Description
Multi Dimensional Scaling
Multidimensional Scaling
Multidimensional Scaling (MDS)
?
?
Multidimensional scaling (MDS) is a class of procedures for representing perceptions of respondents spatially by means of a visual display. These geometric representations are often called spatial maps. The axes of the spatial map are assumed to denote the underlying dimensions respondents use to form perceptions for stimuli.
Statistics and Terms Associated with MDS
?
?
?
?
Similarity judgments. Similarity judgments are ratings on all possible pairs of brands or other stimuli in terms of their similarity using a Likert type scale. Preference rankings. Preference rankings are rank orderings of the brands or other stimuli from the most preferred to the least preferred. They are normally obtained from the respondents. Stress. This is a lack-of-fit measure; higher values of stress indicate poorer fits. R-square. R-square is a squared correlation index that indicates the proportion of variance of the data that can be accounted for by the MDS procedure. This is a goodness-of-fit measure.
Conducting Multidimensional Scaling
Fig. 1
Formulate the Problem Obtain Input Data Select an MDS Procedure Decide on the Number of Dimensions Label the Dimensions and Interpret the Configuration Assess Reliability and Validity
Conducting Multidimensional Scaling
Formulate the Problem
?
?
?
Specify the purpose for which the MDS results would be used. Select the brands or other stimuli to be included in the analysis. The number of brands or stimuli selected normally varies between 8 and 25. The choice of the number and specific brands or stimuli to be included should be based on the statement of the marketing research problem, theory, and the judgment of the researcher.
Input Data for Multidimensional Scaling
Fig. 2 MDS Input Data
Perceptions
Preferences
Direct (Similarity Judgments)
Derived (Attribute Ratings)
Conducting Multidimensional Scaling
Obtain Input Data
?
Perception Data: Direct Approaches. In direct approaches to gathering perception data, the respondents are asked to judge how similar or dissimilar the various brands or stimuli are, using their own criteria. These data are referred to as similarity judgments.
2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 Very Similar 7 7 7
Very Dissimilar Crest vs. Colgate 1 Aqua-Fresh vs. Crest 1 Crest vs. Aim 1 . . . Colgate vs. Aqua-Fresh 1
?
2
3
4
5
6
7
The number of pairs to be evaluated is n (n -1)/2, where n is the number of stimuli.
Similarity Rating Of Toothpaste Brands
Table 1
Aqua-Fresh Aqua-Fresh Crest Colgate Aim Gleem Macleans Ultra Brite Close-Up Pepsodent Dentagard 5 6 4 2 3 2 2 2 1
Crest
Colgate
Aim
Gleem
Macleans
Ultra Brite
Close-Up
Pepsodent Dentagard
7 6 3 3 2 2 2 2
6 4 4 2 2 2 4
5 4 3 2 2 2
5 5 6 6 4
5 5 6 3
6 7 3
6 4
3
Conducting Multidimensional Scaling
Obtain Input Data
?
Perception Data: Derived Approaches. Derived approaches to collecting perception data are attribute-based approaches requiring the respondents to rate the brands or stimuli on the identified attributes using semantic differential or Likert scales.
Does not whiten teeth
Whitens teeth ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
Prevents tooth Does not prevent decay ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ tooth decay . . . . Pleasant Unpleasant tasting ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ tasting
?
If attribute ratings are obtained, a similarity measure (such as Euclidean distance) is derived for each pair of brands.
Conducting Multidimensional Scaling
Obtain Input Data – Direct vs. Derived Approaches
The direct approach has the following advantages and disadvantages: ? The researcher does not have to identify a set of salient attributes. ? The disadvantages are that the criteria are influenced by the brands or stimuli being evaluated. ? Furthermore, it may be difficult to label the dimensions of the spatial map.
Conducting Multidimensional Scaling
Obtain Input Data – Direct vs. Derived Approaches
The attribute-based approach has the following advantages and disadvantages: ? It is easy to identify respondents with homogeneous perceptions. ? The respondents can be clustered based on the attribute ratings. ? It is also easier to label the dimensions. ? A disadvantage is that the researcher must identify all the salient attributes, a difficult task. ? The spatial map obtained depends upon the attributes identified. It may be best to use both these approaches in a complementary way. Direct similarity judgments may be used for obtaining the spatial map, and attribute ratings may be used as an aid to interpreting the dimensions of the perceptual map.
Conducting Multidimensional Scaling
Preference Data
?
?
?
?
?
Preference data order the brands or stimuli in terms of respondents' preference for some property. A common way in which such data are obtained is through preference rankings. Alternatively, respondents may be required to make paired comparisons and indicate which brand in a pair they prefer. Another method is to obtain preference ratings for the various brands. The configuration derived from preference data may differ greatly from that obtained from similarity data. Two brands may be perceived as different in a similarity map yet similar in a preference map, and vice versa..
Conducting Multidimensional Scaling
Select an MDS Procedure
Selection of a specific MDS procedure depends upon: ? The nature of the input data is also a determining factor. ? Non-metric MDS procedures assume that the input data are ordinal, but they result in metric output. ? Metric MDS methods assume that input data are metric. ? The metric and non-metric methods produce similar results. ? Another factor influencing the selection of a procedure is whether the MDS analysis will be conducted at the individual respondent level or at an aggregate level.
Conducting Multidimensional Scaling
?
Decide on the Number of Dimensions
A priori knowledge - Theory or past
?
?
research may suggest a particular number of dimensions. Interpretability of the spatial map - Generally, it is difficult to interpret configurations or maps derived in more than three dimensions. Elbow criterion - A plot of stress versus dimensionality should be examined.
Plot of Stress Versus Dimensionality
Fig. 3
0.3 0.2
Stress
0.1 0.0 0
1
2 3 4 Number of Dimensions
5
A Spatial Map of Toothpaste Brands
Fig. 4
2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 Dentagard Macleans Ultrabrite Pepsodent Colgate Close Up Aqua- Fresh Gleem
Aim
Crest
-2.0 -2.0 -1.5 -1.0 -0.5
0.0
0.5 1.0
1.5
2.0
SPSS Windows
The multidimensional scaling program allows individual differences as well as aggregate analysis using ALSCAL. The level of measurement can be ordinal, interval or ratio. Both the direct and the derived approaches can be accommodated.
To select multidimensional scaling procedures using SPSS for Windows click: Analyze>Scale>Multidimensional Scaling …
doc_546424626.ppt
Multi Dimensional Scaling
Multidimensional Scaling
Multidimensional Scaling (MDS)
?
?
Multidimensional scaling (MDS) is a class of procedures for representing perceptions of respondents spatially by means of a visual display. These geometric representations are often called spatial maps. The axes of the spatial map are assumed to denote the underlying dimensions respondents use to form perceptions for stimuli.
Statistics and Terms Associated with MDS
?
?
?
?
Similarity judgments. Similarity judgments are ratings on all possible pairs of brands or other stimuli in terms of their similarity using a Likert type scale. Preference rankings. Preference rankings are rank orderings of the brands or other stimuli from the most preferred to the least preferred. They are normally obtained from the respondents. Stress. This is a lack-of-fit measure; higher values of stress indicate poorer fits. R-square. R-square is a squared correlation index that indicates the proportion of variance of the data that can be accounted for by the MDS procedure. This is a goodness-of-fit measure.
Conducting Multidimensional Scaling
Fig. 1
Formulate the Problem Obtain Input Data Select an MDS Procedure Decide on the Number of Dimensions Label the Dimensions and Interpret the Configuration Assess Reliability and Validity
Conducting Multidimensional Scaling
Formulate the Problem
?
?
?
Specify the purpose for which the MDS results would be used. Select the brands or other stimuli to be included in the analysis. The number of brands or stimuli selected normally varies between 8 and 25. The choice of the number and specific brands or stimuli to be included should be based on the statement of the marketing research problem, theory, and the judgment of the researcher.
Input Data for Multidimensional Scaling
Fig. 2 MDS Input Data
Perceptions
Preferences
Direct (Similarity Judgments)
Derived (Attribute Ratings)
Conducting Multidimensional Scaling
Obtain Input Data
?
Perception Data: Direct Approaches. In direct approaches to gathering perception data, the respondents are asked to judge how similar or dissimilar the various brands or stimuli are, using their own criteria. These data are referred to as similarity judgments.
2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 Very Similar 7 7 7
Very Dissimilar Crest vs. Colgate 1 Aqua-Fresh vs. Crest 1 Crest vs. Aim 1 . . . Colgate vs. Aqua-Fresh 1
?
2
3
4
5
6
7
The number of pairs to be evaluated is n (n -1)/2, where n is the number of stimuli.
Similarity Rating Of Toothpaste Brands
Table 1
Aqua-Fresh Aqua-Fresh Crest Colgate Aim Gleem Macleans Ultra Brite Close-Up Pepsodent Dentagard 5 6 4 2 3 2 2 2 1
Crest
Colgate
Aim
Gleem
Macleans
Ultra Brite
Close-Up
Pepsodent Dentagard
7 6 3 3 2 2 2 2
6 4 4 2 2 2 4
5 4 3 2 2 2
5 5 6 6 4
5 5 6 3
6 7 3
6 4
3
Conducting Multidimensional Scaling
Obtain Input Data
?
Perception Data: Derived Approaches. Derived approaches to collecting perception data are attribute-based approaches requiring the respondents to rate the brands or stimuli on the identified attributes using semantic differential or Likert scales.
Does not whiten teeth
Whitens teeth ___ ___ ___ ___ ___ ___ ___ ___ ___ ___
Prevents tooth Does not prevent decay ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ tooth decay . . . . Pleasant Unpleasant tasting ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ tasting
?
If attribute ratings are obtained, a similarity measure (such as Euclidean distance) is derived for each pair of brands.
Conducting Multidimensional Scaling
Obtain Input Data – Direct vs. Derived Approaches
The direct approach has the following advantages and disadvantages: ? The researcher does not have to identify a set of salient attributes. ? The disadvantages are that the criteria are influenced by the brands or stimuli being evaluated. ? Furthermore, it may be difficult to label the dimensions of the spatial map.
Conducting Multidimensional Scaling
Obtain Input Data – Direct vs. Derived Approaches
The attribute-based approach has the following advantages and disadvantages: ? It is easy to identify respondents with homogeneous perceptions. ? The respondents can be clustered based on the attribute ratings. ? It is also easier to label the dimensions. ? A disadvantage is that the researcher must identify all the salient attributes, a difficult task. ? The spatial map obtained depends upon the attributes identified. It may be best to use both these approaches in a complementary way. Direct similarity judgments may be used for obtaining the spatial map, and attribute ratings may be used as an aid to interpreting the dimensions of the perceptual map.
Conducting Multidimensional Scaling
Preference Data
?
?
?
?
?
Preference data order the brands or stimuli in terms of respondents' preference for some property. A common way in which such data are obtained is through preference rankings. Alternatively, respondents may be required to make paired comparisons and indicate which brand in a pair they prefer. Another method is to obtain preference ratings for the various brands. The configuration derived from preference data may differ greatly from that obtained from similarity data. Two brands may be perceived as different in a similarity map yet similar in a preference map, and vice versa..
Conducting Multidimensional Scaling
Select an MDS Procedure
Selection of a specific MDS procedure depends upon: ? The nature of the input data is also a determining factor. ? Non-metric MDS procedures assume that the input data are ordinal, but they result in metric output. ? Metric MDS methods assume that input data are metric. ? The metric and non-metric methods produce similar results. ? Another factor influencing the selection of a procedure is whether the MDS analysis will be conducted at the individual respondent level or at an aggregate level.
Conducting Multidimensional Scaling
?
Decide on the Number of Dimensions
A priori knowledge - Theory or past
?
?
research may suggest a particular number of dimensions. Interpretability of the spatial map - Generally, it is difficult to interpret configurations or maps derived in more than three dimensions. Elbow criterion - A plot of stress versus dimensionality should be examined.
Plot of Stress Versus Dimensionality
Fig. 3
0.3 0.2
Stress
0.1 0.0 0
1
2 3 4 Number of Dimensions
5
A Spatial Map of Toothpaste Brands
Fig. 4
2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 Dentagard Macleans Ultrabrite Pepsodent Colgate Close Up Aqua- Fresh Gleem
Aim
Crest
-2.0 -2.0 -1.5 -1.0 -0.5
0.0
0.5 1.0
1.5
2.0
SPSS Windows
The multidimensional scaling program allows individual differences as well as aggregate analysis using ALSCAL. The level of measurement can be ordinal, interval or ratio. Both the direct and the derived approaches can be accommodated.
To select multidimensional scaling procedures using SPSS for Windows click: Analyze>Scale>Multidimensional Scaling …
doc_546424626.ppt