McGraw-Hill/IrwinMcGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

Chapter 17Chapter 17 Overview of Multivariate Overview of Multivariate

Analysis MethodsAnalysis Methods

Chapter 17Chapter 17 Overview of Multivariate Overview of Multivariate

Analysis MethodsAnalysis Methods

1.1. Define multivariate analysis.Define multivariate analysis.

2.2. Understand when and why you Understand when and why you should use multivariate analysis in should use multivariate analysis in marketing research.marketing research.

3.3. Distinguish between dependence Distinguish between dependence and interdependence methods.and interdependence methods.

4.4. Apply factor analysis, cluster Apply factor analysis, cluster analysis, discriminant analysis and analysis, discriminant analysis and conjoint analysis to examine conjoint analysis to examine marketing research problems.marketing research problems.

Learning ObjectivesLearning Objectives

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Multivariate AnalysisMultivariate Analysis

These techniques are important in marketing research These techniques are important in marketing research because most business problems are multidimensional because most business problems are multidimensional

and can only be understood when multivariate and can only be understood when multivariate techniques are used.techniques are used.

These techniques are important in marketing research These techniques are important in marketing research because most business problems are multidimensional because most business problems are multidimensional

and can only be understood when multivariate and can only be understood when multivariate techniques are used.techniques are used.

. . . statistical techniques used when there are multiple . . . statistical techniques used when there are multiple measurements of each element/concept and the measurements of each element/concept and the

variables are analyzed simultaneously.variables are analyzed simultaneously.

. . . statistical techniques used when there are multiple . . . statistical techniques used when there are multiple measurements of each element/concept and the measurements of each element/concept and the

variables are analyzed simultaneously.variables are analyzed simultaneously.

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Classification of Multivariate MethodsClassification of Multivariate Methods

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Summary of Selected Multivariate Summary of Selected Multivariate MethodsMethods

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Multivariate TechniquesMultivariate TechniquesMultivariate TechniquesMultivariate Techniques

InterdependenceInterdependenceInterdependenceInterdependence DependenceDependenceDependenceDependence

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Dependence MethodsDependence Methods

Examples: multiple regression analysis, Examples: multiple regression analysis, discriminant analysis, ANOVA and MANOVAdiscriminant analysis, ANOVA and MANOVA

Examples: multiple regression analysis, Examples: multiple regression analysis, discriminant analysis, ANOVA and MANOVAdiscriminant analysis, ANOVA and MANOVA

. . . multivariate techniques appropriate when . . . multivariate techniques appropriate when one or more of the variables can be identified one or more of the variables can be identified as dependent variables and the remaining as as dependent variables and the remaining as

independent variables.independent variables.

. . . multivariate techniques appropriate when . . . multivariate techniques appropriate when one or more of the variables can be identified one or more of the variables can be identified as dependent variables and the remaining as as dependent variables and the remaining as

independent variables.independent variables.

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Interdependence Interdependence MethodsMethods

Goal of these methods – to group variables Goal of these methods – to group variables together into variates.together into variates.

Examples: cluster analysis, factor analysis, Examples: cluster analysis, factor analysis, and multidimensional scaling.and multidimensional scaling.

Goal of these methods – to group variables Goal of these methods – to group variables together into variates.together into variates.

Examples: cluster analysis, factor analysis, Examples: cluster analysis, factor analysis, and multidimensional scaling.and multidimensional scaling.

. . . multivariate statistical techniques in which a . . . multivariate statistical techniques in which a set of interdependent relationships is examined set of interdependent relationships is examined

– analysis involves either the independent or – analysis involves either the independent or dependent variables separately.dependent variables separately.

. . . multivariate statistical techniques in which a . . . multivariate statistical techniques in which a set of interdependent relationships is examined set of interdependent relationships is examined

– analysis involves either the independent or – analysis involves either the independent or dependent variables separately.dependent variables separately.

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Factor AnalysisFactor Analysis

Purpose – to simplify the data.Purpose – to simplify the data.Dependent and independent variables are Dependent and independent variables are

analyzed separately, not together.analyzed separately, not together.

Purpose – to simplify the data.Purpose – to simplify the data.Dependent and independent variables are Dependent and independent variables are

analyzed separately, not together.analyzed separately, not together.

. . . used to summarize information . . . used to summarize information contained in a large number of variables into contained in a large number of variables into

a smaller number of subsets or factors.a smaller number of subsets or factors.

. . . used to summarize information . . . used to summarize information contained in a large number of variables into contained in a large number of variables into

a smaller number of subsets or factors.a smaller number of subsets or factors.

All variables being examined are analyzed All variables being examined are analyzed together – to identify underlying factors.together – to identify underlying factors.

All variables being examined are analyzed All variables being examined are analyzed together – to identify underlying factors.together – to identify underlying factors.

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A Factor Analysis Application to a A Factor Analysis Application to a Fast-Food RestaurantFast-Food Restaurant

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Factor AnalysisFactor Analysis

StepsSteps

Examine factor Examine factor loadings & loadings &

percentage of percentage of variancevariance

Examine factor Examine factor loadings & loadings &

percentage of percentage of variancevariance

Interpret & name factorsInterpret & name factorsInterpret & name factorsInterpret & name factors

Decide on number of Decide on number of factorsfactors

Decide on number of Decide on number of factorsfactors

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Factor loadings are calculated between all Factor loadings are calculated between all factors and each of the original variables.factors and each of the original variables.

Factor loadings are calculated between all Factor loadings are calculated between all factors and each of the original variables.factors and each of the original variables.

Starting point for interpreting factor analysis.Starting point for interpreting factor analysis.Starting point for interpreting factor analysis.Starting point for interpreting factor analysis.

Factor Loadings = correlations between Factor Loadings = correlations between the variables and the new composite the variables and the new composite

factor.factor.

Factor Loadings = correlations between Factor Loadings = correlations between the variables and the new composite the variables and the new composite

factor.factor.

Measure the importance of each variable relative Measure the importance of each variable relative to each composite factor.to each composite factor.

Measure the importance of each variable relative Measure the importance of each variable relative to each composite factor.to each composite factor.

Like correlations – factor loadings vary from Like correlations – factor loadings vary from +1.0 to –1.0+1.0 to –1.0

Like correlations – factor loadings vary from Like correlations – factor loadings vary from +1.0 to –1.0+1.0 to –1.0

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Factor Loadings for the Two FactorsFactor Loadings for the Two Factors

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Percentage of Variation in Original Percentage of Variation in Original Data Explained by Each FactorData Explained by Each Factor

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Factor Analysis Applications in Marketing Factor Analysis Applications in Marketing Research . . . Research . . . AdvertisingAdvertising – – to better understand to better understand

media habits of various customersmedia habits of various customersPricingPricing – – to identify the characteristics to identify the characteristics

of price-sensitive and prestige-of price-sensitive and prestige-sensitive customerssensitive customers

ProductProduct – – to identify brand attributes to identify brand attributes that influence consumer choicethat influence consumer choice

DistributionDistribution – – to better understand to better understand channel selection criteria among channel selection criteria among distribution channel membersdistribution channel members

Interdependence Interdependence TechniquesTechniques

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SPSS Dialog Boxes for Factor SPSS Dialog Boxes for Factor AnalysisAnalysis

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SPSS Output for Factor Analysis of SPSS Output for Factor Analysis of Restaurant PerceptionsRestaurant Perceptions

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Factor Scores for Factor Scores for Restaurant PerceptionsRestaurant Perceptions

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SPSS Dialog Boxes for Regression SPSS Dialog Boxes for Regression with Factor Scoreswith Factor Scores

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Multiple Regression with Factor Scores Multiple Regression with Factor Scores – Descriptive Statistics– Descriptive Statistics

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Cluster AnalysisCluster Analysis

. . . classifies or segments objects into . . . classifies or segments objects into groups that are similar within groups and as groups that are similar within groups and as

different as possible between segments.different as possible between segments.

. . . classifies or segments objects into . . . classifies or segments objects into groups that are similar within groups and as groups that are similar within groups and as

different as possible between segments.different as possible between segments.

. . . classifies objects into relatively . . . classifies objects into relatively homogeneous groups based on the set of homogeneous groups based on the set of

variables analyzed.variables analyzed.

. . . classifies objects into relatively . . . classifies objects into relatively homogeneous groups based on the set of homogeneous groups based on the set of

variables analyzed.variables analyzed.

. . . identifies natural groupings or segments . . . identifies natural groupings or segments among many variables, none of which are among many variables, none of which are considered a dependent variable.considered a dependent variable.

. . . identifies natural groupings or segments . . . identifies natural groupings or segments among many variables, none of which are among many variables, none of which are considered a dependent variable.considered a dependent variable.

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Multiple Regression with Factor Multiple Regression with Factor Scores – Model ResultsScores – Model Results

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Cluster AnalysisCluster Analysis

Distance between any pair Distance between any pair of points is related to how of points is related to how similar the corresponding similar the corresponding

objects are when the objects are when the clustering variables are clustering variables are

compared.compared.

Distance between any pair Distance between any pair of points is related to how of points is related to how similar the corresponding similar the corresponding

objects are when the objects are when the clustering variables are clustering variables are

compared.compared.

Degree of similarity Degree of similarity between objects is between objects is

determined based on a determined based on a distance measure.distance measure.

Degree of similarity Degree of similarity between objects is between objects is

determined based on a determined based on a distance measure.distance measure.

StatisticalStatisticalProcedureProcedureStatisticalStatisticalProcedureProcedure

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Applications in Marketing ResearchApplications in Marketing ResearchNew product researchNew product research – to examine – to examine

product offerings relative to the competition.product offerings relative to the competition.Test marketingTest marketing – to group test cities into – to group test cities into

homogeneous clusters for test marketing homogeneous clusters for test marketing purposes.purposes.

Buyer behaviorBuyer behavior – to identify similar groups – to identify similar groups of buyers who have similar choice criteria.of buyers who have similar choice criteria.

Market segmentationMarket segmentation – to develop – to develop distinct market segments on the basis of distinct market segments on the basis of geographic, demographic, psychographic, geographic, demographic, psychographic, and behavioral variables.and behavioral variables.

Interdependence TechniquesInterdependence Techniques

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Cluster Analysis Based on Two Cluster Analysis Based on Two CharacteristicsCharacteristics

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SPSS Dialog Boxes for SPSS Dialog Boxes for Cluster AnalysisCluster Analysis

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Cluster Analysis Agglomeration Cluster Analysis Agglomeration ScheduleSchedule

CoefficientsCoefficients

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New New cluster cluster

variablevariable

New Cluster Variable to Identify New Cluster Variable to Identify Group MembershipGroup Membership

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Comparing Cluster Means Comparing Cluster Means Using ANOVAUsing ANOVA

SPSS Dialog BoxesSPSS Dialog Boxes

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Discriminant AnalysisDiscriminant Analysis

Dependent variable – nonmetric or Dependent variable – nonmetric or categorical.categorical.

Dependent variable – nonmetric or Dependent variable – nonmetric or categorical.categorical.

. . . dependence technique used for . . . dependence technique used for predicting group membership on the basis of predicting group membership on the basis of

two or more independent variables.two or more independent variables.

. . . dependence technique used for . . . dependence technique used for predicting group membership on the basis of predicting group membership on the basis of

two or more independent variables.two or more independent variables.

Independent variables – metric, but non-Independent variables – metric, but non-metric dummy variables are possible.metric dummy variables are possible.

Independent variables – metric, but non-Independent variables – metric, but non-metric dummy variables are possible.metric dummy variables are possible.

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SPSS ANOVA Output – Results for SPSS ANOVA Output – Results for Cluster of X23 – X24Cluster of X23 – X24

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Discriminant AnalysisDiscriminant Analysis

Characteristics Characteristics Characteristics Characteristics

Discriminant function – a linear Discriminant function – a linear combination of independent variables combination of independent variables that bests discriminates between the that bests discriminates between the

dependent variable groups.dependent variable groups.

Discriminant function – a linear Discriminant function – a linear combination of independent variables combination of independent variables that bests discriminates between the that bests discriminates between the

dependent variable groups.dependent variable groups.

. . . develops a linear combination of . . . develops a linear combination of independent variables and uses it to independent variables and uses it to

predict group membership.predict group membership.

. . . develops a linear combination of . . . develops a linear combination of independent variables and uses it to independent variables and uses it to

predict group membership.predict group membership.

. . . predicts categorical dependent . . . predicts categorical dependent variable based on group differences variable based on group differences

using a linear combination of using a linear combination of independent variables.independent variables.

. . . predicts categorical dependent . . . predicts categorical dependent variable based on group differences variable based on group differences

using a linear combination of using a linear combination of independent variables.independent variables.

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Discriminant score (Z-score)Discriminant score (Z-score) – – basis for basis for predicting to which group the particular individual predicting to which group the particular individual belongs and is determined by a linear function. belongs and is determined by a linear function. Each respondent is assigned a score by the Each respondent is assigned a score by the calculated discriminant function.calculated discriminant function.

ZZii == bb11XX1i1i + b + b22XX2i2i ⋅ ⋅ ⋅ + b ⋅ ⋅ ⋅ + bnnXXnini

ZZii = ith individual’s discriminant score= ith individual’s discriminant score

bbnn = discriminant coefficient for the nth = discriminant coefficient for the nth variablevariable

XXnini = individual’s value on the nth independent = individual’s value on the nth independent variablevariable

Analysis of Dependence

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Discriminant Discriminant AnalysisAnalysis

. . . multipliers of . . . multipliers of variables in the variables in the

discriminant function discriminant function when variables are in when variables are in the original units of the original units of

measurement.measurement.

. . . multipliers of . . . multipliers of variables in the variables in the

discriminant function discriminant function when variables are in when variables are in the original units of the original units of

measurement.measurement.

. . . estimates of the . . . estimates of the discriminatory discriminatory

power of a particular power of a particular independent independent

variable.variable.

. . . estimates of the . . . estimates of the discriminatory discriminatory

power of a particular power of a particular independent independent

variable.variable.DiscriminantDiscriminantFunctionFunction

CoefficientsCoefficients

DiscriminantDiscriminantFunctionFunction

CoefficientsCoefficients

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Discriminant AnalysisDiscriminant Analysis

..

..

Classification (Prediction) Matrix – Classification (Prediction) Matrix – shows whether the estimated discriminant shows whether the estimated discriminant

function is a good predictor.function is a good predictor.

. . . shows the number of correctly . . . shows the number of correctly and incorrectly classified cases .and incorrectly classified cases .

. . . the prediction is . . . the prediction is referred to as the hit ratio.referred to as the hit ratio.

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Discriminant Analysis Scatter Plot Discriminant Analysis Scatter Plot of Lifestyle and Income Data for of Lifestyle and Income Data for Fast-Food Restaurant PatronageFast-Food Restaurant Patronage

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Classification Matrix for BYB Patrons Classification Matrix for BYB Patrons and Non-patronsand Non-patrons

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Applications for Marketing ResearchApplications for Marketing ResearchProduct researchProduct research – to distinguish – to distinguish

between heavy, medium, and light users of a between heavy, medium, and light users of a product in terms of their consumption habits product in terms of their consumption habits and lifestyles.and lifestyles.

Image researchImage research – to discriminate – to discriminate between customers that exhibit favorable between customers that exhibit favorable perceptions of a store or company and those perceptions of a store or company and those who do not.who do not.

Advertising researchAdvertising research – to determine – to determine how market segments differ in media how market segments differ in media consumption habits.consumption habits.

Direct marketingDirect marketing – to identify – to identify characteristics of consumers who respond to characteristics of consumers who respond to direct marketing solicitations and those who do direct marketing solicitations and those who do not.not.

Analysis of Dependence

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SPSS Dialog Boxes for SPSS Dialog Boxes for Discriminant Analysis Discriminant Analysis

Comparing Two RestaurantsComparing Two Restaurants

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SPSS Discriminant Analysis of Favorite SPSS Discriminant Analysis of Favorite Mexican RestaurantMexican Restaurant

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Discriminant Output for Favorite Mexican Discriminant Output for Favorite Mexican Restaurant (continued)Restaurant (continued)

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Group Means for Favorite Mexican Group Means for Favorite Mexican Restaurants (continued)Restaurants (continued)

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Discriminant Analysis of Customer Discriminant Analysis of Customer Loyalty Clusters and Nutrition Loyalty Clusters and Nutrition

Lifestyle VariablesLifestyle Variables

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Discriminant Analysis – Customer Discriminant Analysis – Customer Loyalty ClustersLoyalty Clusters

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Nutrition Variable Means for Nutrition Variable Means for Customer Loyalty ClustersCustomer Loyalty Clusters

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Sample Conjoint Survey ProfilesSample Conjoint Survey Profiles

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Conjoint Part-Worth Estimates for Conjoint Part-Worth Estimates for Restaurant SurveyRestaurant Survey

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Importance Calculations for Importance Calculations for Restaurant DataRestaurant Data

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