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3.3.1
Identifying the Different Views
In identifying the different views that an individual might hold, one tries to model
the individual's perceptions in one or more non-trivial K-dimensional models, each
explaining adequately a part of his/her attribute judgments. Individual views should
provide close matches between the measured and the modeled attributes that are
associated with that view. Therefore, defining a goodness-of-fit will be an essential
step in creating views.
The maximum dimensionality K is limited by the number of degrees of freedom
in the data, but may also be set a priori by the data analyst. For the example data
set considered below the dimensionality was fixed to K=2 so that different visual-
izations can be easily presented on paper. Note that models of degree higher than
2 need multiple 2D views to be assessed anyhow. However, in this latter case, the
views are different 2D projections of a shared multi-dimensional configuration. The
2D views that result from the analysis presented in this chapter, on the other hand,
can be independent. Views of 2 or higher dimensionality provide relations not only
about the stimuli but also about the relations between the different attributes and are
thus preferred over 1D views.
A two-step procedure is proposed to establish whether zero, one or two models
with dimension K=2 can adequately model the attribute scores of a single observer.
In the first step, all attributes of a participant are modeled together, as is common
practice in MDS (average model). However, only the attributes that satisfy a par-
ticular goodness-of-fit criterion are considered to be adequately modeled. These at-
tributes are analyzed to form the first model, i.e. the individual's most dominant
view on the set of products.
In the second step, the attributes that displayed the least fit to the average model
are grouped and used to attempt a second model. By selecting the least-fit attributes,
instead of all remaining attributes, we promoted the diversity between the two mod-
els. The same goodness-of-fit criteria are applied for the second model to select the
attributes that are retained.
Ta b l e 3 . 2 Goodness of fit Criteria. Attributes that are adequately predicted are employed in
model 1. A second model is attempted only on attributes that display the least fit, to ensure
diversity between the two models.
R 2
R k
R 2
> .5 R k > 6
1. Adequate fit
2. Average fit (Excluded)
4
<
R k <
6
R k <
3. Least fit (attempt 2nd model)
4
3.3.2
Defining Goodness-of-Fit Criteria
We suggest a combined goodness of fit criterion. First, for an adequately predicted
attribute, a substantial amount of its variance should be accounted for by the model.
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