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  • 1
    Electronic Resource
    Electronic Resource
    A generalized solution of the orthogonal procrustes problem (1966)
    Springer
    Psychometrika 31 (1966), S. 1-10 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract A solutionT of the least-squares problemAT=B +E, givenA andB so that trace (E′E)= minimum andT′T=I is presented. It is compared with a less general solution of the same problem which was given by Green [5]. The present solution, in contrast to Green's, is applicable to matricesA andB which are of less than full column rank. Some technical suggestions for the numerical computation ofT and an illustrative example are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02289451
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fitting a simplex symmetrically (1970)
    Springer
    Psychometrika 35 (1970), S. 1-21 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract A method for fitting a perfect simplex [Guttman, 1954] is suggested which, in contrast to Kaiser's [1962], is independent of the order of the manifest variables. It is based on a procedure for scaling a set of points from their pairwise distances [Torgerson, 1958; Young & Householder, 1938] which is reviewed in compact notation in the Appendix. The method is extended to an iterative algorithm for fitting a quasi-simplex. Some empirical results are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02290590
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On metric multidimensional unfolding (1970)
    Springer
    Psychometrika 35 (1970), S. 349-366 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract The problem of locating two sets of points in a joint space, given the Euclidean distances between elements from distinct sets, is solved algebraically. For error free data the solution is exact, for fallible data it has least squares properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02310794
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Some new results on factor indeterminacy (1972)
    Springer
    Psychometrika 37 (1972), S. 61-91 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix ψ. Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02291413
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    An individual difference model for the multidimensional analysis of preference data (1972)
    Springer
    Psychometrika 37 (1972), S. 275-309 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02306784
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    An algebraic solution for a class of subjective metrics models (1972)
    Springer
    Psychometrika 37 (1972), S. 441-451 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract It is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. This solution is readily adapted to the special case treated by Bloxom, Horan, Carroll and Chang. In addition to being very simple, this algebraic solution also permits testing the constraints of these models explicitly. A numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02291220
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    The minimum average correlation between equivalent sets of uncorrelated factors (1973)
    Springer
    Psychometrika 38 (1973), S. 149-149 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02291183
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Alternative measures of fit for the Schönemann-carroll matrix fitting algorithm (1974)
    Springer
    Psychometrika 39 (1974), S. 423-427 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract In connection with a least-squares solution for fitting one matrix,A, to another,B, under optimal choice of a rigid motion and a dilation, Schönemann and Carroll suggested two measures of fit: a raw measure,e, and a refined similarity measure,e s , which is symmetric. Both measures share the weakness of depending upon the norm of the target matrix,B,e.g.,e(A,kB) ≠e(A,B) fork ≠ 1. Therefore, both measures are useless for answering questions of the type: “DoesA fitB better thanA fitsC?”. In this note two new measures of fit are suggested which do not depend upon the norms ofA andB, which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02291666
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function (1976)
    Springer
    Psychometrika 41 (1976), S. 547-550 
    Details
    ISSN: 1860-0980
    Keywords: rotation ; matching
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract This paper provides a generalization of the Procrustes problem in which the errors are weighted from the right, or the left, or both. The solution is achieved by having the orthogonality constraint on the transformation be in agreement with the norm of the least squares criterion. This general principle is discussed and illustrated by the mathematics of the weighted orthogonal Procrustes problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02296976
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Varisim: A new machine method for orthogonal rotation (1966)
    Springer
    Psychometrika 31 (1966), S. 235-248 
    Details
    ISSN: 1860-0980
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract The derivative of Kaiser's Varimax criterion, if set to zero, yields a set of equations which are quite similar to those obtained for a least-squares problem of the “Procrustes” type. This similarity suggested an iterative technique for orthogonal rotation, dubbed “Varisim,” which was programmed for the IBM 7094 in FORTRAN. An empirical comparison between Varimax and Varisim, which was based on a number of data sets taken from the literature yielded three major results so far: (i) Varisim is slower than Varimax, roughly by a factor of 3, (ii) Varisim yields factors which in general contribute more evenly to the common test variance than Varimax factors, and which (iii) line up more closely with oblique configurations obtained with Binormamin than Varimax factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02289510
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    Paper (German National Licenses)
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