A method of successive cumulations for the scaling of pair-comparison preference judgments

Greenberg, Marshall G.

doi:10.1007/bf02289533

Cited by 16 publications

(18 citation statements)

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“…He arrived at it by adding parametric assumptions to a relation between choice probabilities and interaltemative midpoints, detected by Greenberg (1965).…”

Section: Models Of the Coombs-zinnes-griggs Theorymentioning

confidence: 99%

“…In that case, all intersubjective variability in choices has to be attributed to differences in individual ideals. This is the kind of choice situation Greenberg (1965) conceived his model specification for. In this case, individual choices need not be described probabilistically, yet the location of each ideal in the joint unfolding space can be described probabilistically.…”

Section: ) Different Ideals -Individual Choices Not Randommentioning

confidence: 99%

“…Assign the remaining y to positions in the ranking isotonically with the choice proportions q^. This heuristic has been described by Greenberg (1965), who refers to a suggestion from Coombs. It works best for binary choice frequency structures generated by a probability structure that satisfies characteristic monotonicity.…”

Section: Ideal Point Conditionsmentioning

confidence: 99%

“…For characteristic monotonicity, we also use the heuristic described by Greenberg (1965) to generate the initial provisional solution, and the same additional device to cut branches as described earlier for the ideal point con ditions.…”

Section: (2) Unidimensional Unfoldingmentioning

confidence: 99%

“…However, Bechtel did not do so with the intention of defining a variation of Coombs' theory. Bechtel arrived at his model by adding parametric assumptions to a monotonie relation between choice probabilities and interaltemative midpoints, analyzed by Greenberg (1965). Because of the selection of the normal distribution for the ideal coordinate, Bechtel's model is a limiting case of Zinnes & Griggs' model.…”

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confidence: 99%

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A Comparison of Probabilistic Unfolding Theories for Paired Comparisons Data

Bossuyt

1990

Recent Research in Psychology

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“…He arrived at it by adding parametric assumptions to a relation between choice probabilities and interaltemative midpoints, detected by Greenberg (1965).…”

Section: Models Of the Coombs-zinnes-griggs Theorymentioning

confidence: 99%

Section: ) Different Ideals -Individual Choices Not Randommentioning

confidence: 99%

Section: Ideal Point Conditionsmentioning

confidence: 99%

Section: (2) Unidimensional Unfoldingmentioning

confidence: 99%

mentioning

confidence: 99%

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A Comparison of Probabilistic Unfolding Theories for Paired Comparisons Data

Bossuyt

1990

Recent Research in Psychology

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Combinatorial data analysis: Confirmatory comparisons between sets of matrices

Hubert

Arabie

1989

Appl. Stochastic Models Data Anal.

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AWhat's promised, you'll enjoy with naught subtracted, With naught unduly snipped off or exacted.-Mephistopheles (Translation by G. M. Priest, 1941) FUUS~ 1, 1416-1417 SUMMARYThe task of assessing the similarity of pattern between the entries of two square matrices has been discussed extensively over the last decade, as a unifying strategy for approaching a variety of seemingly disparate statistical problems. As typically defined, the comparison depends on a measure of matrix correspondence, usually a normalized cross-product measure of some form, that is evaluated for relative size by the use of a reference distribution constructed through an equally likely permutation hypothesis defined at the level of the objects corresponding to the rows and columns of the two matrices. The extreme generality provided by this very simple framework subsumes a variety of different statistical problems, ranging from the study of spatial autocorrelation for variables observed over a set of geographic locations,to the topics of analysis of variance, the measurement of rank correlation, and confirmation techniques concerned with various conjectures of combinatorial structure that might be posited for an empirically determined measure of relationship between pairs of a given set of objects. The comparison strategies extant always assume that both matrices are fixed, and in those cases where one of the matrices codifies a given theoretical structure to be evaluated according to a second, this assumption can lead to substantial arbitrariness in how matrix similarity might be indexed, and thus, in how the comparison is implemented.As developed in this paper, exactly the same principles appropriate for use in the fixed comparison context can be extended to include matrices constructed through optimally weighted linear combinations of other sets of matrices. This generalization provides one mechanism for developing comparison strategies that allow assessment against very broad classes of matrices, which in turn serve to represent very general conjectures of possible combinatorial structure. This paper reviews some of these extensions in detail, with a particular emphasis on categorical and ordered categorical variables and whether they may reflect an empirically generated measure of object relationship.

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A Probabilistic Feature Model for Unfolding Tested for Perfect and Imperfect Nestings

Candel¹

1997

Journal of Mathematical Psychology

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A method of successive cumulations for the scaling of pair-comparison preference judgments

Cited by 16 publications

References 4 publications

A Comparison of Probabilistic Unfolding Theories for Paired Comparisons Data

A Comparison of Probabilistic Unfolding Theories for Paired Comparisons Data

Combinatorial data analysis: Confirmatory comparisons between sets of matrices

A Probabilistic Feature Model for Unfolding Tested for Perfect and Imperfect Nestings

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