network models. These methods are described in detail and then applied to two real data sets: the relations in a monastry (Sampson 1968), and the friendship ties among a set of college students (Newcomb 1963).

  

• Iacobucci, D. (1990).
  Derivation of subgroups from dyadic interactions. Psychological Bulletin, 107, 114-132.
  This article presents a simulation study that compares several methods for deriving empirical subgroups from sociometric data. The Monte Carlo study was used to investigate how well the methods recovered the subgroup structure that had been built into the actors' and partners' modes. Fortyeight sociomatrices were generated using a 24 × 3 factorial design. The factors included the number of individuals in the network, the true number of subgroups into which the individuals were classified, the proportion of individuals falling into each of the subgroups, the structure of the dyadic interactions, and the clarity of the subgroup structure. On the basis of the simulation study's results, subgroups were derived for two real data sets. The first data set described the relations in a monastery (Sampson, 1968). The second data set described the referral network of a service provider (Reingen & Kernan, 1986).

  
   

• Ibraghimov, I. (2002).
  Application of the three-way decomposition for matrix comprehenssion. Numerical Linear Algebra with Applications, 1, 1-16.
  We present a new method to compress and invert 3D integral operators on rectangular non-regular grids. This method requires a small amount of memory to store the compressed matrix and in most cases can provide a good preconditioner for the solution of linear systems with this matrix. We demonstrate efficiency of this method for the solution of some model discrete problems associated with integral(R) (3) A((x) over bar, (y) over bar )f((x) over bar )d((x) over bar) = u((y) over bar), (x) over bar, (y) over bar is an element of R-3 where A((x) over bar, (y) over bar) such as 1/\(x) over bar - (y) over bar vertical bar is considered on a non-regular grid. The arithmetical complexity of matrix-vector and preconditioner-vector multiplications are about N-4/3 operations and there are only about N-2/3 words of memory to store.

     

• Idborg-Bjorkman, H., Edlund, P. O., Kvalheim, O. M., Schuppe-Koistinen, I. & Jacobsson, S. P. (2003).
  Screening of biomarkers in rat urine using LC/electrospray ionization-MS and two-way data analysis. Analytical Chemistry, 75, 4784-4792.
  Biofluids, like urine, form very complex matrixes containing a large number of potential biomarkers, that is, changes of endogenous metabolites in response to xenobiotic exposure. This paper describes a fast and sensitive method of screening biomarkers in rat urine. Biomarkers for phospholipidosis, induced by an antidepressant drug, were studied. Urine samples from rats exposed to citalopram were analyzed using solid-phase extraction (SPE) and liquid chromatography mass spectrometry (LC/MS) analysis detecting negative ions. A fast iterative method, called Gentle, was used for the automatic curve resolution, and metabolic fingerprints were obtained. After peak alignment principal component analysis (PCA) was performed for pattern recognition, PCA loadings were studied as a means of discovering potential biomarkers. In this study a number of potential biomarkers of phospholipidosis in rats are discussed. They are reported by their retention time and base peak, as their identification is not within the scope of the study. In addition to the fact that it was possible to differentiate control samples from dosed samples, the data were very easy to interpret, and signals from xenobiotic-related substances were easily removed without affecting the endogenous compounds. The proposed method is a complement or an alternative to NMR for metabolomic applications.

• Idborg, H., Edlund, P. O., & Jacobsson, S. P. (2004).
  Multivariate approaches for efficient detection of potential metabolites from liquid chromatography/mass spectrometry data. Rapid Communications in Mass Spectrometry, 18, 944-954.
  This work describes a novel method for rapid screening of unknown metabolites in urine samples that narrows down the list of potential metabolites. Prior to analysis by liquid chromatography/electrospray ionization mass spectrometry (LC/ESI-MS), urine samples were prepared using solid-phase extraction (SPE). Automatic curve resolution was used for deconvolution of the LC/MS data, followed by peak alignment. Preprocessed data were then used for metabolite pattern recognition using principal component analysis (PCA), parallel factor analysis (PARAFAC), and multilinear partial least squares (N-PLS). This approach enabled the rapid detection of metabolites of citalopram in urine by maximizing the information extracted. The metabolites thus identified were compared with earlier studies on the metabolism of citalopram. In addition, new, unreported metabolites were found and characterized by LC/MS/MS and accurate mass measurements. A combination of data from positive and negative ionization enhanced the identification of metabolites.

           

• Iizuka, K., & Aishima, T. (1999).
  Starch Gelation Process Observed by FT-IR/ATR Spectrometry with Multivariate Data Analysis. Journal of Food Science, 64, 653-658.
  For directly observing changes related to the gelation process of starch, IR spectra of starch in water while heating were obtained using FT-IR/ATR spectrometry. Relationships between gelation and spectral changes were examined using factor analysis, evolving factor analysis (EFA) and three-way principal component analysis (PCA). Absorption at 3300 and 1610 cm-1 decreased with temperature but absorption at 1000 cm-1 increased. The factor score plot patterns of amylose, amylopectin and rice starches were similar but those of potato and corn starches were unique. EFA indicated variances relating to changes caused in starch and water as different factors. Loadings of the starch component 2 in three-way PCA correlated with starch granule sizes.

         

• Imada, A.S. & London, M. (1979).
  Relationships between subjects, scales and stimuli in research on social perception. Perceptual and Motor Skills, 48, 691-697.
  260 college students of varying ethnic backgrounds rated 6 ethnic stimuli on 24 bipolar semantic scales T3. Varimax on factors for stimuli and subjects, but not on those for scales. The core matrix was difficult to evaluate.

   

• Inn, A., Hulin, C.L., & Tucker, L. (1972).
  Three sources of criterion variance: Static dimensionality, dynamic dimensionality, and individual dimensionality. Organizational Behavior and Human Performance, 8, 58-83.
  11 performance measures were collected from 184 airline reservation agents for each of 5 consecutive months. Discussion of input scaling. Detailed analysis of solution (time-mode components are overall level, trend, 'acceleration'). 'Idealized subjects' were used to characterize the subject dimensions. The computations for and the results of this procedure are shown in great numerical detail.

  

• Inukai, Y. (1981).
  Analysis of perceptual dimensions of schematic facial expressions via three-way multidimensional scaling. Behaviormetrika, 9, 1-20.
  In order to investigate perceptual dimensions of facial expressions, three-way multidimensional scaling methods were applied to the analysis of two types of judgment data. That is, dissimilarity judgments among facial expressions and rating judgments of each face on 20 emotion-term scales were obtained in experiments, and analyzed by the scaling methods which yielded uniquely oriented configurations. The faces used in the experiments consisted of seventeen schematic facial expressions constructed by combinations of different curvatures of the mouth and eyes. The results successfully exposed two perceptual dimensions, which were interpreted as friendliness-unfriendliness and high activation - low activation. And it was clarified that these dimensions were fairly consistent over the different data types and scaling methods used in the present study.

• Inukai, Y., Saito, S., & Mishima, I. (1980).
  A vector model analysis of individual differences in sensory measurement of surface roughness. Human Factors, 22, 25-36.
  In order to investigate the structure of individual differences in sensory measurement of surface roughness, paired-comparisons data of judged roughness on metal surfaces were subjected to vector model analysis. Both of the derived most parsimonious configurations of test pieces for the data from tactual and visual experiments were two-dimensional and well-predicted by the physical variables of root mean square deviations in profile (Rrms) and mean spacing of profile irregularities (pitch). Individual differences were observed in the wide variety of weighted combinations of the two physical variables. The effects of training of inspectors on their structures of sensory measurement were clarified in the observed group differences. On the basis of these findings, some guidelines for instructing and training inspectors were discussed.

• Inukai, Y., Taya, H., Miyano, H., & Kuriyama, H. (1985).
  Multidimensional evaluation method for psychological effects of pure tones at low and infrasonic frequencies. Paper presented at the 3rd International Conference on Low Frequency Noise and Vibration, London, UK. Sept. 12 - 13.
  Subjective ratings of pure tones at low and infrasonic frequencies (3-40 Hz) were obtained on a set of semantic-differential-type scales and were analysed by factor analytic methods. As the results, it was concluded that there were three main factors of the human responses to the stimulus sound, that is: 1) the factor of pressure, 2) the factor of vibration, 3) the factor of loudness. Then, in order to predict the human responses from the physical variables of the sound stimuli, prediction equations were derived for each of the three factors. Also, equal sensation contours for the factors were obtained. From these results, a new evaluation method for the psychological effects was proposed, which considers the multidimensional aspects of human perception of low and infrasonic frequencies.

• Inukai Y. (1996).
  Some applications of PARAFAC and INDSCAL to the analysis of perceptual judgement data. Japanese Psychological Review, 39, 476-500. (in Japanese with English abstract)
  Applications of PARAFAC and INDSCAL to the analysis of perceptual judgement are presented, in particular similarity judgements and rating scale data on schematic facial expressions, and rating scale data on low frequency noise. Reliability of the analyses and problems in their applications are discussed.

• Islam, F. M. A., Basford, K. E., Redden, R. J., Gonzalez, A. V., Kroonenberg, P. M., & Beebe, S. (2002).
  Genetic variability in cultivated common bean beyond the two major gene pools. Genetic Roesources and Crop Evolution, 49, 271-283.
  It is generally accepted that two major gene pools exist in cultivated common bean (Phaseolus vulgaris L.), a Middle American and an Andean one. Some evidence, based on unique phaseolin morphotypes and AFLP analysis, suggests that at least one more gene pool exists in cultivated common bean. To investigate this hypothesis, 1072 accessions from a common bean core collection from the primary centres of origin, held at CIAT, were investigated. Various agronomic and morphological attributes (14 categorical and 11 quantitative) were measured. Multivariate analyses, consisting of homogeneity analysis and clustering for categorical data, clustering and ordination techniques for quantitative data and nonlinear principal component analysis for mixed data, were undertaken. The results of most analyses supported the existence of the two major gene pools. However, the analysis of categorical data of protein types showed an additional minor gene pool. The minor gene pool is designated North Andean and includes phaseolin types CH, S and T; lectin types 312, Pr, B and K; and mostly A5, A6 and A4 types a -amylase inhibitor. Analysis of the combined categorical data of protein types and some plant categorical data also suggested that some other germplasm with C type phaseolin are distinguished from the major gene pools.

  
           

• Israelsson, A. (1969).
  Three-way (or second order) component analysis. In H. Wold & E. Lyttkens (Eds.), Nonlinear iterative partial least- squares (NIPALS) estimation procedures. Bulletin of the International Statistical Institute, 43, 29-51.
  Proposal of T2, and a short discussion of its estimation within the NIPALS framework.

  
   

• Itakura, H., Nishikawa, Y., & Yamauchi, T. (1982).
  An iterative solution procedure for individual differences multidimensional scaling with weighted inner-product model. Behaviormetrika, 11, 1-15.
  The weighted inner-product model is discussed for a class of techniques of multidmensional scaling incorporating individual differences. Data to be analyzed are sets of arbitrary ones, from some individuals, expressing similarity between objects. The model discussed is such that an inner product of position vectors, inn a space, corresponding to the objects represents given similarity between the objects. A set of parameters called weights is utilized for indicating individual differences. In order to determine the vectors and the parameters, a least-squares criterion to be minimized is defined. For minimization of the criterion, an iterative computation procedure is proposed considering quantitative data. The model and the procedure are further extended to treat ordinal data. Illustrative examples are attached with using artificial data and real survey data.

  
       

• Iwatsubo, S. (1974).
  Two classification techniques of 3-way discrete data: Quantification by means of correlation ratio and three-dimensional correlation coefficient. Kodokeiryogaku (Japanese Journal of Behaviormetrics), 2, 54-65; English abstract, p. 79.
  Two new classification methods are proposed to find out clusters from 3-way discrete data. They are quantification methods using the criteria maximizing correlation ratio and three-dimensional correlation coefficient, which lead to solving eigenequations. Three-dimensional correlation coefficient is defined by an equation, which is convenient to estimate the degree of joint relation among three variables of 3-way data. Some properties of three-dimensional correlation coefficient are given. Results of applying the methods to small data are also presented.

       

• Izquierdo-Ridorsa, A., Saurina, J., Hernández-Cassou, S., & Tauler, R. (1997).
  Second-order multivariate curve resolution applied to rank-deficient data obtained from acid-base spectrophotometric titrations of mixtures of nucleic bases. Chemometrics and Intelligent Laboratory Systems, 38, 183-196.
  Rank-deficient data matrices, obtained from simulated spectrophotometric acid-base titrations of mixtures of up to four nucleic bases (adenine, cytosine, hypoxanthine and uracil), were analyzed by second-order multivariate curve resolution. The analysis of these individual mixture data matrices gives a rank value of n + 1, where n is the number of nucleic bases present in the system. This number is, however, lower than 2n, the number of spectrometrically active species theoretically present in the systems under study, since each nucleic base is expected to give two species, a protonated and a deprotonated species. This rank deficiency is solved when more than one titration is simultaneously analyzed by second-order multivariate curve resolution. Full rank recovery is achieved when the titration of the mixture of rt nucleic bases and other n: 1 titrations, each one corresponding to a different base, are simultaneously analyzed. Results obtained by second-order multivariate curve resolution indicate that for a total resolution of the system full rank is necessary. However, resolution and quantitative determinations of individual nucleic bases in mixtures in the presence of interferences can be achieved (with a prediction error lower than 2% in most cases) even in the case of rank deficiency.

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