# Multidimensional Scaling

Multidimensional scaling attempts to find the structure in a set of distance measures between objects or cases. This task is accomplished by assigning observations to specific locations in a conceptual space (usually two- or three-dimensional) such that the distances between points in the space match the given dissimilarities as closely as possible. In many cases, the dimensions of this conceptual space can be interpreted and used to further understand your data.

If you have objectively measured variables, you can use multidimensional scaling as a data reduction technique (the Multidimensional Scaling procedure will compute distances from multivariate data for you, if necessary). Multidimensional scaling can also be applied to subjective ratings of dissimilarity between objects or concepts. Additionally, the Multidimensional Scaling procedure can handle dissimilarity data from multiple sources, as you might have with multiple raters or questionnaire respondents.

**Example.** How do people perceive relationships between different
cars? If you have data from respondents indicating similarity ratings
between different makes and models of cars, multidimensional scaling
can be used to identify dimensions that describe consumers' perceptions.
You might find, for example, that the price and size of a vehicle
define a two-dimensional space, which accounts for the similarities
that are reported by your respondents.

**Statistics.** For each model: data matrix, optimally scaled
data matrix, S-stress (Young's), stress (Kruskal's), RSQ, stimulus
coordinates, average stress and RSQ for each stimulus (RMDS models).
For individual difference (INDSCAL) models: subject weights and weirdness
index for each subject. For each matrix in replicated multidimensional
scaling models: stress and RSQ for each stimulus. Plots: stimulus
coordinates (two- or three-dimensional), scatterplot of disparities
versus distances.

Multidimensional Scaling Data Considerations

**Data.** If your data are dissimilarity data, all dissimilarities
should be quantitative and should be measured in the same metric.
If your data are multivariate data, variables can be quantitative,
binary, or count data. Scaling of variables is an important issue--differences
in scaling may affect your solution. If your variables have large
differences in scaling (for example, one variable is measured in dollars
and the other variable is measured in years), consider standardizing
them (this process can be done automatically by the Multidimensional
Scaling procedure).

**Assumptions.** The Multidimensional Scaling procedure is
relatively free of distributional assumptions. Be sure to select the
appropriate measurement level (ordinal, interval, or ratio) in the
Multidimensional Scaling Options dialog box so that the results are
computed correctly.

**Related procedures.** If your goal is data reduction, an
alternative method to consider is factor analysis, particularly if
your variables are quantitative. If you want to identify groups of
similar cases, consider supplementing your multidimensional scaling
analysis with a hierarchical or *k*-means cluster analysis.

To Obtain a Multidimensional Scaling Analysis

This feature requires the Statistics Base option.

- From the menus choose:
- Select at least four numeric variables for analysis.
- In the Distances group, select either Data are distances or Create distances from data.
- If you select Create distances from data, you can also select a grouping variable for individual matrices. The grouping variable can be numeric or string.

Optionally, you can also:

- Specify the shape of the distance matrix when data are distances.
- Specify the distance measure to use when creating distances from data.

This procedure pastes ALSCAL command syntax.