Three-Mode Abstracts, Part V

INDEX

• Van Benthem, M. H., Keenan, M. R., & Haaland, D. M. (2002).
  Application of equality constraints on variables during alternating least squares procedures. Journal of Chemometrics, 16, 613-622.
  We describe several methods of applying equality constraints while performing procedures that employ alternating least squares. Among these are mathematically rigorous methods of applying equality constraints, as well as approximate methods, commonly used in chemometrics, that are not mathematically rigorous. The rigorous methods are extensions of the methods described in detail in Lawson and Hanson's landmark text on solving least squares problems, which exhibit well-behaved least squares performance. The approximate methods tend to be easy to use and code, but they exhibit poor least squares behaviors and have properties that bare not well understood. This paper explains the application of rigorous equality-constrained least squares and demonstrates the dangers of employing non-rigorous methods. We found that in some cases, upon initiating multivariate curve resolution with the exact basis vectors underlying synthetic data overlaid with noise, the approximate method actually results in an increase in the magnitude of residuals. This phenomenon indicates that the solutions for the approximate methods May actually diverge from the least squares solution.

• Van Benthem, M. H., & Keenana, M. R. (2008).
  Tucker1 model algorithms for fast solutions to large PARAFAC problems. Journal of Chemometrics, 22, 345-354.
  We describe a method of performing trilinear analysis on large data sets using a modification of the PARAFAC-ALS algorithm. Our method iteratively decomposes the data matrix into a core matrix and three loading matrices based on the Tucker1 model. The algorithm is particularly useful for data sets that are too large to upload into a computer's main memory. While the performance advantage in utilizing our algorithm is dependent on the number of data elements and dimensions of the data array, we have seen a significant performance improvement over operating PARAFAC-ALS on the full data set. In one case of data comprising hyperspectral images from a confocal microscope, our method of analysis was approximately 60 times faster than operating on the full data set, while obtaining essentially equivalent results.

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• Van de Geer, J.P. (1974).
  Toepassing van drieweg-analyse voor de analyse van multiple tijdreeksen. In C.J. Lammers, Groei en ontwikkeling van de ziekenhuisorganisaties in Nederland. Interim rapport, Institute of Sociology, University of Leiden, Leiden, The Netherlands.
  The application of T3 for the analysis of multivariate time series is illustrated with a mini- example. The data are a subset from a study of the growth of 188 Dutch hospitals over 11 years as measured by 27 variables. The computational procedures are shown step by step to aid the explanation of the technique.

  

• Van de Geer, J.P. (1975).
  Drieweg komponenten analyse (Memo). Department of Data Theory, University of Leiden, Leiden, The Netherlands.
  A detailed and clear discussion of many technical aspects of T3 making extensive use of sums of squares interpretations. Ample discussion of scaling of the input data and the effects of this on the analysis. Description of the use of an interactive APL three-mode program.

• Van den Broek, W. H. A. M., Wienke, D., Melssen, W. J., Decrom, C. W. A., & Buydens, L. (1995).
  Identification of plastics among nonplastics in mixed waste by remote-sensing near-infrared imaging spectroscopy .1. Image inmprovement and analysis by singular-value decomposition. Analytical Cemistry, 67, 3753-3759.
  A near-IR camera has been installed in an experimental setup for real-time plastic identification. Singular value decomposition (SVD) has been used for qualitative analysis and substantial improvement of the measured multivariate images. The obtained score plots provided spatial correlations between different pixel structures caused by sample material on the one hand and image artifacts on the other. In this way, the score plots have been used as a tool to optimize the experimental setup and image quality. The improved images were offered to a new classification algorithm called multivariate image rank analysis, based on SVD, as described in part 2 of this series of articles, which follows in this issue (Wienke, D.; et al. Anal. Chem. 1995, 67, 3760).

• Van der Burg, E., De Leeuw, J., & Dijksterhuis, G. (1994).
  OVERALS: Nonlinear canonical correlation with k sets of variables. Computational Statistics & Data Analysis, 18, 141-163.
  OVERALS is a technique for canonical correlation analysis with two or more sets of variables. Any three way table can be used as input for the OVERALS program. In OVERALS terminology the ways are called objects, variables and sets. Three measurement levels of the data can be handled: numerical, ordinal and nominal. They can be defined for each variable separately. Also the conditionality of the data is defined variable-wise. The OVERALS technique searches for what is common between sets of variables measured on the same objects. The mathematical model and the algorithm are discussed. In addition an illustration of the technique is given in the form of an application.

  

• Van der Burg, E., De Leeuw, J., & Verdegaal, R. (1988).
  Homogeneity analysis with k sets of variables: An alternating least squares method with optimal scaling features. Psychometrika, 53, 177-197.
  Homogeneity analysis, or multiple correspondence analysis, is usually applied to k separate variables. In this paper it is applied to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consists of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological survey is presented.

• Van der Heijden, P. G. M., De Falguerolles, A., & De Leeuw, J. (1989).
  A combined approach to contingency table analysis using correspondence-analysis and log-linear analysis (with discussion). Applied Statistics, 38, 249-292.
  Correspondence analysis and one of its generalizations are presented as tools that can be ised for the analysis of residuals from log-linear models. By recognizing relations between correspondence analysis and log-linear analysis a better understanding of correspondence analysis is obtained. Furthermore, it is shown how these relations can be used to arrive at a combined approach to contingency table analysis using both log-linear analysis and correspondence analysis.

• Vander Heyden, Y., Pravdova, V., Questier, F., Tallieu, L., Scott, A., & Massart, D. L. (1989).
  Parallel co-ordinate geometry and principal component analysis for the interpretation of large multi-response experimental designs. Analytica Chimica Acta, 458, 397-415.
  In the evaluation of large or complex data sets the use of visualization methods can be of great benefit. In this paper, the use of parallel co-ordinate geometry (PCG) plots, principal component analysis (PCA) and N-way PCA as visualization procedures for large multi-response experimental designs was compared with the more traditional approach of calculating factor effects by multiple linear regression. PCG plots are a recent addition to the visualization tools and offer a possibility to visualize multi-dimensional data in two dimensions while no calculations are required. It was found that PCA and PCG each have their own benefits and disadvantages. Both methods can be used to some extent to select optimal conditions. Moreover, it was possible to use the PCA score plot as a Pareto optimality plot that allowed to select the experiments considered to be Pareto optimal. Therefore, the examined visualization methods can be useful and complementary aids in the interpretation of large multi-response experimental d esign data and they add a multivariate dimension to the more classical univariate analysis of such data.

• Van der Kloot, W.A. & Kroonenberg, P.M. (1982)
  Group and individual implicit theories of personality: An application of three-mode principal component analysis. Multivariate Behavioral Research, 17, 471-492.
  The data of 60 subjects who rated 31 stimulus persons on 11 personality trait rating scales were analysed with Kroonenberg & De Leeuw's (1980) method of three-mode principal component analysis. The study showed the advantages of including data of 'artificial subjects', and of partitioning the residual sum of squares (badness of fit) for the elements of each of the modes.

• Van der Kloot, W.A., & Kroonenberg, P.M. (1985).
  External analysis with three-mode principal component models. Psychometrika, 50, 479-494.
  Through external analysis of two-mode data one attempts to map the elements of one mode (e.g., attributes) as vectors in a fixed space of the elements of the other mode (e.g., stimuli). This type of analysis is extended to three-mode data, for instance, when the ratings are made by more individuals. It is described how alternating least squares algorithms for three-mode principal component analysis (PCA) are adapted to enable external analysis, and it is demonstrated that these techniques are useful for exploring differences in the individuals' mappings of the attribute vectors in the fixed stimulus space. Conditions are described under which individual differences may be ignored. External three-mode PCA is illustrated with data from a person perception experiment designed after two studies by Rosenberg and his associates whose results were used as external information.

• Van der Kloot, W.A., Kroonenberg, P.M., & Bakker, D. (1985).
  Implicit theories of personality: Further evidence of extreme response style. Multivariate Behavioral Research, 20, 369- 387.
  Five groups of 19 subjects made ratings on 11 personality trait scales of overlapping subsets of 59 artificial stimulus persons who were described by one to five personality trait adjectives. The data were analyzed per group of subjects (blockwise) and per type of stimulus person (questionnaire-wise) by means of three-mode principal component analyses. This yielded highly similar structures for the scales, and in the blockwise analyses, for the stimulus persons. This similarity was substantiated by external three-mode analyses, which showed that all stimulus persons can be mapped into one overall configuration. In all analyses it was found that differences between subjects consisted of differences in extremity of judgment, which suggests the operation of response style.

• Van der Ven, C., Muresan, S., Gruppen, H., De Bont, D. B. A., Merck, K. B., & Voragen, A. G. J. (2002).
  FTIR spectra of whey and casein hydrolysates in relation to their functional properties. Journal of Agricultural and Food Chemistry, 50, 6943-6950.
  Mid-infrared spectra of whey and casein hydrolysates were recorded using Fourier transform infrared (FTIR) spectroscopy. Multivariate data analysis techniques were used to investigate the capacity of FTIR spectra to classify hydrolysates and to study the ability of the spectra to predict bitterness, solubility, emulsifying, and foaming properties of hydrolysates. Principal component analysis revealed that hydrolysates prepared from different protein sources or with different classes of proteolytic enzymes are distinguished effectively on basis of their FTIR spectra. Moreover, multivariate regression analysis showed satisfactory to good prediction of functional parameters; the coefficient of determination (R-2) varied from 0.60 to 0.92. The accurate prediction of bitterness and emulsion forming ability of hydrolysates by using only one uncomplicated and rapid analytical method has not been reported before. FTIR spectra in combination with multivariate data analysis proved to be valuable in. protein hydrolysate fingerprinting and can be used as. an. alternative for laborious functionality measurements.

• Van Eeuwijk, F.A. (1992).
  Multiplicative models for genotype-environment interaction in plant breeding. Statistica Applicata, 4, 393-406.
  In this paper multiplicative models for the interaction between genotype and environment are presented, which have not yet found broad application in plant breeding. These models are compared to the popular regression on the environmental mean model.

• Van Eeuwijk, F.A., & Kroonenberg, P.M. (1995).
  The simultaneous analysis of genotype by environment interaction for a number [of] traits using three-way multiplicative modelling. Biuletyn Oceny Odmian/Cultivar Testing Bulletin, 26/27, 83-96.
  For the description of genotype by environment interaction in individual trait two-way multiplicative models have become a popular means of analysis. For the simultaneous analysis of genotype by environment interaction in a number of traits three-way multiplicative models are proposed. Theory for such models is reviewed and illustrated by an application to sugar beet resistance data.

• Van Eeuwijk, F.A., & Kroonenberg, P.M. (1998).
  Multiplicative models for interaction in three-way ANOVA, with applications to plant breeding. Biometrics, 54, 1315-1333. [Also appeared in F.A. van Eeuwijk (1996), Beyond Additivity and Non- Additivity, Unpublished doctoral thesis, University of Groningen.]
  In plant breeding, multiplicative models for two-way analysis of variance interaction have become a general means of describing genotype-by-environment interaction. These models offer parsimonious descriptions and facilitate interpretations in biological terms. A disadvantage of the prevailing dominance of two-way multiplicative models is that data with more complicated environmental structure are often forced to fit the two-way framework. As a partial solution to this problem, three-way multiplicative models are presented that can be used in addition to the more familiar two-way multiplicative models. Most importantly, a three-way generalization is given of the two-way singular-value decomposition that can be applied for closer inspection of three- way analysis of variance interaction, much in the same way as its two-way counterpart is used for two-way interaction. Two real data sets are analyzed to illustrate how two- and three-way multiplicative models for interaction jointly provide parsimonious descriptions of various types of genotype-by-environment interaction. These parsimonious descriptions are often open to meaningful biological interpretations as well.

• Van Espen, P., Janssens, G., Van Hoolst, W., & Geladi, P.(1992).
  Imaging and image-processing in analytical/chemistry. Analusis, 20, 81-90.
  The concepts of acquisition and analysis of digital images obtained from spatially resolved chemical analysis are introduced. Classical image processing techniques can be used to study these "chemical images". However, chemical images are often multivariate in nature and require specific methods for improving the chemical interpretation. Multivariate image analysis is introduced and explained. An example with 8 different images generated by secondary ion microscopy and electron microscopy is given.

• Van IJzendoorn, M. H., & Kroonenberg, P. M. (1990).
  Cross-cultural consistency of doding in the strange situation. Infant Behavior & Development, 13, 469-485.
  This study tested wether or not cross-cultural differences in attachment classification distributions result from systematic differences in coding practices. First, we investigated wether or not the interactive scales have been scored consistently in several different cross-cultural samples. Second, the Richters, Waters and Vaughn (1988) functions were applied to address the question of wether or not attachment classifications were consistently based upon the same pattern of interactive behaviors. Third, cross-cultural coding differences were described from a multivariate perspective. Data sets from seven investigators in six countries were available for analysis. Analyses on this 'multinational data set' revealed that except for distance interaction, the interactive scales in the two reunion episodes were scored in accordance with the original coding rules. Furthermore, a good to reasonable agreement appeared to exist between the original classifications and those computed by the functions, except for infants older than 20 months of age. The multivariate principal compnent analysis showed that classification groups across cultures were more alike than cultures across classification groups. Our data showed, therefore, that attachment classifications have been consistently coded across cultures.

• Van Mechelen, I., & Kiers, H. A. L. (1999).
  Individual Differences in Anxiety Responses to Stressful Situations: A Three-Mode Component Analysis Model. European Journal of Personality, 13, 409-428.
  The three-mode component analysis model is discussed as a tool for a contextualized study of personality. When applied to person x situation x response data, the model includes sets of latent dimensions for persons, situations, and responses as well as a so- called core array, which may be considered a summary description of the individual di€erences in response profiles across situations. Underlying psychological processes may be further revealed by relating the model to external data on cognitive±a€ective personality system (CAPS) variables. The model as well as its validation in CAPS terms is illustrated with self-report data on anxiety responses displayed by several persons in a sample of situations. Furthermore, the model is tested against recently formulated criticisms regarding the use of (two-mode) factor analysis in personality research, and its relation to the triple typology model recently proposed by Vansteelandt and Van Mechelen (1998) is briefly discussed.

• Van Mispelaar, V. G., Tas, A. C., Smilde, A. K., Schoenmakers, P. J. & van Asten, A. C. (2003).
  Quantitative analysis of target components by comprehensive two-dimensional gas chromatography. Journal of Chromatography A, 1019, 15-29.
  Quantitative analysis using comprehensive two-dimensional (2D) gas chromatography (GC) is still rarely reported. This is largely due to a lack of suitable software. The objective of the present study is to generate quantitative results from a large GC x GC data set, consisting of 32 chromatograms. In this data set, six target components need to be quantified. We compare the results of conventional integration with those obtained using so-called "multiway analysis methods". With regard to accuracy and precision, integration performs slightly better than Parallel Factor (PARAFAC) analysis. In terms of speed and possibilities for automation, multiway methods in general are far superior to traditional integration.

• Van Sprang, E. N. M., Ramaker, H. J., Westerhuis, J. A., Gurden, S. P, & Smilde, A. K. (2002).
  Critical evaluation of approaches for on-line batch process monitoring. Chemical Engineering Science, 57, 3979-3991.
  Since the introduction of batch process monitoring using component models in 1992, different approaches for statistical batch process monitoring have been suggested in the literature. This is the first evaluation of five proposed approaches so far. The differences and similarities between the approaches are highlighted. The derivation of control charts for these approaches are discussed. A control chart should give a fast and reliable detection of disturbances in the process. These features are evaluated for each approach by means of two performance indices. First, the action signal time for various disturbed batches is tested. Secondly, the probability of a false warning in a control chart is computed. In order to evaluate the five approaches, five different data sets are studied: one simulation of a batch process, three batch processes obtained from industry and one laboratory spectral data set. The obtained results for the performance indices are summarised and discussed. Recommendations helpful for practical use are given.

• Vansteelandt, K., & Van Mechelen, I. (1998).
  Individual differences in situation-behaviour profiles: A triple typology model. Journal of Personality and Social Psychology, 75, 751-765.
  A model is proposed to represent individual differences in situation-behaviour profiles. The model consists of 3 components: a) Typologies of person, situation, and behaviour classes; b) hierarchical relations between the classes of each typology; and c) a characterization of the person types in terms of different sets of if (situation class) then (behaviour class) rules by which the 3 typologies are linked to one another. A data analysis technique (INDCLAS) is available to induce a triple typology model from empirical data. To reveal the psychological mechanisms behind such a model, the classes of the model can be related to situation, behaviour and person features. As a result, person types can be interpreted in terms of systems of cognitive-affective variables that mediate between active situation features and behavioural manifestations. This is illustrated with a study on self-reported hostile behaviour in frustrating situations.

• Van Stokkum, I. H. M., Larsen, D. S., & Van Grondelle, R. (2004).
  Global and target analysis of time-resolved spectra. Biochimica et Biophysica Acta-Bioenergetics, 1657, 82-104.
  In biological/bioenergetics research the response of a complex system to an externally applied perturbation is often studied. Spectroscopic measurements at multiple wavelengths are used to monitor the kinetics. These time-resolved spectra are considered as an example of multiway data. In this paper, the methodology for global and target analysis of time-resolved spectra is reviewed. To fully extract the information from the overwhelming amount of data, a model-based analysis is mandatory. This analysis is based upon assumptions regarding the measurement process and upon a physicochemical model for the complex system. This model is composed of building blocks representing scientific knowledge and assumptions. Building blocks are the instrument response function (IRF), the components of the system connected in a kinetic scheme, and anisotropy properties of the components. The combination of a model for the kinetics and for the spectra of the components results in a more powerful spectrotemporal model. The model parameters, like rate constants and spectra, can be estimated from the data, thus providing a concise description of the complex system dynamics. This spectrotemporal modeling approach is illustrated with an elaborate case study of the ultrafast dynamics of the photoactive yellow protein.

• Van Zomeren, P. V., Hoogvorst, A., Coenegracht, P. M. J., & de Jong, G. J. (2004).
  Optimisation of high-performance liquid chromatography with diode array detection using an automatic peak tracking procedure based on augmented iterative target transformation factor analysis. Analyst, 129, 241-248.
  An automated method for the optimisation of high-performance liquid chromatography is developed. First of all, the sample of interest is analysed with various eluent compositions. All obtained data are combined into one augmented data matrix. Subsequently, augmented iterative target transformation factor analysis performs the integrated tasks of curve resolution and peak tracking. Since this type of curve resolution processes all data at once, it can deal with strong peak overlap and reveal the correspondence of compounds between runs, i.e. peak tracking. The retention time and peak width at half height for each component of the sample are determined for every eluent composition. Next, models are built for the retention time and the peak width at half height. These models are used to predict the resolution and the analysis time for each point in factor space. Finally, a multi-criterion decision-making method, Pareto optimality, is used to find the optimum. The method completes all calculations within a few minutes and without user intervention. By means of this procedure, a mixture of three benzodiazepines is successfully separated using a ternary mobile phase. There are two requirements for the automated optimisation method to work correctly. Firstly, all components of the sample must have sufficiently different spectra. Secondly, each compound should have the same spectrum under all experimental conditions.

• Vasilescu, M. A. O., & Terzopoulos, D. (2002).
  Multilinear Analysis of Image Ensembles: TensorFaces. In A. Heyden, G. Sparr, M. Nielsen, and P. Johansen (Eds.), Computer Vision - ECCV 2002, Part II, (pp. 447-460). Springer-Verlag, Berlin.
  Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the N-mode SVD. As a concrete example, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. Our resulting "TensorFaces" representation has several advantages over conventional eigenfaces. More generally, multilinear analysis shows promise as a unifying framework for a variety of computer vision problems.

• Vasilescu, M. A. O., & Terzopoulos, D. (2004).
  TensorTextures: Multilinear Image-based rendering. ACM Transactions on Graphics, 23, 336-342.
  This paper introduces a tensor framework for image-based rendering. In particular, we develop an algorithm called TensorTextures that learns a parsimonious model of the bidirectional texture function (BTF) from observational data. Given an ensemble of images of a textured surface, our nonlinear, generative model explicitly represents the multifactor interaction implicit in the detailed appearance of the surface under varying photometric angles, including local (per-texel) reflectance, complex mesostructural self-occlusion, interreflection and self-shadowing, and other BTF-relevant phenomena. Mathematically, TensorTextures is based on multilinear algebra, the algebra of higher-order tensors, hence its name. It is computed through a decomposition known as the N-mode SVD, an extension to tensors of the conventional matrix singular value decomposition (SVD). We demonstrate the application of TensorTextures to the image-based rendering of natural and synthetic textured surfaces under continuously varying viewpoint and illumination conditions.

• Vavra, T.G. (1972).
  An application of three-mode factor analysis to product perception. In F.D. Allvine (Ed.) Marketing in motion/Relevance in Marketing. Chicago: American Marketing Association, Series no.33 (Pp. 578-583).

  

• Vavra, T.G. (1973).
  A three-mode factor analytic investigation into the effectiveness of advertising. Unpublished doctoral thesis, University of Illinois, Urbana-Champaign, IL. (Dissertation Ab stracts International, 1974, 34 (12-A), 7802.)
  T3 is used to assess the effectiveness of various types of commercials for specific groups of customers. The problem of interpreting the solution is discussed, and two alternative procedures are shown.

  
         

• Vega-Montoto, L. & Wentzell, P. D. (2003).
  Maximum likelihood parallel factor analysis (MLPARAFAC) Journal of Chemometrics, 17, 237-253.
  Algorithms for carrying out maximum likelihood parallel factor analysis (MLPARAFAC) for three-way data are described. These algorithms are based on the principle of alternating least squares, but differ from conventional PARAFAC algorithms in that they incorporate measurement error information into the trilinear decomposition. This information is represented in the form of an error covariance matrix. Four algorithms are discussed for dealing with different error structures in the three-way array. The simplest of these treats measurements with non-uniform measurement noise which is uncorrelated. The most general algorithm can analyze data with any type of noise correlation structure. The other two algorithms are simplifications of the general algorithm which can be applied with greater efficiency to cases where the noise is correlated only along one mode of the three-way array. Simulation studies carried out under a variety of measurement error conditions were used for statistical validation of the maximum likelihood properties of the algorithms. The MLPARAFAC methods are also shown to produce more accurate results than PARAFAC under a variety of conditions.

• Vega-Montoto, L, & Wentzell, P. D. (2005).
  Mathematical improvements to maximum likelihood parallel factor analysis: experimental studies. Journal of Chemometrics, 19, 236-252.
  In this paper, the application of a number of simplified algorithms for maximum likelihood parallel factor analysis (MLPARAFAC) to experimental data is explored. The algorithms, described in a companion paper, allow the incorporation of a variety of correlated error structures into the three-way analysis. In this work, three experimental data sets involving fluorescence excitation-emission spectra of synthetic three-component mixtures of aromatic compounds are used to test these algorithms. Different experimental designs were employed for the acquisition of these data sets, resulting in measurement errors that were correlated in either two or three modes. A number of data-analysis methods were applied to characterize the error structures of these data sets. In all cases, the introduction of statistically meaningful information translated to estimates of better quality than the conventional PARAFAC estimates of concentrations and spectra. The use of the algorithms that employ the error structure suggested by the analysis of the error covariance matrix yielded the best results for each data set.

• Veldscholte, C.M. (1994).
  A three-mode principal component analysis of perceptions of economic activities: TUCKALS3 also compared with two-mode PCA. Master's Thesis, Department of Method and Technique, Leiden University.
  Three-dimensional data of four countries from a research project on 'perceptions on economic activities', originally analysed with the help of two-mode principal component analyses (PCA), were re-analysed with TUCKALS3, a program for three- mode PCA. The objective of the analysis was to trace the similarities and differences in perceptual structure of the four countries, and to compare the results with those of the two-mode PCA's.

• Veldscholte, C.M., Antonides, G., & Kroonenberg, P.M. (1995).
  Converging perceptions of economic activities between East and West: A three-mode principal component analysis. (Research Report R9519/A), Rotterdam Institute for Business Economic Studies, Erasmus University, Rotterdam. (also: Tinbergen Institute Research Report Nr. TI 1-95-192).
  The similarities and differences in perceptual structure of economic activities in Hungary, Poland, the Netherlands and the United Kingdom are the focus of this study. The three-mode data consisted of economic activities (mode 1) scored on rating scales (mode 2) by a number of individuals (mode 3). The data were analysed with three-mode principal component analysis (PCA) using the program TUCKALS3. The primary result is that there is a perceptual space common to all four nations. It is characterised by a contrast between economic and social values in the first dimension, by immediate or delayed consequences of activities in the second dimension, and finally by an occupational-private dimension. The most striking difference between countries is that the British have another view of the financial resources necessary for certain detail in order to show how it can be applied to unravel structures in complicated three- mode data such as these, which frequently arise in the field of perception.

• Veldscholte, C. M., Kroonenberg, P. M., & Antonides, G. (1998).
  Three-mode analysis of perceptions of economic activities in Eastern and Western Europe. Journal of Economic Psychology, 19, 321-351.
  Data on similarities and differences in perceptions of economic activities in Hungary, Poland, the Netherlands and the United Kingdom were collected. The data set is a three-mode one consisting of economic activities (mode 1) scored on rating scales (mode 2) by a number of individuals or judges (mode 3). The major thesis of this paper is that such data should be analyzed by three-mode analysis methods rather than two-mode methods. To demonstrate this, the data were analyzed with three-mode principal component analysis (PCA) using the program TUCKALS3. Both the decisions which precede the three-mode analysis, the three-mode analysis itself, and its interpretation are illustrated and explained. The paper treats three-mode PCA in some detail in order to show how it can be applied to unravel structures in complicated three-mode data which frequently arise in the field of economic perception. The substantive result is that there is a perceptual space common to all four nations. It is characterized by contrasts between economic and social values, by immediate or delayed consequences of activities, and by a difference between occupational and private activities. The most striking difference between countries is that the British have a different view of the financial resources necessary for certain activities compared to inhabitants of the other three countries.

• Venth, K., Danzer, K., Kundermann, G., & Blaufuss, K. H. (1996).
  Multisignal evaluation in ICP-MS - Determination of trace elements in Mo-Zr-alloys. Fresenius Journal of Analytical Chemistry, 354, 811-817.
  The existence of isobaric and polyatomic ion interferences has been considered to be a significant shortcoming of inductively coupled plasma - mass spectrometry (ICP-MS). In the special case of Mo-Zr-alloys problems caused by polyatomic ions are substantial. The determination of trace elements by using classical univariate linear regression of single signals or any correction equations presented by the instrumental software is impossible. There are various possibilities to overcome spectral interferences, in principle. The application of high-resolution ICP-MS, separation methods or alternative sample introduction systems is limited by the high cost and the apparative expenditure. In this report methods of multisignal calibration, like partial least squares (PLS) regression and canonical correlation analysis (CCA), are used to overcome isobaric or chemical interferences in ICP-MS. It is shown, that PLS and CCA are able to handle or tolerate, respectively, spectral interferences existing in a Mo-Zr-O-H-F system. The results of quantitative analysis provided by PLS and CCA were comparable.

• Verhees, J. (1989).
  Econometric analysis of multidimensional models. Unpublished doctoral thesis, Department of Econometrics, University of Groningen, the Netherlands.
  Part 1. Matrix algebra.
  1. Matrices and properties; 2. Kronecker product and vec operator; 3. (0,1)- matrices and their properties.
  Part 2. Multidimensional data analysis models.
  4. k-mode principal component analysis; 5. k-mode factor analysis; 6. k-mode covariance structure analysis; 7. k-mode interdependent regression; 8. k-mode Poisson regression; 9. From formulas to programs; 10. Conclusion.

• Verhees, J., & Wansbeek, T.J. (1990).
  A multimode direct product model for covariance structure analysis. British Journal of Mathematical and Statistical Psychology, 43, 231-240.
  In psychometrc literature, there is evidence that the modes (facets, dimensions, etc.) in multimode data interact mutliplicatively. A basic expression of this idea is that a covariance matrix may then be written as repeated Kronecker product of k, say, parameter matrices, where k is the number of modes. For such a 'factorial covariance structure' we give an integrated treatment of ML, WLS, and ULS estimators. A modification of the ULS estimator appears to be non-iteratively computable.

         

• Vichi, M. (1988).
  Two-way data matrix representative syntheses of a three-way data matrix. Statistica, 48, 91-106.
  This paper deals with three-way data of individuals and variables observed on r different occasions. We are interested 1) in defining properties which have hold for two-way syntheses of three-way matrices; 2) in detecting matrices that possess these properties. A two-way matrix X* is a representative synthesis of a three-way data matrix if: a) it minimizes differences between itself and the three-way matrix, over all possible two-way matrices, according to a predefined distance between three and two-way matrices; b) it satisfies a specific internality property. It turns out that the median matrix and the arithmetic mean matrix possess properties a) and b). Also Rizzi's matrix (1987) is a representative synthesis of the three-way transformed matrix, while the matrix of Escoufier does not possess properties a) and b). We compute some representative syntheses in order to compare different X*'s, and to give intuitive reasons for the choice of one matrix instead of another in different research situations.

• Vichi, M. (1989).
  La connessione e la correlazione tra due matrici dei dati componenti una matrice a tre indici. [Association and regression between data matrices in a three-way matrix]. Statistica, 49, 225-243.
  A systematic study and a critical examination is carried out on the connections and correlations between all pairs of slices of a three-way matrix. Correlations between two matrices have to reflect whether all variables of a matrix are more frequently concordant or discordant with all variables of the other matrix. Two such correlations are proposed which revert to appropriate correlation measures if the matrices each contain one variable.

• Vichi, M. (1990).
  L'analisi in matrici fattoriali di una matrice a tre indici. [Factorial matrix analysis for a three-way matrix]. Statistica, 50, 525-546.
  In this paper the FAMA model (FActorial Matrix Analysis) is proposed and studied. FAMA is characterised by three steps. The analysis of dependence, in which a suitable correlation index between matrices Z_h and Z_m (frontal slices of Z) is chosen. The index quantifies the statistical relationships between couples of situations h and m. Different measures can be derived by the generalised index of dependence between matrices (Vichi, 1989). Furthermore the matrices Z_h are geometrically represented as points in an appropriate Euclidean space in order to examine the trend of the phenomenon in different occasions. The synthesis: The g-th factorial matrix is the normalised linear combination of Z_h (h= 1, ..., r), which summarises the g-th largest amount of dependence (according to generalised index of dependence) and it is independent of the former factorial matrices (following the meaning of the generalised index). The singular decomposition, which allows us to represent into a cartesian reference system simultaneously the individuals and the variables of the three- way data matrix and the factorial matrix.

• Vichi, M. (1991).
  Le techniche che derivano dall'analisi in matrici fattoriali di una matrice a tre indici. [Factorial matrices derived from a three-way matrix]. Statistica, 51, 53-77.
  In this paper, after introducing the Factorial Matrices Analysis (FAMA) in order to study a three-way matrix (Vichi, 1990), the author examines techniques already known in literature, that can be derived from FAMA, adding new tools of analysis. Furthermore, the author introduces new methodologies from FAMA to overcome problems connected with some of the known techniques.

• Vichi, M. (1998).
  Principal classifications analysis: a method for generating consensus dendograms and its application to three-way data. Computational Statistics & Data Analysis, 27, 311-331.
  A three-way data set is the result of the observation of data characterized by three modes: units, variables, and occasions. It is often useful to classify the elements of one mode on the basis of the other two. This is referred to as One Mode Classification (OMC) of a three-way data set and it can be seen as a synthesis of a set of hierarchical classifications, each one defined by applying a hierarchical algorithm to a two-mode matrix of the three-way data set (after standardizing variables if necessary). For example, the OMC of the units according to variables and occasions is a consensus of the set of hierarchical classifications defined by clustering the same units according to variables for each different occasion; i.e., the classification of the same multivariate units observed in different occasions. This last case will be considered in this paper.
  Many consensus methods can be used to achieve OMC of a three-way data set, however, often the set of hierarchical classifications is wide and some of these are dissimilar, hence a single synthesis, is generally not representative of the entire set. This might happen because in the observed three-way data set there are several groups of similar hierarchical classifications, i.e., formed by dendrograms that partially or completely repeat in different occasions without systematic differences. Therefore a consensus classification for each subset of similar classifications can be defined. Furthermore, when a single consensus is used for a set of classifications relative to different time situations, a loss of meaningful information on the evolution of the set of classifications is generally observed. To overcome these difficulties we propose the PRINcipal CLassifications Analysis of a three-way data set. The idea, in PRINCLA, is to find few non-observable hierarchical classifications, called principal classifications, each defined as a weighted mean hierarchical classification. No pairs of principal classifications are computed with the contribution of a same original hierarchical classification.

• Vives, M., Gargallo, R., & Tauler, R. (2001).
  Three-way multivariate curve resolution applied to speciation of acid-base and thermal unfolding transitions of an alternating polynucleotide. Biopolymers, 59, 477-488.
  Analytical speciation of acid-base equilibria and thermal unfolding transitions of an alternating random polynucleotide containing cytosine and hypoxanthine, poly(C, I). is studied. The results (ire compared with those obtained previously for single-stranded polynucleotides, poly(I) and poly(C), and for the double-stranded poly(I). poly(C), to examine the influence of the secondary structure on the acid-base properties of bases. This study is based on monitoring acid-base titrations and thermal unfolding experiments by molecular absorption, CD, and molecular fluorescence spectroscopies. Experimental data were analyzed by a novel chemometric approach based on a recently developed three-way Multivariate Curve Resolution method, which allowed the simultaneous analysis of data from several spectroscopies. This procedure improves the resolution of the concentration profiles and pure spectra for the species and conformations present in folding-unfolding and acid-base equilibria. The results from acid-base studies showed the existence of only three species in the pH range 2-12 at 37 degreesC and 0.15M ionic strength. No cooperative effects were detected front the resolved concentration profiles, showing that equilibria concerning alternating polynucleotides like poly(C, I) are simpler than those involving poly(I) . poly(C). T hermal unfolding experiments at neutral pH confirmed the existence of two transitions and one intermediate conformation. This intermediate conformation could only be detected and resolved without ambiguities when molecular absorption and CD spectral data were analyzed simultaneously.

• Vivien, M., & Sabatier, R. (2001b).
  Une extension multi-tableaux de la régression PLS. Revue Statistique Appliquée, 49, 31-54.
  In this article, an extension for the PLS method, OMCIA-PLS, is presented. It allows a "global" modelling of K data sets measured on the same n individuals. The optimization of the criterion that is proposed amounts to resolving usual PLS, but gives extra objects and help to interpretation. An example based on real data is processed.

• Vivien, M., & Sabatier, R. (2003).
  Generalized orthogonal multiple co-inertia analysis(-PLS): new multiblock component and regression methods. Journal of Chemometrics, 17, 287-3001.
  The purpose of this paper is to develop new component-wise component and regression multiblock methods that overcome some of the difficulties traditionally associated with multiblocks, such as the step-by-step optimization and component orthogonalities. Generalized orthogonal multiple co-inertia analysis (GOMCIA) and generalized orthogonal multiple co-inertia analysis-partial least squares (GOMCIA-PLS) are proposed for modelling two sets of blocks measured on the same observations. We especially emphasize GOMCIA-PLS methods in which we consider one of the sets as predictive. All these methods are based on the step-by-step maximization of the same criterion under normalization constraints and produce orthogonal components or super-components. The solutions of the problem have to be computed with an iterative algorithm (which we prove to be convergent). We also give some interesting special cases and discuss the differences compared with a few other multiblock and/or multiway methods. Finally, short examples of real data are processed to show how GOMCIA-PLS can be used and its properties.

• Vivien, M., & Sabatier, R. (2004).
  A generalization of STATIS-ACT strategy: DO-ACT for two multiblocks tables. Computational Statistics & Data Analysis, 46, 155-171.
  A new strategy is introduced for analyzing two multiblocks tables:DO-ACT.This method is closely related to the STATIS (or ACT)methodology and the Tucker inter-battery method.The length of two multiblocks are not necessarily the same and the optimal solution obtained is that of a global optimization problem.The advantage of using DO-ACT is that the rst step provides a summary of the two multiblocks tables,in the second step two optimal representations (one for each multiblock)of the observations can be plotted and in the third step a global description of each table of each multiblock can be made.An example of DO-ACT performance is illustrated with a real data set.The program implementing the method has been developed using the S-Plus 6 :0 J (2000)language.

                                   

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