Three-mode Factor Analysis Research Articles

The Structure of Affect and Trait Judgments of Political Figures.

The roles of affective and cognitive processes in judgment have been the focus of much recent research and theoretical debate. This study was designed to investigate the structure of voters' affective reactions and trait attributions to national political figures. Three-mode factor analysis was used to determine the structure of the affect and trait scales. Politician factors and subject types were also derived, as were the interrelationships among these modes. Positive and negative affect factors, and affect and trait factors, were distinct but correlated; Democratic and Republican politician factors were uncorrelated. Information on the subject types moderated these relationships.

Addressing Temporal Change in Strategic Groups Analysis: A Three-Mode Factor Analysis Approach

This paper focuses upon the issue of considering temporal changes in strategy as well as temporal variations in the importance of strategic criterion variables when analyzing the strategic group structure within industries. Three-mode factor analysis is proposed as a procedure to allow such joint considerations. The usefulness of this procedure is further demonstrated through an example set in the computer industry.

Competitive Maps: The Structure Underlying Asymmetric Cross Elasticities

A special case of three-mode factor analysis is used to portray the systematic structure underlying asymmetric cross elasticities for a broad class of market-share attraction models. Analysis of the variation over retail outlets and weeks reveals competitive patterns corresponding to sales for the major brands in the market as well as patterns reflecting shelf-price competition. Analysis of the brand domain results in a joint space. One set of brand positions portrays how brands exert influence over the competition. The other set of points portrays how brands are influenced by others. The interset distances (angles) provide direct measures of competitive pressures. Maps are formed as spatial representations of each of the competitive patterns discovered.

Structure of the organizational image based on the quasi three-mode factor analysis

In order to identify the basic dimensions of the image of organizations, a quasi threemode factor analysis (exactly, a quasi three-mode principal component analysis) was used. Subjects (691 university students) were asked to rate five organizations on the 21 seven-point adjective pairs. Three factors were extracted from this analysis: likeability, dependability, flashiness. Some interesting points were derived from examinations on the core matrices and the factor-score correlation matrix obtained from the quasi threemode factor analysis. On the likeability dimension, each organization was rated independently. However, on dependability and flashiness dimensions, it was found that the higher the dependability for some organizations, the more flashy they become, but for the other organizations, the relationship is just the opposite.

Simultaneous description of the influence of solvent, reaction type, and substituent on equilibrium constants by means of three-mode factor analysis

The equations, proposed by Hammett, Taft, and Nieuwdorp et al., respectively, for the simultaneous description of the influence of reaction type and substituent on equilibrium and reaction rate constants are discussed. The latter equation represents an example of factor analysis. This mathematical–statistical technique has also been applied to describe simultaneously the influence of solvent and substituent and the influence of solvent and reaction type. It is thus a logical step to classify equilibrium and reaction rate constants with respect to three modes, solvent, reaction type, and substituent, and to try to describe the influence of these three variables by three-mode factor analysis. Two examples of the application of this technique to literature data are given. The first concerns data on ionization constants for 15 series of substituted compounds in three solvents. The second example concerns data on phase equilibrium constants of six series of substituted compounds in nine two-phase systems. The two-phase systems comprise gas–liquid as well as liquid–liquid and solid–liquid systems. The precision of the fit of the observations and the precision of the prediction of the missing data are discussed. In the first example 237 data are missing. Among them are 90 data that cannot be predicted at all by the Hammett, Taft, or Nieuwdorp equations (viz., for reactions on which no measurements at all are available in a particular solvent). The standard deviation of the prediction of the latter data by three-mode factor analysis ranges from 0.1 to 0.2. In the second example nearly all missing data are for reactions on which no measurements at all are available in a particular solvent. They can be predicted by three-mode factor analysis with a standard deviation that ranges from 0.09 to 0.13. Further, it is shown that the number of parameters that is required to fit the observations by three-mode factor analysis is far less than the number of parameters in the corresponding regression analysis model, viz., the Taft model.

建築の形象での図像性に関する研究 : 第3報 住宅外形における類

In reports one and two, studies were carried out on different levels concerning the iconology of house facades seeking to classify them into different groups. In this report, the focus will be on the similarity between groups derived by looking at two different aspects of the same subject sample in order to find the main types of groups these house facades fall into. This was achieved by performing a three-mode factor analysis on both the nine perceptual scales used in report one, and the four categories in report two. The building groupings were established by changing the number of factors (variables). As a result, it was found that the buildings under investigation could be divided into seven groups, which were included in both the nine scales and the four categories. In addition, it was found that these seven building groups showed similarities to the types derived in reports one and two. In other words, similarity between building groups not categorized in reports one and two was discovered. As a result of the three-mode factor analysis, these buildings were shown to form a group which suggests another factor. Combining the results so far in this report, seven groups of house facades have been found. Finally, the basic character and image of each group was clarified by arranging the phenomena occurring in the sum of the nine scales and four categories of the seven types, and giving them a possible societal interpretation.

The Perception of Crowding in Interpersonal Situations

Recent research on crowding has not always separated the situational from the affective and behavioral components of this construct. The present study represents an attempt to distinguish among these components, and to explore the dimensions underlying the perception of crowded interpersonal situations and the behavioral and affective responses to such situations. Likelihood judgments of responses to crowded situations were subjected to three-mode factor analysis. The dimensionality of the components, as well as the interrelationships among them, are discussed in detail, and behavior patterns particularly appropriate or likely in different situational contexts are identified.

Three-mode factor analysis of data on retention in normal-phase high-performance liquid chromatography

It is shown that the Snyder equation is not quite satisfactory for fitting retention data in normal-phase high-performance liquid chromatography (HPLC) on chemically bonded phases. This equation is a special case of the mathematical—statistical three-mode factor analysis model. This model, in its general form, has been used to fit two sets of literature data on the retention in normal-phase HPLC for 19 solutes on six adsorbents with two eluents, and for 39 solutes on three adsorbents with two eluents, respectively. This study represents the first application of three mode factor analysis with missing data, and also the first application of three-mode factor analysis in the field of the natural sciences. The accuracy of the fit of the observations and of the prediction of the missing data, for various numbers of extracted factors, is discussed.

Quasi Three-Mode Principal Component Analysis — A Method for Assessing the Factor Change —

This paper describes an exploratory procedure for assessing the factor change, quasi three-mode factor analysis, which is applicable to longitudinal or multitrait-multimethod data. The model is a simplified case of Tucker’s three-mode factor analysis, and formally equivalent to Kroonenberg and de Leeuw’s Tucker 2 model. That is, it intends to decompose the standardized data matrix for each occasion into the product of three matrices, namely, the factor score matrix, the core matrix, and the factor loading matrix. It is illustrated that the patterns to which core matrices conform can distinguish the change of factor loadings from the change of factor scores. A practical least squares algorithm for the model is formulated, and a way of scalings of parameters which facilitates the interpretation of the results and the comparison with the output of other factor analytic methods is discussed. Analysis of a multitrait-multimethod matrix is attached as a numerical example.

The COMSTAT algorithm for multimodal factor analysis: an improvement of Tucker's three-mode factor analysis method.

Three-mode factor analysis, as developed by Tucker in 1966, is a method for nonredundant representation of data arrays with three subscripts (e.g. observations classified according to persons by variables by conditions). Tucker , however, did not succeed in obtaining a least-squares solution for his model. We derive in this paper a necessary condition for a least-squares solution and construct an algorithm which improves any given initial solution in the least-squares sense. We show that this algorithm converges to a representation satisfying the necessary conditions for a least-squares solution. The method is in no way restricted to three dimensions, but can be applied to any multimodal data array.

Example for applying the COMSTAT multimodal factor analysis algorithm to EEG data to describe variance sources.

An example is given for the application of the COMSTAT algorithm for multimodal factor analysis to EEG power spectral data. The COMSTAT algorithm enlarges Tucker 's three-mode factor analysis to a multimodal one, and improves his algorithm by a least squares solution. The EEG power spectral data from 65 healthy subjects with an occipital rhythm between 8 and 12 Hz were taken. For demonstration purposes we selected three modes, which have been used by other authors: mode 1: 29 frequency classes, 1n of relative power, in delta f = 1.0-Hz steps between 1 and 30 Hz; mode 2: 16 segments, 40 s each, during the two situational vigilance conditions reaction time (RT) and resting (RS), and mode 3: 65 persons. The frequency mode could be described sufficiently by five factors which we called: delta F/alpha F1; nu F/alpha F2; beta F1/alpha F1; beta F2; beta F3. The factor-loading profiles were similar to those described earlier in independent data. Thus, in the three-mode model we obtained results comparable to those of two-mode models. In the level of 16 situational segments only two factors were extractable. They described the two situations RT, higher vigilance level, and RS, lower vigilance level. In order to demonstrate the changes in factor structure, if a two-mode model is enlarged by a third mode, we used two models for the description of personal (P) variance. When the matrix persons X segments (P X V) was taken, only two factors were extractable.(ABSTRACT TRUNCATED AT 250 WORDS)

Application of the Three-mode Factor Analysis to Industrial Design of Chair Styles

Application of the Three-mode Factor Analysis to Industrial Design of Chair Styles

Individual differences in conceptual behaviour following manipulated controllability

Expectations of controllability are thought to influence subsequent behaviour, such that perceived non-contingency between behaviour and outcomes can produce a “learned helplessness” reaction by the organism. Since cognitive processes are implicated in this debilitation, the present study examines the influence of manipulated controllability upon the intrinsic individual differences (among females) in a disjunctive conceptual behaviour recovery task. Three-mode factor analysis is used to explore the process variability in a multivariate time-series design. Results indicate that intrinsic task processes are altered by the controllability pretreatment, but the nature of the impact reflects substantial individual differences in reaction.

The Structure Of Self-Reported Difficulty In Assertiveness: An Application Of Three-Mode Common Factor Analysis.

The Difficulty in Assertiveness Inventory (DAI) was developed, based on a two-facet model of assertiveness for item specification -- referents (interpersonal contexts or partners) x response classes (types of assertive behavior). Data from two samples of female university students were subjected to three-mode factor analysis. Two referent, two response class, and five individual differences factors were extracted. The proportion of variance accounted for by each factor matched across solutions. The patterns of factor loadings indicated that the two referent factors (distant and close), the two response class factors (positive and negative), and four of the five individual differences factors (labeled Assertiveness A, B, C, and D) were stable across subject samples. Solutions for the individual differences factor matrix and the counter-rotated and transformed core matrix were reciprocally beneficial to interpretation of the structure of the data. Correlations of DAI subscales with the Marlowe-Crowne Social Desirability Scale were not significantly different from zero. The potential uses of the instrument in applied research and in the clinical setting were discussed.

Three-Mode Common Factor Analysis: Procedure And Computer Programs.

As psychologists increasingly recognize the limitations of single-occasion, single-measure research designs and employ more elaborate and comprehensive data collection schemes, sophisticated analytic techniques will play an ever more important role in understanding behavioral data. This paper outlines one such promising technique, Tucker's three-mode factor analysis, which enables the researcher to explore new taxonomic structures in three-way designs. The procedure is described in step-by-step format, which should be easy to follow for anyone familiar with traditional two-mode factor analysis. Appropriate computer programs are available to interface with the widely used SPSS package to calculate Tucker's common factor model.

Three-mode factor analysis of self-reported difficulty in assertiveness

Self-reported difficulties, in terms of assertive response classes and referent individuals, were analysed across university student and hospital worker female samples. A modified three-mode common factor analysis model was used to provide information on generalizable (or “idealized”) individual differences, assertive behaviours, and referents, plus an interactional core bounded by these idealized dimensions. Similar two-dimensional structures were noted for assertive response classes and referents in both samples. The two response class factors were labelled positive and negative assertiveness; the two referent factors were labelled close and distant referents. Sizable variations in individual differences patterns and different interactional core solutions somewhat nullified the precision and utility of these nomothetic behavioural and referent categories. It was concluded that the Difficulty in Assertiveness Inventory (DAI) and, by implication, other self-report inventories can be used for wideband individual or group assessments, but would probably not be appropriate for individualized therapeutic programme evaluations.

Identifying Interindividual Judgment Differences: Indscal Or Three-Mode Factor Analysis?

Seventy subjects judged 9 key-politicians of the German parliamentary scene on 22 bipolar seven-point attribute scales. Profile similarities were computed for each possible stimulus pair separately for each individual. The resulting proximity matrices were analyzed with "INDSCAL." Additionally, three-mode factor analysis was applied to the original three-way data matrix. The results of the two methods are compared. Special attention is given to the problem of how interindividual judgment differences are reflected by the individual parameters of the two models; these are the INDSCAL-weights and the factor scores of an extended core matrix. The results suggest that three-mode factor analysis is more suitable, if interindividual judgment differences are to be described by means of a spatial model.

Interrelations Among Models For The Analysis Of Moment Structures.

Factor analysis in several populations, covariance structure models, three-mode factor analysis, structural equation systems with measurement model, and analysis of covariance with measurement model are all shown to be specializations of a general moment structure model published previously in this journal. Some new structured linear models are also described; they may be considered either generalizations or special cases of existing models. Simple representations are developed for complex linear models, and some applications to behavioral data are cited.

Affection and Evaluation as Logical Processes of Meaningfulness Independent of Associative Frequency

Summary The concept of Reinforcement Value (RV) has been used by logical learning theory as the methodological equivalent of affection. Osgood's Evaluation (E) dimension shares methodological similarities with RV which Potency (P) and Activity (A) do not. Two experiments were conducted which tested the proposition that RV and E are related if not identical methodological constructs. The first experiment (N = 43 male and female undergraduates) employed a three-mode factor analysis of ratings made of various verbal items. Both RV and E ratings loaded on the same factor, in contrast to various frequency ratings of meaningfulness. The second study (N = 64 male and female high school students) tested the influence of ratings for RV, E, P, and A on retention of trigrams in a free-recall task. Both RV and E were found to influence recall, but P and A did not. The findings are discussed in light of the incompatibility between Osgoodian associationistic theory and the nonfrequency nature of E. Logical learning the...

THREE-MODE: A FORTRAN IV program for three-mode factor analysis

Data from social science research may frequentlybe classified and cross-classified in a variety of ways.Traditionally, factor analysis has been defined in termsof two modes of classification, variables and subjects.Its use for multiple classification data beyond twomodes typically involves summation methods thatignore the effects beyond the two modes being analyzed.Tucker (1964, 1966) has extended the factor-analyticmodel to allow the investigation of relations in dataclassified in three or more ways. The Tucker approachnot only uses all the sources of variance in data butalso specifies the relations between the factors ofeachof the modes, analogous to the interaction effectsfound in analysis of variance. One example ofa three­mode classification of data is the now familiar personsby situations by responses paradigm found in interac­tional psychology. Indeed, researchers in this field haverecognized the potential of three-mode factor analysisfor investigating the systematic nature of person­situation interaction (Golding, 1975), but they havelacked a suitable computational tool for accomplishingthis analysis. The program described here was designedto meet this need, although its range is restricted todata sets defined in two or three modes.The essence of Tucker's (1964, 1966) model isthat a data matrix can be described as the productof the factor loading matrices ofeach mode ofclassifi­cation and the matrix of weights relating the factorsof each mode (the core matrix). To date, one of theprincipal problems in implementing procedures tosolve for these matrices has been the difficulty offactoring a very large matrix (as is usually the casefor the subjects mode). Tucker (1966) suggestedprocedures to avoid this problem, but each of themhad the drawback that the loadings for the subjectson factors could not be estimated. The advent ofvirtualstorage capabilities on many large computers hasalleviated this factoring difficulty to some extent, andthe present program takes advantage of this develop­ment.The program follows Method 1, as described byTucker (1966), but differs in that the calculation ofCopyright