# Multidimensional Unfolding (PREFSCAL)

The Multidimensional Unfolding procedure attempts to find a common quantitative scale that allows you to visually examine the relationships between two sets of objects.

Examples. You have asked 21 individuals to rank 15 breakfast items in order of preference, 1 to 15. Using Multidimensional Unfolding, you can determine that the individuals discriminate between breakfast items in two primary ways: between soft and hard breads, and between fattening and non-fattening items.

Alternatively, you have asked a group of drivers to rate 26 models of cars on 10 attributes on a 6-point scale ranging from 1="not true at all" to 6="very true." Averaged over individuals, the values are taken as similarities. Using Multidimensional Unfolding, you find clusterings of similar models and the attributes with which they are most closely associated.

Statistics and plots. The Multidimensional Unfolding procedure can produce an iteration history, stress measures, stress decomposition, coordinates of the common space, object distances within the final configuration, individual space weights, individual spaces, transformed proximities, stress plots, common space scatterplots, individual space weight scatterplots, individual spaces scatterplots, transformation plots, and Shepard residual plots.

Multidimensional Unfolding Data Considerations

Data. Data are supplied in the form of rectangular proximity matrices. Each column is considered a separate column object. Each row of a proximity matrix is considered a separate row object. When there are multiple sources of proximities, the matrices are stacked.

Assumptions. At least two variables must be specified. The number of dimensions in the solution may not exceed the number of objects minus one. If only one source is specified, all models are equivalent to the identity model; therefore, the analysis defaults to the identity model.

To Obtain a Multidimensional Unfolding

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