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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of classification 12 (1995), S. 57-71 
    ISSN: 1432-1343
    Keywords: Weighted Euclidean model ; INDSCAL ; Multidimensional scaling ; Specificities ; Monotone splines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The INDSCAL individual differences scaling model is extended by assuming dimensions specific to each stimulus or other object, as well as dimensions common to all stimuli or objects. An “alternating maximum likelihood” procedure is used to seek maximum likelihood estimates of all parameters of this EXSCAL (Extended INDSCAL) model, including parameters of monotone splines assumed in a “quasi-nonmetric” approach. The rationale for and numerical details of this approach are described and discussed, and the resulting EXSCAL method is illustrated on some data on perception of musical timbres.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of classification 6 (1989), S. 105-119 
    ISSN: 1432-1343
    Keywords: Individual differences ; Multidimensional scaling ; Rational starting configuration ; INDSCAL
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Five different methods for obtaining a rational initial estimate of the stimulus space in the INDSCAL model were compared using the SINDSCAL program for fitting INDSCAL. The effect of the number of stimuli, the number of subjects, the dimensionality, and the amount of error on the quality and efficiency of the final SINDSCAL solution were investigated in a Monte Carlo study. We found that the quality of the final solution was not affected by the choice of the initialization method, suggesting that SINDSCAL finds a global optimum regardless of the initialization method used. The most efficient procedures were the methods proposed by by de Leeuw and Pruzansky (1978) and by Flury and Gautschi (1986) for the simultaneous diagonalization of several positive definite symmetric matrices, and a method based on linearly constraining the stimulus space using the CANDELINC approach developed by Carroll, Pruzansky, and Kruskal (1980).
    Type of Medium: Electronic Resource
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  • 3
    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
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