User Guide

Chapter
38
Multidimens
ional Scaling
Multidimensional scaling attempts to find the structure in a set of distance measures
between obj
ects or cases. This 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
techniqu
e (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
Multidi
mensional 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 fro
m 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
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
multi
dimensional scaling models: stress and RSQ for each stimulus. Plots: stimulus
coordinates (two- or three-dimensional), scatterplot of disparities versus distances.
Data. If your data are dissimilarity data, all dissimilarities should be quantitative and
shoul
d 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
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