A scalar product model for the multidimensional scaling of choice

Bechtel, Gordon G.; Tucker, Ledyard R.; Chang, Wei-Ching

doi:10.1007/bf02291364

Cited by 29 publications

(11 citation statements)

References 11 publications

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“…This matrix with homogeneous column variances was column-centered and analyzed by UVA and PCA. Such procedures, in which persons are treated as variables and represented as vectors, are often used in psychometric preference studies (Bechel et al 1971;Tucker 1960). In UVA, the solution was given by L = 5 starts.…”

Section: Journal Preference Data With Homogeneous Variancesmentioning

confidence: 99%

Constrained principal component analysis of standardized data for biplots with unit-length variable vectors

Adachi

2010

Adv Data Anal Classif

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Section: Journal Preference Data With Homogeneous Variancesmentioning

confidence: 99%

Constrained principal component analysis of standardized data for biplots with unit-length variable vectors

Adachi

2010

Adv Data Anal Classif

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“…Although MDS profile analysis has not been used widely, the model discussed in this paper is not new. Bechtel, Tucker, and Chang (1971), Davison (1994), Davison and Skay (1991), and Tucker (1960) call it the “vector” model. Benzecri (1969), Greenacre (1984), and Weller and Romney (1990) call it the “correspondence analysis” model.…”

Section: Predicting Psychological Well‐being From the Model‐derived Pmentioning

confidence: 99%

Multidimensional scaling modelling approach to latent profile analysis in psychological research

Ding

2006

Int J Psychol

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B ecause profile analysis is widely used in studying types of people, we propose an alternative technique for such analysis in this article. As an application of the multidimensional scaling (MDS) model, MDS profile analysis is proposed as an approach for studying both group and/or individual profile patterns. This approach requires one to think of MDS solutions as profiles. The MDS profile analysis approach re-parameterizes the linear latent variable model in such a way that the latent variables can be interpreted in terms of profile patterns rather than factors. It is an exploratory profile analysis method to identify major patterns among psychological variables and can serve as the basis for further study of correlates and/or predictors of profiles and other background and external variables. In the article, we have outlined the procedure of MDS profile analysis and discussed the issues that are related to parameter estimation and interpretation of the results. Such a discussion is presented in the context of studying psychosocial adjustment of adolescents in the US. The results of MDS profile analysis indicated that two psychosocial profiles could be derived from the data. Profile 1 represents a prototypical adolescent with high scores on Body Image and low scores on the Vocational-Educational (Voc-Ed) Goal scale. Profile 2 represents a prototypical adolescent with high scores on the Peer Relationships scale and low scores on the Family Relationships scale. These profiles suggested several types of adolescents with different psychosocial adjustment orientations, which may be linked to different subgroups of adolescents in the population. In addition, these profiles are also associated with the outcomes of mental health, which implies profiles' potential utility when studying relationships among different variables. Finally, this article discusses some advantages and disadvantages of this approach in psychological research.

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“…(The iso-utility contours in two dimensions therefore are parallel straight lines perpendicular to a subject's vector.) Work by Bechtel, Tucker, and Chang (1971), Cooper and Nakanishi (1983), Carroll (1980), De Soete and Carroll (1983), and DeSarbo, Oliver, and De Soete (1986 present alternative probabilistic vector MDS models that operate on such paired comparisons data.…”

Section: Introductionmentioning

confidence: 99%

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

1991

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A scalar product model for the multidimensional scaling of choice

Cited by 29 publications

References 11 publications

Constrained principal component analysis of standardized data for biplots with unit-length variable vectors

Constrained principal component analysis of standardized data for biplots with unit-length variable vectors

Multidimensional scaling modelling approach to latent profile analysis in psychological research

A stochastic multidimensional scaling procedure for the empirical determination of convex indifference curves for preference/choice analysis

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