Proposition 1 and 3 below), his efforts fell short on two aspects. First, he only hints at the existence
proof that we provide in Proposition 2. Our Proposition 2 provides the key linkages to a robust calibration
procedure. And second, his calibration procedure for real data is cumbersome, at b...
We believe that marketing practitioners and academics have lost interest in multidimensional
scaling (MDS) in general, and joint-space solutions in particular, in recent years because neither
marketing academics nor psychometricians have developed straightforward answers for the most
compelling questions. Users look at a perceptual map and interpret the distance between objects as just
that – a distance. Yet, with most current methods we cannot interpret the distance between an ideal
point for an individual and a brand as a simple distance. The metric among brands it typically a distance,
but the metric between brands and people is a function of squared distance or a function of angles
between a personal preference vector and the brands. When we try to relate the words people use to
describe brands to the positions of those brands in a perceptual space, the simple meaning of distance is
lost. The origin for the relations between brands is not the same as the origin for the relations between
adjectives, leaving the distance between brands and adjectives as undefined. Using MDS to represent
brand switching patterns over purchase occasions has not been possible without linguistic gymnastics that
leave even sophisticated investigators scratching their heads. The distance of a brand at time one from an
average time-one profile compared to the distance of a brand at time two from the average time-two
profile, is too convoluted to follow. Thus we take the shortcut, and inappropriately interpret the apparent
distance as if it were a real distance.
These basic marketing-research questions inherently involve two sets of objects: people and
brands, brands and adjectives describing those brands, or brands at time one versus brands at time two.
For instance, when we collect consumers’ judgments about their preferences for brands or how they
describe brands, these are in reality inter-set judgments, since they relate one set of objects (adjectives)
with another set of objects (brands). As we describe below, simple distance solutions for these basic
inter-set data have never been developed. We want a common space for the objects in both sets, and a
simple distance to properly represent what we see in that common spatial map. This work develops that
common map, and illustrates its utility representing marketing data from both historic examples and new
research.
Background
Most multidimensional scaling (MDS) methods are conceptually based on some measures of
distance. Observed similarity (or proximity) measures between objects are assumed to be monotonically
2
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