Empirical studies of competitive product/service positioning

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Empirical studies of competitive product/service
positioning

• Wind(1982) recommends to collect
• Brand-by-brand proximity judgments
• Brand-by-attribute ratings
• Consumer by brand preferences
• Relevant consumer characteristics
• Different models to analyze such datasets

Wind(1982) Product Policy Concepts, methods and
strategy, Addison-Wesley
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B1 B2 .. Bk
B1 B2 .. . Bk
B1 B2 .. Bk
B1 B2 .. . Bk
I1
Symmetric, two way one mode
B1 B2 .. Bk
B1 B2 .. . Bk
B1 B2 .. Bk
I2
I1 I2 I3 . . . In
Rectangular Two-way two mode
Three way, two mode
Ways Number of dimensions in a data set Mode
Number of sets of stimuli
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Two-way one modeMultidimensional scaling
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Overall purpose with MDS.

• To map a set of products (objects) in a
  multidimensional space in such a way, that the
  relative position of the products in the space
  reflect the perceived (dis)similarity between the
  products.

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The overall idea in MDS.
Map
Proximity-matrix
P1
P2
P4
P3
P5
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Notation.
Map
Proximity-matrix
P1
d41
P2
P4
P3
P5
Dataset in p-dimensions (5) mapped in
q-dimensions (2) (qltp)
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The perfect fit.
Metric MDS. - our data (proximities) are
considered to have interval/ratio scale
properties Criterion Non-metric MDS - our
data (proximities) are considered to have
ordinal properties. Criterion
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An example.
Proximities (sij) Distances (dij)
Perfect fit in non-metric MDS.
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The classical example metric MDS.
Distancetable ( in mm measured from a map of
Denmark ) Source Blunch Analyse af
markedsdata, Systime 1990
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How to read in a proximity matrix in SPSS
Matrix Data variableskbh aarhus aalborg odense
silkeb skagen svendb gillelej soenderb korsoer
/contentsprox. Begin Data 0 87 0 126 59 0
78 48 107 0 109 23 62 54 0 146
102 48 149 110 0 80 70 129 22 76 170 0 29 7
4 102 82 97 118 91 0 109 79 136 37 75 181 30 117
0 54 61 118 27 75 153 27 64 55 0 End Data.
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Estimation result from SPSS
Iteration history for the 2 dimensional
solution (in squared distances)
Young's S-stress formula 1 is used.
Iteration S-stress Improvement
1 ,00316
Iterations stopped because
S-stress is less than ,005000
Stress and squared correlation (RSQ) in
distances RSQ values are the proportion of
variance of the scaled data (disparities)
in the partition (row, matrix, or entire data)
which is accounted for by their
corresponding distances. Stress
values are Kruskal's stress formula 1.
For matrix Stress ,00287
RSQ ,99995
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Configuration derived in 2 dimensions
Stimulus Coordinates
Dimension Stimulus Stimulus 1
2 Number Name 1 GILLELEJ
-,1555 -1,2630 2 KBH ,4638
-1,4145 3 KORSOER ,8989 -,2997
4 ODENSE ,7837 ,2997 5
SILKEB -,2684 ,9027 6 SKAGEN
-2,5145 -,0981 7 SOENDERB 1,4157
,8213 8 SVENDB 1,2645 ,1805 9
AALBORG -1,6016 ,4953 10 AARHUS
-,2865 ,3758
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South
North
East
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6 steps in multidimensional scaling

• Problem
• Data collection
• Choice of MDS procedure
• Determine number of dimensions
• Name dimensions and interpret structure
• Judge reliability and validity

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Problem

• Purpose of investigation
• Choice of brands
• Number of brands (at least 8, less than 25) and
  type determines the dimensions, that are the
  result of the analysis

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Collection of proximity-data-similarity/dissimila
rity data

• Direct measure of proximity
• paired comparisons
• sorting
• conditional ranking
• Constructed measure of proximity (derived
  approach)
• ie. based on evaluations pr. attribute on a
  Likert scale

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Data collectiondirect approach

• Sorting
• sorting of products in groups with respect to
  similarity. if two produkter are in the same
  group the pair will have a 1 in the matrix
  otherwise 0. Summed across respondents
• Paired comparisons (n(n-1)/2)
• all pairwise comparisons are presented. All pairs
  are evaluated on a rating scale. Full matrix pr.
  respondent
• Conditional rankings
• Evaluation of products compared to a reference
  product. All products become reference products.
  Each row in the proximity matrix consist the
  evaluation with the row product as a standard.

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Conditional data collection- asymmetric matrices
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Derived approach
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Euclidean distance measure.
Derived proximities
In the MDS procedure
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Choice of MDS procedure

• Non-metric MDS
• input data are on an ordinal scale
• ordinal correspondence between input and output
• Metric MDS
• input data on an interval scale
• Based on individual data or on aggregated data

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History of MDS

• Metric MDS
• Torgerson(1952) teh first well-known
  MDS-proposal. Fits the Euclidean model
• Non-metric MDS
• Kruskal(1964)
• Individual differences are taken into account
• CarrollChang(1970) introduces the INDSCAL
  model
• Consolidation
• Takane,YoungdeLeeuw(1977) ALSCAL combines
  metric/non-metric scaling in one algorithm.
• Ramsay(1977) MultiScale introduceres tests of
  significance based on maximum-likelihood

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Torgersons contribution.
Notation
D (proximity-matrix) X matrix of coordinates
in the map. Number of dimensions in the map q
If X is known, it is straightforward to calculate
B and D . Torgersons contribution is to show,
that B and X can be found , if D is known.
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Torgersons contribution.
From the definition of B it follows
Hence D can be calculated from B and B can be
calculated from D
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Torgersons contribution.
D D2 B
Scalar- product matrix
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Torgersons contribution.
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Example continued.
P
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If B is not positive semi-definite.(if the
observed dissimilarity matrix is not Euclidean)
Example
If many big negative eigenvalues, then the
classical MDS solution is not trustworthy.
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Important

• X is not a unique solution
• Rotation
• Reflection
• Move from one place to another
• Classical scaling is often called
• Principal coordinates analysis

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Non- metric scaling.

• Disparities

Optimal scaling The monotone transformation of
proximities leading
to the greatest possible correspondence
to the distances in the
map. Kruskals least squares monotonic
transformation
closest in a least-squares sense.
If metric then linear regression. If non-metric
then monotone regression
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Example Dillon p.132.
Iteration history for the 2 dimensional
solution (in squared distances)
Young's S-stress formula 1 is used.
Iteration S-stress Improvement
1 ,14147
2 ,10118 ,04029
3 ,08784 ,01334
4 ,07757 ,01026
5 ,06898
,00859 6 ,06263
,00635 7 ,05815
,00448 8
,05479 ,00336 9
,05204 ,00276 10
,04977 ,00227
11 ,04789 ,00188
12 ,04632 ,00157
13 ,04503 ,00128
14 ,04410 ,00094
Iterations stopped
because S-stress improvement is
less than ,001000
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Shepard- diagram.
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Example 2.

• Perceived similarity between 12 countries

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Syntax to SPSS
ALSCAL VARIABLES brazil congo cuba egypt
france india israel japan china ussr usa yugo
/SHAPESYMMETRIC /LEVELORDINAL(similar)
/CONDITIONMATRIX /MODELEUCLID
/CRITERIACONVERGE(.001) STRESSMIN(.005)
ITER(30) CUTOFF(0) DIMENS(2,2) /PLOTDEFAULT .
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Young's S-stress formula 1 is used.
Iteration S-stress Improvement
1 ,28855
2 ,26085 ,02770
3 ,25752 ,00333
4 ,25648 ,00103
5 ,25618
,00030 Iterations
stopped because S-stress
improvement is less than ,001000
Stress and squared correlation (RSQ) in
distances RSQ values are the proportion of
variance of the scaled data (disparities)
in the partition (row, matrix, or entire data)
which is accounted for by their
corresponding distances. Stress
values are Kruskal's stress formula 1.
For matrix Stress ,20327
RSQ ,70335
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The fundamental equation in least-squares
scaling.
t
Simila- Disparity Distance
Error rity
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STRESS-statistic.

• Different STRESS-values dependent upon program,
  but often Kruskal STRESS1

Dillon p.129.
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Treatment of ties

• Primary approach
• Secondary approach

No restrictions on distances in map
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Monotonicity
If (dis)similarities are ranked then
Normally weak monotonicity and primary approach
to ties
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Size of STRESS1
Kruskals rule of thumb
Stress-value Goodness of fit 0,20
Poor 0,10
Fair 0,05
Good 0,025
Excellent
Guttman lt0,15
Scree-plot
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Number of dimensions

• Trade-off
• best fit in fewest possible dimensions
• STRESS
• lack of fit measure
• Apriori knowledge
• Interpretation of result
• Elbow criterion

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Interpretation

• Fit regression
• Correspondence to evaluation of attributes
• The same with objective criteria
• Show the map to a person with intensive knowledge
  about the market
• Take your starting point in the most extreme
  products in the map

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Reliability and validity

• Coefficient of determination(gt0,6)
• If aggregated solution then split and make
  separate analyses
• Drop one product and see what happens
• Add a stochastic element to the input