Additive Clustering Techniques for Market Segmentation: An Empirical Comparison Using Real and Simul

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• Additive Clustering Techniques for Market
  Segmentation An Empirical Comparison Using Real
  and Simulated Data
• Prof. Dr. Daniel Baier, Institute of Business
  Administration and Economics, Chair of Marketing
  and Innovation Management, Brandenburg
  University of Technology Cottbus, Germany
• Introduction
• Advances in Additive Clustering
• Two-mode additive clustering models
• The overlapping clustering procedure
• The non-overlapping clustering procedure
• Constrained clustering procedures
• Empirical Applications
• Monte Carlo Comparisons
• Conclusions and Outlook

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Introduction

• Which groups of consumers compete for which
  groups of brands/products?
• Data set 1
• Data set 2

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Advances in Additive Clustering

• The modeling ideaconsumers accumulatebrand
  quantities accordingto segment-memberships

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Advances in Additive Clustering

• Two-mode additive clustering models
• Observed data
• i1,...,I first mode objects (e.g. respondents),
• j1,...,J second mode objects (e.g. brands),
• k1,...,K first mode clusters (e.g. market
  segments),
• l1,...,L second mode clusters (e.g. brand
  clusters),
• S(sij)I x J matrix of observed responses
• Model parameters
• P(pik)I x K matrix describing first mode cluster
  membership (1 yes, 0 no),
• Q(qjl)J x L matrix describing second mode
  cluster membership (1 yes, 0 no),
• W(wkl)K x L matrix of weights
• Objective function

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Advances in Additive Clustering
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Advances in Additive Clustering
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Advances in Additive Clustering

• The overlapping clustering procedure (Baier et
  al. 1997)
• Main idea separating the loss function w.r.t.
  different parameter sets
• sijk is constant w.r.t. the parameters of first
  mode cluster k,
• sijl is constant w.r.t. the parameters of second
  mode cluster l.

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Advances in Additive Clustering

• Algorithm
• Determine initial estimates of P, W, and Q
• While Z can be improved
• For k1 to K improve p1k,..., pIk by setting
• For k1 to K improve wk1,..., wkL by minimizing
• For l1 to L improve q1l,..., qJl by setting
• For l1 to L improve w1l,..., wKl by minimizing

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Advances in Additive Clustering

• The non-overlapping clustering procedure
• Algorithm
• Determine initial estimates of P, W, and Q
• While Z can be improved
• For k1 to K improve p1k,..., pIk
• For k1 to K improve wk1,..., wkL
• For l1 to L improve q1l,..., qJl
• For l1 to L improve w1l,..., wKl

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Advances in Additive Clustering

• Constrained clustering
• by fixing some or all cluster-membership
  parameters P and/or Q, e.g.
• fixing brand clusters according to a priori known
  attributes and levels of the brands
• l1 mild brands
• l2 premium brands
• l3 Tchibo brands
• l4 Jacobs brands
• ...

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Empirical Applications
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Empirical Applications

• Example (Baier, Gaul, Schader 1997)
• A major German producer of luxury bathroom
  fittings plans the introduction of new
  ecologically benefical water-taps
• Segmentation basis
• Buying intentions (1,...,11 points) for 25
  prototypes from 82 respondentssystematically
  varying w.r.t. the following attributes and
  levels
• Segmentation method
• Constrained clustering with L21 overlapping
  prototype(second mode) clusters (constant term
  plus level indicator)
• last level for each attribute is used as a
  reference

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Empirical Applications
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Empirical Applications

• Segmentation results (using background variables
  for description)
• Segment 1 (28.0)
• technical interest
• Segment 2 (13.4)
• conservative
• Segment 3 (34.2)
• practical interest
• Segment 4 (24.4)
• price
• Target segment for the new productGrotherm 1000

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Monte Carlo Comparisons

• Is the overlapping procedure able to recover a
  priori specified clusterings?
• Data sets used
• 360 generated data sets with I40, J20
• overlapping structures with varying overlap
  (measured via cluster-memberships) and numbers of
  first mode and second mode clusters
• weight matrix gamma distributed (for simulating
  buying intensities across clusters)
• additional gamma distributed measurement errors
• Factors used for generating data
• Number of first mode and second mode clusters
• Low (KL2), medium (KL3), high (KL4)
• Intensity of overlap
• Low (10 ), High (30 )
• Disturbance (gamma distributed additive error)
• Low, Medium, High
• Recovery measures VAF, Percentage of correctly
  predicted cluster-memberships after optimum
  permutation
• alternatively Omega index (Collins, Dent 1988,
  Krolak-Schwerdt, Wiedenbeck 2006)

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Monte Carlo Comparisons

• Results

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Monte Carlo Comparisons

• Is the non-overlapping procedure able to recover
  a priori specified clusterings?
• Data sets used
• 180 generated data sets with I40, J20
• non-overlapping structures
• weight matrix gamma distributed (for simulating
  buying intensities across clusters)
• additional gamma distributed measurement errors
• Factors used for generating data
• Number of first mode and second mode clusters
• Low (KL2), medium (KL3), high (KL4)
• Disturbance (gamma distributed additive error)
• Low
• Medium
• High
• Recovery measures VAF, Percentage of correctly
  predicted cluster-membershipsafter optimum
  permutation
• alternatively Adjusted Rand Index (Hubert,
  Arabie 1985, Krolak-Schwerdt, Wiedenbeck 2006)

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Monte Carlo Comparisons

• Results

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Conclusions and Outlook

• New two-mode (non-)overlapping clustering
  procedures perform quite well
• in case of synthetically generated data according
  to the additive clustering model
• Have nice practical applications for market
  segmentation
• e.g. in case of constrained clustering
• However
• show many problems in identifying "correct" or
  "practically plausible" models