# 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

This feature requires the Categories option.

- From the menus choose:
- Select two or more variables that identify the columns in the rectangular proximity matrix. Each variable represents a separate column object.
- Optionally, select a number of weights variables equal to the number of column object variables. The order of the weights variables should match the order of the column objects they weight.
- Optionally, select a rows variable. The values (or value labels) of this variable are used to label row objects in the output.
- If there are multiple sources, optionally select a sources variable. The number of cases in the data file should equal the number of row objects times the number of sources.

Additionally, you can define a model for the multidimensional unfolding, place restrictions on the common space, set convergence criteria, specify the initial configuration to be used, and choose plots and output.

This procedure pastes PREFSCAL command syntax.