To further test the appropriateness of the algorithm we developed, a small scale validity
study was conducted. Because the subject of the data collection task is part of an
on-going project with proprietary client information, we must necessarily mask the
specifics of the data collection.
Eight different binary attributes form the underlying basis of the hypothetical product
mix. Respondents were asked to rate each binary attribute on a 1-5 scale, and to then rank
the relative importance of each attribute. These data constitute the alternative model
In addition, a fractionated factorial design was used to select 16 unique combinations
of the attributes from the 2 to the eighth or 256 total possible combinations. The eight
respondents in the test ranked these combinations in a manner identical to the classic
conjoint data gathering exercise.
Together with the alternative model, these data constitute the full test data set for
the small validity study.
An individual differences conjoint model was fit to each subject's rank or derived
preference score for the alternative model and the overall average for the product
combination. These scores were monotonically transformed with a quadratic monotone spline
transformation, and a single knot was specified at the median. The classification
variables in the model (i.e., the eight attributes that define the conjoint profile) are
optimally scored in an additive model with a mean of zero.
While only the sixteen combinations included in the fractionated factorial design could
be tested for the classic conjoint model, the mathematical transformations of the
alternative model make it possible to test all of the possible combinations in the
theoretical design. This was done for this test. Throughout this discussion, however, only
the comparable pairs across the two models are used.
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