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  • 1
    Electronic Resource
    Electronic Resource
    Confidence regions for INDSCAL using the jackknife and bootstrap techniques (1984)
    Springer
    Psychometrika 49 (1984), S. 475-491 
    Details
    ISSN: 1860-0980
    Keywords: Individual differences ; multidimensional scaling ; stability ; standard errors ; pseudovalues ; maximum likelihood ; resampling schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02302586
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Three-way metric unfolding via alternating weighted least squares (1985)
    Springer
    Psychometrika 50 (1985), S. 275-300 
    Details
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; unfolding ; preference analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02294106
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model (1989)
    Springer
    Psychometrika 54 (1989), S. 217-229 
    Details
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; monotone spline ; specific dimensions ; maximum likelihood estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02294516
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: constrained least-squares ; multilinear models ; bilinear models ; INDSCAL ; multidimensional scaling ; 3-mode factor analysis ; CANDECOMP ; LINCINDS ; multivariate analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02293596
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Spatial versus tree representations of proximity data (1982)
    Springer
    Psychometrika 47 (1982), S. 3-24 
    Details
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; clustering ; tree structures ; additive trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02293848
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Potential applications of three-way multidimensional scaling and related techniques to integrate knowledge from multiple experts (1990)
    Springer
    Annals of mathematics and artificial intelligence 2 (1990), S. 77-92 
    Details
    ISSN: 1573-7470
    Keywords: Expert systems ; knowledge acquisition ; multiple experts ; multidimensional scaling ; clustering ; trees ; unfolding methods ; data analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Theknowledge transfer problem in artificial intelligence consists of finding effective ways to elicit information from a human expert and represent it in a form suitable for use by an expert system. One approach to formalizing and guiding this knowledge transfer process for certain types of expert systems is to use psychometric scaling methods to analyze data on how the human expert compares or groups solutions. For example, Butler and Corter [1] obtained judgments of thesubstitutability of solutions from an expert, then analyzed the resulting data via techniques for fitting trees and extended trees [2]. The expert's interpretation of certain aspects of the solutions were directly encoded as production rules, allowing rapid prototyping. In this paper we consider the problem of combining information from multiple experts. We propose the use of three-way or “individual differences” multidimensional scaling, tree-fitting, and unfolding models to analyze two types of data obtainable from the multiple experts: judgments of the substitutability of pairs of solutions, and judgments of the appropriateness of specific solutions to specific problems. An application is described in which substitutability data were obtained from three experts and analyzed using the SINDSCAL program [3] for three-way multidimensional scaling [4].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01530998
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Spatial, non-spatial and hybrid models for scaling (1976)
    Springer
    Psychometrika 41 (1976), S. 439-463 
    Details
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; hierarchical tree structures ; clustering ; geometric models ; multivariate data analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract In this paper, hierarchical and non-hierarchical tree structures are proposed as models of similarity data. Trees are viewed as intermediate between multidimensional scaling and simple clustering. Procedures are discussed for fitting both types of trees to data. The concept of multiple tree structures shows great promise for analyzing more complex data. Hybrid models in which multiple trees and other discrete structures are combined with continuous dimensions are discussed. Examples of the use of multiple tree structures and hybrid models are given. Extensions to the analysis of individual differences are suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02296969
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    Paper (German National Licenses)
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