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  • 1
    Digitale Medien
    Digitale Medien
    A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model (1989)
    Springer
    Psychometrika 54 (1989), S. 217-229 
    Details
    ISSN: 1860-0980
    Schlagwort(e): multidimensional scaling ; monotone spline ; specific dimensions ; maximum likelihood estimation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the “standard” (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.) We further assume that δ ij =F(d ij ) +e ij where δ ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d ij is the extended Euclidean distance defined above, whilee ij is an error term assumed i.i.d.N(0, σ2).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions. This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02294516
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  • 2
    Digitale Medien
    Digitale Medien
    Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters (1980)
    Springer
    Psychometrika 45 (1980), S. 3-24 
    Details
    ISSN: 1860-0980
    Schlagwort(e): constrained least-squares ; multilinear models ; bilinear models ; INDSCAL ; multidimensional scaling ; 3-mode factor analysis ; CANDECOMP ; LINCINDS ; multivariate analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract Very general multilinear models, called CANDELINC, and a practical least-squares fitting procedure, also called CANDELINC, are described for data consisting of a many-way array. The models incorporate the possibility of general linear constraints, which turn out to have substantial practical value in some applications, by permitting better prediction and understanding. Description of the model, and proof of a theorem which greatly simplifies the least-squares fitting process, is given first for the case involving two-way data and a bilinear model. Model and proof are then extended to the case ofN-way data and anN-linear model for generalN. The caseN = 3 covers many significant applications. Two applications are described: one of two-way CANDELINC, and the other of CANDELINC used as a constrained version of INDSCAL. Possible additional applications are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02293596
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  • 3
    Digitale Medien
    Digitale Medien
    Spatial versus tree representations of proximity data (1982)
    Springer
    Psychometrika 47 (1982), S. 3-24 
    Details
    ISSN: 1860-0980
    Schlagwort(e): multidimensional scaling ; clustering ; tree structures ; additive trees
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract In this paper we investigated two of the most common representations of proximities, two-dimensional euclidean planes and additive trees. Our purpose was to develop guidelines for comparing these representations, and to discover properties that could help diagnose which representation is more appropriate for a given set of data. In a simulation study, artificial data generated either by a plane or by a tree were scaled using procedures for fitting either a plane (KYST) or a tree (ADDTREE). As expected, the appropriate model fit the data better than the inappropriate model for all noise levels. Furthermore, the two models were roughly comparable: for all noise levels, KYST accounted for plane data about as well as ADDTREE accounted for tree data. Two properties of the data proved useful in distinguishing between the models: the skewness of the distribution of distances, and the proportion of elongated triangles, which measures departures from the ultrametric inequality, Applications of KYST and ADDTREE to some twenty sets of real data, collected by other investigators, showed that most of these data could be classified clearly as favoring either a tree or a two-dimensional representation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02293848
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  • 4
    Digitale Medien
    Digitale Medien
    Confidence regions for INDSCAL using the jackknife and bootstrap techniques (1984)
    Springer
    Psychometrika 49 (1984), S. 475-491 
    Details
    ISSN: 1860-0980
    Schlagwort(e): Individual differences ; multidimensional scaling ; stability ; standard errors ; pseudovalues ; maximum likelihood ; resampling schemes
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract Bootstrap and jackknife techniques are used to estimate ellipsoidal confidence regions of group stimulus points derived from INDSCAL. The validity of these estimates is assessed through Monte Carlo analysis. Asymptotic estimates of confidence regions based on a MULTISCALE solution are also evaluated. Our findings suggest that the bootstrap and jackknife techniques may be used to provide statements regarding the accuracy of the relative locations of points in space. Our findings also suggest that MULTISCALE asymptotic estimates of confidence regions based on small samples provide an optimistic view of the actual statistical reliability of the solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02302586
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  • 5
    Digitale Medien
    Digitale Medien
    Three-way metric unfolding via alternating weighted least squares (1985)
    Springer
    Psychometrika 50 (1985), S. 275-300 
    Details
    ISSN: 1860-0980
    Schlagwort(e): multidimensional scaling ; unfolding ; preference analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Psychologie
    Notizen: Abstract Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02294106
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