Multivariate Techniques
Content
Chapter Fifteen
Overview of Other Multivariate Techniques and Data Mining
Dependence and Interdependence Techniques
• Dependence technique
– One variable is designated as the dependent variable and the rest are treated as independent variables
• Interdependence technique
– There are no dependent and independent variable designations, all variables are treated equally in a search for underlying patterns of relationships
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15 | 2
Dependence Technique – Regression Analysis
• Input Data
– Dependent variable(s) - metric – Independent variable(s) - metric
• Primary Purpose of the Technique
– Ascertain the relative importance of independent variable(s) in explaining variation in the dependent variable – Predict dependentvariable values for given values of the independent variable(s)
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15 | 3
Table 15.1 Overview of Multivariate Techniques
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15 | 4
Analysis of Variance
• ANOVA is appropriate in situations where the independent variable is set at certain specific levels (called treatments in an ANOVA context) and metric measurements of the dependent variable are obtained at each of those levels
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15 | 5
Example
24 Stores Chosen randomly for the study 8 Stores randomly chosen for each treatment
Treatment 1
Store brand sold at the regular price
Treatment 2 Store brand sold at 50¢ off the regular price
Treatment 3
Store brand sold at 75¢ off the regular price
monitor sales of the store brand for a week in each store
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 6
Table 15.2 Unit Sales Data Under Three Pricing Treatments
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15 | 7
After Only Design
EG1(R) EG2(R) EG3(R) X1 X2 X3 O1 O2 O3
EG1 -- Experiment Group 1, X1-- Regular Price EG2 -- Experiment Group 2, X2-- 50c off EG3 -- Experiment Group 3, X3-- 75c off O1 -- Observation (monitoring unit sales data in each store)
O2 -- Observation (monitoring unit sales data in each store)
O3 -- Observation (monitoring unit sales data in each store)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 8
After Only Design
EG1(R) EG2(R) EG3(R) X1 X2 X3 O1 O2 O3
X1-- Regular Price X2-- 50c off
EG1 -- Experiment Group 1,
EG2 -- Experiment Group 2,
EG3 -- Experiment Group 3,
X3-- 75c off
O1 -- Observation (monitoring unit sales data in each store) O2 -- Observation (monitoring unit sales data in each store) O3 -- Observation (monitoring unit sales data in each store)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 9
ANOVA –Grocery Store Hypothesis
• Grocery Store Example
– Ho 1 = 2 = 3 – Ha At least one is different from one or more of the others
• Hypotheses for K Treatment groups or samples
– Ho 1 = 2 = . . . = k – Ha At least one is different from one or more of the others
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15 | 10
Bank Customer Perceptions Study
Bank Customers Gender
Male
< 35 Years > 64 Years < 35 Years
Female
35-64 Years > 64 Years
35-64 Years
Measure Overall Perceptions
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 12
Discriminant Analysis
• Identifies the distinguishing features of prespecified subgroups of units that are formed on the basis of some dependent variable • Examples of subgroups
– Heavy, moderate, and light users of a product – Homeowners and renters – Viewers and nonviewers of a television program
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15 | 19
Discriminant Analysis (Cont’d)
• Dependent Variable
– Categorical: as many categories as there are subgroups
• Heavy, moderate, and light users: 3 categories • Independent Variable
– Metric-scaled
• Purpose of discriminant analysis is to classify new units into one of the subgroups given the new units’ values of the independent variable
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15 | 20
Example
Computer Manufacturer
Household
income
Number of years of formal education
PC Ownership
Copyright © Houghton Mifflin Company. All rights reserved.
Not Owning A PC
15 | 21
Exhibit 15.3 Scatter Plot of Income and Education Data for Personal Computer Owners and Nonowners
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15 | 22
Evaluating a Discriminant Function
• Confusion Matrix
– Indicates the degree of correspondence, or lack thereof, between the actual groupings of the sample units and the predicted groupings obtained by classifying the same units through the discriminant function
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15 | 24
Table 15.3 Confusion Matrix
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Usefulness of Discriminant Analysis
• Discriminant analysis is very useful for
– Defining customer segments – Identifying critical characteristics capable of distinguishing among them – Classifying prospective customers into appropriate segments
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15 | 26
Factor Analysis
• A data and variable reduction technique that attempts to partition a given set of variables into groups of maximally correlated variables
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 27
Intuitive Explanation
• Consider two statements from the Star Brand Inc.(SBI) survey
– S1. “I have been satisfied with the Star products I have purchased” – S2. “When I have to purchase a home appliance in the future, it will likely be a Star product”
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15 | 28
Factor Analysis Output and Its Interpretation
• Primary output of factor analysis is a factorloading matrix • Achieved Communality
– represents the proportion of variance in an original variable accounted for by all the extracted factors. – Each original variable will have an achieved communality value in the factor analysis output
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15 | 31
Factor Analysis Output (cont)
• The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor.
– Note that the eigenvalue is not the percent of variance explained but the amount of variance in relation to total variance – (since variables are standardized to have means of 0 and variances of 1, total variance is equal to the number of variables). – SPSS will output a corresponding column titled '% of variance'. A factor's eigenvalue may be computed as the sum of its squared factor loadings for all the variables.
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 32
Potential Applications of Factor Analysis
• Used to
– Develop concise but comprehensive, multipleitem scales for measuring various marketing constructs – Illuminate the nature of distinct dimensions underlying an existing data set – Convert a large volume of data into a set of factor scores on a limited number of uncorrelated factors
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15 | 35
Cluster Analysis
• Segment objects into groups so that members within each group are similar to one another in a variety of ways • Useful for segmenting customers, market areas, and products
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 36
Use of Cluster Analysis
• Firm offering recreational services wanted to enter a new region of the country • They gathered data on more than 100 characteristics including
– – – – Demographics Expenditures on recreation Leisure time activities Interests of household members
• The firm identified one or several household segments that are likely to be most responsive to its advertising and to its services
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 37
How Does Cluster Analysis Work?
• Cluster analysis measures the similarity between objects on the basis of their values on the various characteristics
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 38
Exhibit 15.8 Clusters Formed by Using Data on Two Characteristics
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 39
Multidemensional Scaling
• Uncovers key dimensions underlying customers' evaluations from a series of similarity and/or preference judgments provided by customers about products or brands within a given set
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 40
Multi-Dimensional Scaling on SUV’s
• A customer is asked to compare pairs of SUVs and rank the pairs from most similar to least similar
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 41
Table 15.5 Similarity Rankings of Six 2005 SUVs
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 42
Exhibit 15.9 Multidimensional Map of 2005 SUVs Based on Similarity Rankings
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 43
Conjoint Analysis
• Technique for deriving the utility values that customers presumably attach to different levels of an object's attributes • Requires respondents to compare hypothetical product profiles or, brands
– The hypothetical stimuli are descriptive profiles formed by systematically combining varying levels of certain key attributes
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 44
Personal Computer Study
• To assess the role played by attributes in customer evaluations of personal compters
– Price: 3 levels - $299, $649, $999 – Processor: 2 levels – 2.6 GHz , 2.8 GHz – Hard Drive: 4 levels - 80 GB, 120 GB, 160 GB, 200 GB
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 45
Personal Computer Study (Cont’d)
• 3 Levels of Price X, 2 Levels of Processor Speed X, 4 Levels of Hard Drive Capacity = 24 different descriptive profiles of personal computers are possible • Data Collection in Conjoint Analysis
– Two-Factors-at-a-Time Approach – Full-Profile Approach
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 46
Personal Computer Study: Full-Profile Approach
PERSONAL COMPUTER – DESKTOP Price $299 Speed 2.6 GHz Hard Drive 80 GB PERSONAL COMPUTER – DESKTOP Price $299 Speed 2.6 GHz Hard Drive 120 GB PERSONAL COMPUTER PERSONAL - DESKTOP COMPUTER -DESKTOP Price $299 Speed 2.6 GHz Hard Drive 160 GB Price $299 Speed 2.6 GHz Hard Drive 200 GB
Note: Customers are asked to rank order their preferences for the 24 different profiles representing all possible combinations of the three attributes
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 48
Exhibit 15.10 Utility Values for Three Personal -Computer Attributes
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 49
Exhibit 15.10 Utility Values for Three Personal - Computer Attributes (Cont’d)
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15 | 50
Relative Attributes of the 3 Attributes
• Range for price = 0.8 - 0.3 = 0.5
– Price is the most critical
• Range for hard drive capacity = 0.8 - 0.4 = 0.4
– Hard drive capacity is the next most critical
• Range for processor speed = 0.9 - 0.6 = 0.3
– Processor speed Ii the least critical
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15 | 51
Potential Attractiveness of Different Personal Computer Configurations
• PC Configuration A
– 2.6 GHz, 120 GB, $649 – Total utility for the personal computer = 0.6 + 0.7 + 0.4 = 1.7
• PC Configuration B
– 2.8 GHz, 160 GB, $999 – Total utility for the personal computer = 0.9 + 0.8 + 0.3 = 2.0
• Personal Computer B is more attractive
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 52
Overview of Other Multivariate Techniques and Data Mining
Dependence and Interdependence Techniques
• Dependence technique
– One variable is designated as the dependent variable and the rest are treated as independent variables
• Interdependence technique
– There are no dependent and independent variable designations, all variables are treated equally in a search for underlying patterns of relationships
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 2
Dependence Technique – Regression Analysis
• Input Data
– Dependent variable(s) - metric – Independent variable(s) - metric
• Primary Purpose of the Technique
– Ascertain the relative importance of independent variable(s) in explaining variation in the dependent variable – Predict dependentvariable values for given values of the independent variable(s)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 3
Table 15.1 Overview of Multivariate Techniques
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 4
Analysis of Variance
• ANOVA is appropriate in situations where the independent variable is set at certain specific levels (called treatments in an ANOVA context) and metric measurements of the dependent variable are obtained at each of those levels
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 5
Example
24 Stores Chosen randomly for the study 8 Stores randomly chosen for each treatment
Treatment 1
Store brand sold at the regular price
Treatment 2 Store brand sold at 50¢ off the regular price
Treatment 3
Store brand sold at 75¢ off the regular price
monitor sales of the store brand for a week in each store
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 6
Table 15.2 Unit Sales Data Under Three Pricing Treatments
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 7
After Only Design
EG1(R) EG2(R) EG3(R) X1 X2 X3 O1 O2 O3
EG1 -- Experiment Group 1, X1-- Regular Price EG2 -- Experiment Group 2, X2-- 50c off EG3 -- Experiment Group 3, X3-- 75c off O1 -- Observation (monitoring unit sales data in each store)
O2 -- Observation (monitoring unit sales data in each store)
O3 -- Observation (monitoring unit sales data in each store)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 8
After Only Design
EG1(R) EG2(R) EG3(R) X1 X2 X3 O1 O2 O3
X1-- Regular Price X2-- 50c off
EG1 -- Experiment Group 1,
EG2 -- Experiment Group 2,
EG3 -- Experiment Group 3,
X3-- 75c off
O1 -- Observation (monitoring unit sales data in each store) O2 -- Observation (monitoring unit sales data in each store) O3 -- Observation (monitoring unit sales data in each store)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 9
ANOVA –Grocery Store Hypothesis
• Grocery Store Example
– Ho 1 = 2 = 3 – Ha At least one is different from one or more of the others
• Hypotheses for K Treatment groups or samples
– Ho 1 = 2 = . . . = k – Ha At least one is different from one or more of the others
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 10
Bank Customer Perceptions Study
Bank Customers Gender
Male
< 35 Years > 64 Years < 35 Years
Female
35-64 Years > 64 Years
35-64 Years
Measure Overall Perceptions
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 12
Discriminant Analysis
• Identifies the distinguishing features of prespecified subgroups of units that are formed on the basis of some dependent variable • Examples of subgroups
– Heavy, moderate, and light users of a product – Homeowners and renters – Viewers and nonviewers of a television program
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 19
Discriminant Analysis (Cont’d)
• Dependent Variable
– Categorical: as many categories as there are subgroups
• Heavy, moderate, and light users: 3 categories • Independent Variable
– Metric-scaled
• Purpose of discriminant analysis is to classify new units into one of the subgroups given the new units’ values of the independent variable
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 20
Example
Computer Manufacturer
Household
income
Number of years of formal education
PC Ownership
Copyright © Houghton Mifflin Company. All rights reserved.
Not Owning A PC
15 | 21
Exhibit 15.3 Scatter Plot of Income and Education Data for Personal Computer Owners and Nonowners
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 22
Evaluating a Discriminant Function
• Confusion Matrix
– Indicates the degree of correspondence, or lack thereof, between the actual groupings of the sample units and the predicted groupings obtained by classifying the same units through the discriminant function
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 24
Table 15.3 Confusion Matrix
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 25
Usefulness of Discriminant Analysis
• Discriminant analysis is very useful for
– Defining customer segments – Identifying critical characteristics capable of distinguishing among them – Classifying prospective customers into appropriate segments
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 26
Factor Analysis
• A data and variable reduction technique that attempts to partition a given set of variables into groups of maximally correlated variables
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 27
Intuitive Explanation
• Consider two statements from the Star Brand Inc.(SBI) survey
– S1. “I have been satisfied with the Star products I have purchased” – S2. “When I have to purchase a home appliance in the future, it will likely be a Star product”
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 28
Factor Analysis Output and Its Interpretation
• Primary output of factor analysis is a factorloading matrix • Achieved Communality
– represents the proportion of variance in an original variable accounted for by all the extracted factors. – Each original variable will have an achieved communality value in the factor analysis output
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 31
Factor Analysis Output (cont)
• The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor.
– Note that the eigenvalue is not the percent of variance explained but the amount of variance in relation to total variance – (since variables are standardized to have means of 0 and variances of 1, total variance is equal to the number of variables). – SPSS will output a corresponding column titled '% of variance'. A factor's eigenvalue may be computed as the sum of its squared factor loadings for all the variables.
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 32
Potential Applications of Factor Analysis
• Used to
– Develop concise but comprehensive, multipleitem scales for measuring various marketing constructs – Illuminate the nature of distinct dimensions underlying an existing data set – Convert a large volume of data into a set of factor scores on a limited number of uncorrelated factors
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 35
Cluster Analysis
• Segment objects into groups so that members within each group are similar to one another in a variety of ways • Useful for segmenting customers, market areas, and products
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 36
Use of Cluster Analysis
• Firm offering recreational services wanted to enter a new region of the country • They gathered data on more than 100 characteristics including
– – – – Demographics Expenditures on recreation Leisure time activities Interests of household members
• The firm identified one or several household segments that are likely to be most responsive to its advertising and to its services
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 37
How Does Cluster Analysis Work?
• Cluster analysis measures the similarity between objects on the basis of their values on the various characteristics
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 38
Exhibit 15.8 Clusters Formed by Using Data on Two Characteristics
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 39
Multidemensional Scaling
• Uncovers key dimensions underlying customers' evaluations from a series of similarity and/or preference judgments provided by customers about products or brands within a given set
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 40
Multi-Dimensional Scaling on SUV’s
• A customer is asked to compare pairs of SUVs and rank the pairs from most similar to least similar
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 41
Table 15.5 Similarity Rankings of Six 2005 SUVs
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 42
Exhibit 15.9 Multidimensional Map of 2005 SUVs Based on Similarity Rankings
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 43
Conjoint Analysis
• Technique for deriving the utility values that customers presumably attach to different levels of an object's attributes • Requires respondents to compare hypothetical product profiles or, brands
– The hypothetical stimuli are descriptive profiles formed by systematically combining varying levels of certain key attributes
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 44
Personal Computer Study
• To assess the role played by attributes in customer evaluations of personal compters
– Price: 3 levels - $299, $649, $999 – Processor: 2 levels – 2.6 GHz , 2.8 GHz – Hard Drive: 4 levels - 80 GB, 120 GB, 160 GB, 200 GB
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 45
Personal Computer Study (Cont’d)
• 3 Levels of Price X, 2 Levels of Processor Speed X, 4 Levels of Hard Drive Capacity = 24 different descriptive profiles of personal computers are possible • Data Collection in Conjoint Analysis
– Two-Factors-at-a-Time Approach – Full-Profile Approach
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 46
Personal Computer Study: Full-Profile Approach
PERSONAL COMPUTER – DESKTOP Price $299 Speed 2.6 GHz Hard Drive 80 GB PERSONAL COMPUTER – DESKTOP Price $299 Speed 2.6 GHz Hard Drive 120 GB PERSONAL COMPUTER PERSONAL - DESKTOP COMPUTER -DESKTOP Price $299 Speed 2.6 GHz Hard Drive 160 GB Price $299 Speed 2.6 GHz Hard Drive 200 GB
Note: Customers are asked to rank order their preferences for the 24 different profiles representing all possible combinations of the three attributes
Copyright © Houghton Mifflin Company. All rights reserved. 15 | 48
Exhibit 15.10 Utility Values for Three Personal -Computer Attributes
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 49
Exhibit 15.10 Utility Values for Three Personal - Computer Attributes (Cont’d)
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 50
Relative Attributes of the 3 Attributes
• Range for price = 0.8 - 0.3 = 0.5
– Price is the most critical
• Range for hard drive capacity = 0.8 - 0.4 = 0.4
– Hard drive capacity is the next most critical
• Range for processor speed = 0.9 - 0.6 = 0.3
– Processor speed Ii the least critical
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 51
Potential Attractiveness of Different Personal Computer Configurations
• PC Configuration A
– 2.6 GHz, 120 GB, $649 – Total utility for the personal computer = 0.6 + 0.7 + 0.4 = 1.7
• PC Configuration B
– 2.8 GHz, 160 GB, $999 – Total utility for the personal computer = 0.9 + 0.8 + 0.3 = 2.0
• Personal Computer B is more attractive
Copyright © Houghton Mifflin Company. All rights reserved.
15 | 52
