A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data

MacKay, David B.; Zinnes, Joseph L.

doi:10.1287/mksc.5.4.325

Cited by 63 publications

(33 citation statements)

References 28 publications

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“…Market analysis, in this context, involves understanding customers' perceptions, analyzing the nature of competition, and identifying market opportunities. An increasingly sophisticated number of algorithms for analyzing proximity data with the use of both spatial and tree-based techniques have emerged over the years to handle problems ranging from individual differences, to asymmetric data, to uncertainty (DeSarbo, Johnson, Manrai, Manrai, & Edwards 1992;DeSarbo & Rao, 1984;MacKay & Zinnes, 1986). There are also hybrid techniques, which simultaneously represent proximities with the use of both types of structures (Carroll, 1976;Shepard, 1980).…”

Section: Spatial and Tree-based Similarity Scalingmentioning

confidence: 99%

On the perceived usefulness of scaling techniques in market analysis

Johnson

Hudson

1996

Psychol. Mark.

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This study examines the perceived usefulness of alternative spatial and tree-based similarity scaling techniques in a market analysis task. These techniques are typically evaluated on their ability to fit or explain customer input data. The psychological reaction of individuals who use these techniques to analyze markets has been largely ignored. The study reveals that spatial representations are perceived as more useful than tree-based clustering techniques, even though the latter provide a better fit to customer perceptions. The results have implications for both the use and development of scaling techniques in psychology and marketing.

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Section: Spatial and Tree-based Similarity Scalingmentioning

confidence: 99%

On the perceived usefulness of scaling techniques in market analysis

Johnson

Hudson

1996

Psychol. Mark.

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“…Theoretical and empirical comparisons of probabilistic MDS models have shown that they provide results that are often equal or better than those of deterministic MDS models (MacKay 1983; MacKay andZinnes 1981, 1986).…”

Section: Spatial Variation Estimation In Geography and Surveyingmentioning

confidence: 99%

“…In the spatial behavior literature, cognitive maps have been estimated using a variety of methods which include sketch maps (Buttenfield 1986;Lynch 1960;Wood and Beck 1989), direct numerical estimation of coordinates (MacKay and Zinnes 1981;Muller 1985), MDS (Golledge 1978;MacKay and Zinnes 19811, map boards (Richardson 1981;Sherman, Croxton, and Giovanatto 19791, and point estimation on a CRT or digitizer (Baird 1979;Lloyd 1989).…”

Section: Spatial Variation Estimation In Geography and Surveyingmentioning

confidence: 99%

Dimensional Variation Estimation: A Methodological Comparison

MacKay

1991

Geographical Analysis

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Estimation of the dimensional variation of points from data on the distances between pairs of points is a task commn to several disciplines, disciplines which include behavioral geography, surveying and cartography. Three methods for estimating dimensional variation are described and compared using an experiment involving simulated data and using empirical data from two studies, one based on distance judgments and the other based on direct coordinate judgments. The methods are shown to have different mathematical properties and to result in very different estimates.The spatial behavior literature in geography, the positional error analysis in surveying, and the multidimensional scaling (MDS) literature in psychology have all developed procedures for estimating the dimensional variation about points in a multidimensional space from distances between pairs of points. All three methods start with a set of interpoint distance judgments or measurements. All three methods end up with estimates of the location and dimensional variation of the points. All three methods are quite different in their approach, and, their accuracy.

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“…Maximum likelihood MDS methods have been developed by Ramsay (1982), Takane (1982), MacKay (1989) and MacKay and Zinnes (1986), among others. Least squares MDS methods have been proposed by DeLeeuw and Heiser (1982), Heiser and Groenen (1997), Groenen (1993), and Groenen, Mathar, and Heiser (1995) among others.…”

Section: Introductionmentioning

confidence: 99%

Model-Based Clustering With Dissimilarities: A Bayesian Approach

Raftery

2007

Journal of Computational and Graphical Statistics

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A Bayesian model-based clustering method is proposed for clustering objects on the basis of dissimilarites. This combines two basic ideas. The first is that the objects have latent positions in a Euclidean space, and that the observed dissimilarities are measurements of the Euclidean distances with error. The second idea is that the latent positions are generated from a mixture of multivariate normal distributions, each one corresponding to a cluster. We estimate the resulting model in a Bayesian way using Markov chain Monte Carlo. The method carries out multidimensional scaling and model-based clustering simultaneously, and yields good object configurations and good clustering results with reasonable measures of clustering uncertainties. In the examples we study, the clustering results based on low-dimensional configurations were almost as good as those based on high-dimensional ones. Thus, the method can be used as a tool for dimension reduction when clustering high-dimensional objects, which may be useful especially for visual inspection of clusters.We also propose a Bayesian criterion for choosing the dimension of the object configuration and the number of clusters simultaneously. This is easy to compute and works reasonably well in simulations and real examples.

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A Probabilistic Model for the Multidimensional Scaling of Proximity and Preference Data

Cited by 63 publications

References 28 publications

On the perceived usefulness of scaling techniques in market analysis

On the perceived usefulness of scaling techniques in market analysis

Dimensional Variation Estimation: A Methodological Comparison

Model-Based Clustering With Dissimilarities: A Bayesian Approach

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