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CHAPTER-19D R D E E PA K C H A W L A NEENA SONDHI
MULTIDIMENSIONAL SCALING
RESEARCH
CONCEPTS AND
SLIDE 19-1
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Multidimensional Scaling (MDS) Basic tenets MDS is only one of the techniques that can be used for perceptual
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mapping.
The inputs obtained could be for objects, individuals, brands,
corporations or countries.
As a thumb rule, objects are grouped together. The grouped objects are usually evaluated and compared
with each other so that they can coexist on a spatial map.CONCEPTS AND
RESEARCH
SLIDE 19-2
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Multidimensional Scaling (MDS) Basic tenets The basis of evaluation is that objects exist not in
unidimensional but multidimensional space.D R D E E PA K C H A W L A NEENA SONDHI
The basis of evaluation might be on defined dimensions. The basis of evaluation might be on perceived /subjective
dimensions.
The basis of evaluation could be on similarity/ dissimilarity or
preferences.
RESEARCH
CONCEPTS AND
SLIDE 19-3
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Uses of Multidimensional Scaling Scale construction: Based on similarity or preference data the obtained
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dimensions can be reproduced as attributes in a structured- attributebased questionnaire to validate the existence of the parameters of comparison.
Brand image analysis: To measure the gap or match between brand
positioning and brand perception.
New product development: To identify quadrants that are less
crowded and where a launch opportunity exists. Pricing studies: Spatial maps with and without the price dimension can be made to assess the relevance of price/benefit trade off. Communication effectiveness: Before and after spatial maps can be made to measure new advertising impact or repositioning exercise. CONCEPTS AND
RESEARCH
SLIDE 19-4
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Multidimensional Scaling ProcedureFormulate the Research Objectives Identify objects to be compared Identify unit of analysis
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Similarity data Ordinal / Interval
Preference data Ordinal / Interval
MDS output (Metric or Non Metric)
Identify number of dimensions
Interpret the solution
Establish strength of MDS solution
RESEARCH
CONCEPTS AND
SLIDE 19-5
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Formulating the research objectiveThe method of multidimensional scaling is used under two conditions: For an exploratory study to decipher the probable underlying attributes or causes of certain observed patterns of behaviour. For descriptive research studies when the causal
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variables are not defined and the objective is simply to present the comparative evaluations of objects, individuals or brands in the consumers mind space.
RESEARCH
CONCEPTS AND
SLIDE 19-6
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Selecting the objects for comparison The objects to be compared must have a dimension
or dimensions of commonality.D R D E E PA K C H A W L A NEENA SONDHI
Generally, objects to be compared should be on a
4:1 ratio of the dimensions desired. Thus for a one dimensional solution we need to have a minimum of four objects.
It is advisable not to have more than 25 objects for
evaluation.
RESEARCH
CONCEPTS AND
SLIDE 19-7
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Conducting MDS with similarity data Respondent evaluates objects/brands for their relative
similarity/dissimilarity. The data can be obtained for both metric and non metric comparisons. Data from non-metric inputs would be converted into derived distances and plotted. Data from metric data can be plotted as Euclidean distance. The stress between the respondents scores and researchers interpretation is measured using Kruskal stress formula.CONCEPTS AND
D R D E E PA K C H A W L A NEENA SONDHI
RESEARCH
SLIDE 19-8
Illustration of similarity dataWhere VS-very similar=1 to VDS-very dissimilar=10
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Frontline Frontline Society .00 3.00 4.00 7.00 1.00 5.00 1.00 8.00
Society 3.00 .00 2.00 4.00 7.00 7.00 8.00 6.00
Indiatoday 4.00 2.00 .00 1.00 3.00 6.00 7.00 3.00
Outlook 7.00 4.00 1.00 .00 2.00 4.00 7.00 7.00
Businessindia 1.00 7.00 3.00 2.00 .00 2.00 4.00 5.00
Open 5.00 7.00 6.00 4.00 2.00 .00 3.00 6.00
Busworld 1.00 8.00 7.00 7.00 4.00 3.00 .00 2.00
Investor 8.00 6.00 3.00 7.00 5.00 6.00 2.00 .00
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Indiatoday Outlook Businessindia Open Busworld Investor
RESEARCH
CONCEPTS AND
SLIDE 19-9
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Conducting MDS with preference data Respondent evaluates objects/brands for their relative
selection or rejection. The data can be obtained for both metric and non metric comparisons. Data from non-metric inputs would be in the form of ranking or paired comparison data. Data from metric data can be plotted as Euclidean distance. The stress between the respondents scores and researchers interpretation is measured using Kruskal stress formula.CONCEPTS AND
D R D E E PA K C H A W L A NEENA SONDHI
RESEARCH
SLIDE 19-10
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Illustration of preference data ranking scale (N=10)S no. India Today 4 9 9 7 8 9 9 1 1 1 3 6 1 3 3 4 7 5 7 5 Outlook Business World 2 7 2 2 2 2 6 4 6 4 9 4 8 9 9 8 5 9 9 9 5 5 6 4 4 6 4 3 2 3 Open Investor Business India 1 8 3 1 1 5 8 2 3 2 7 2 4 5 5 1 1 7 5 7 6 3 5 6 6 3 2 6 4 6 Society Frontline Life Times 8 1 7 8 7 7 3 8 8 8 &
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1 2 3 4 5 6 7 8 9 10
RESEARCH
CONCEPTS AND
SLIDE 19-11
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Identifying the number of dimensions Subject knowledge
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Readers comprehension Scree plots R-square value
RESEARCH
CONCEPTS AND
SLIDE 19-12
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Scree plot-ranking data example.40
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.35 .30
Stress Scores
.25
.20
.15
.10
.05
1
2
3
4
Number of Dimensions
RESEARCH
CONCEPTS AND
SLIDE 19-13
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MDS solution-ranking data
RESEARCH
CONCEPTS AND
SLIDE 19-14
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Establishing the strength of the MDS solution The Kruskal Stress score, i.e. the discrepancy scores
obtained between the derived distances on a configured map and the actual distance as indicated by the respondents choice. The ideal representation would be a stress value of 0%. However, it is acceptable to consider a solution till a 20% stress between the actual and the derived configuration. The R-square value: measures the proportion of the variance of the final scaled solution that can be accounted for by the MDS procedure. The ideal would be 1. However, an R-square value of 0.6 or above is acceptable.CONCEPTS AND
D R D E E PA K C H A W L A NEENA SONDHI
RESEARCH
SLIDE 19-15
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Establishing the strength of the MDS solution Split half technique: obtained by splitting the entire
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sets of obtained responses into two groups and the MDS obtained by the two groups should more or less match with each other.different intervals of time to see if the spatial maps stay constant over a time period. brand to measure the resulting spatial map is another way of observing the consistency of results.
Test-retest: the same group could be measured at
The leave-one-out technique or eliminating one
RESEARCH
CONCEPTS AND
SLIDE 19-16
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Establishing the strength of the MDS solutionNumber of dimensions 4 Stress value 0.00058 0.00256 0.07677 0.26536 R square values 1.0 0.99993 0.95947 0.78040
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3 2 1
RESEARCH
CONCEPTS AND
D R D E E PA K C H A W L A NEENA SONDHI
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RESEARCH
END OF CHAPTER
CONCEPTS AND