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1.Define multivariate analysis.

2.Understand how to use multivariate analysis in marketing research.

3.Distinguish between dependence and interdependence methods.

4.Define and understand factor analysis and cluster analysis.

5.Define and use discriminant analysis.Learning Objectives

McGraw-Hill/Irwin

Multivariate analysis--statistical techniques used when there are two or more measurements of each element and the variables are analyzed simultaneously. Multivariate techniques are concerned with the simultaneous relationships among two or more phenomena.

Important in marketing research because most business problems are multidimensional

Define multivariate analysisValue of Multivariate Techniques in Data Analysis

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Exhibit 17.1Define multivariate analysis

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Exhibit 17.2Define multivariate analysis

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Dependence Method multivariate technique appropriate when one or more of the variables can be identified as dependent variables and the remaining as independent variables

Dependence techniquesmultiple regression analysis, discriminant analysis, and MANOVA

Multiple discriminant analysisdependence technique which predicts customer usage based on several independent variablesAge, income, peer group, education, lifestyle.

Dependence MethodClassification Multivariate Techniques

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Interdependence techniques multivariate statistical techniques in which a whole set of interdependent relationships is examinedNo single variable is defined as dependent or independent

Multivariate procedureanalysis of all variables in the data set simultaneously

Goal of this methodto group things togetherSimplify data

No one variable is predicted or explained by the others

Interdependence techniques factor analysis, cluster analysis, Perceptual Mapping and multidimensional scalingInterdependence techniquesClassification Multivariate Techniques

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Nature of the Measurement Scales

Determine which multivariate technique is appropriate to analyze the data Dependence vs. Interdependence

Dependent variable

Measured nonmetrically(Nominal)Discriminant analysis, Conjoint

Measured metrically (ratio or interval) multiple regression, ANOVA, and MANOVA

First StepClassification Multivariate Techniques

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Independent variable

Require metric independent variablemultiple regression and discriminant analysiscan use nonmetric dummy variables

Nonmetric independent variablesANOVA and MANOVA

Metrically measured variables and nonmetric adaptionsfactor analysis and cluster analysis

Classification Multivariate Techniques

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Factor Analysisused to summarize information contained in a large number of variables into a smaller number of subsets or factors

Purpose of Factor Analysisto simplify the data

No distinction between dependent and independent variables

all variables under investigation are analyzed togetherto identify underlying factors

Factor Analysis Interdependence Techniques

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Factor Analysis Exhibit 17.3

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Factor Loadingsimple correlation between the variables

Starting Pointinterpreting factor analysis is factor loadings

Factor loadingmeasure of the importance of the variable in measuring each factor

Like correlationsvary from +1.0 to 1.0

Statistical analysis associated with factor analysisproduces factor loadings between each factor and each of the original variablesFactor Analysis Interdependence Techniques

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Factor Analysis Exhibit 17.4

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Next Step in Factor Analysisname the resulting factorsFactor 1 Service QualityFactor 2 Food Quality

Final Aspect of Factor Analysisthe number of factors to retain

Factor Analysis Interdependence Techniques

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Factor Analysis Exhibit 17.5

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Factor Analysis Applications in Marketing Research

Advertisingto better understand media habits of various customers

Pricingto identify the characteristics of price-sensitive and prestige-sensitive customers

Productto identify brand attributes that influence consumer choice

Distributionto better understand channel selection criteria among distribution channel members

Define and understand factor analysis and cluster analysisInterdependence Techniques

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Define and understand factor analysis and cluster analysisExhibit 17.6

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Define and understand factor analysis and cluster analysisExhibit 17.7

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Define and understand factor analysis and cluster analysisExhibit 17.8

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Define and understand factor analysis and cluster analysisExhibit 17.9

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Define and understand factor analysis and cluster analysisExhibit 17.10

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Cluster analysismultivariate interdependence technique whose primary objective is to classify objects into relatively homogeneous groups based on the set of variables considered

Basic Purpose

To classify or segment objects into groups so that objects within each group are similar to one another on a variety of variables

To classify segments or objects such that there will be as much similarity within segments and as much difference between segments as possible

To identify natural groupings or segments among many variables, without designating any of the variables as a dependent variable

Cluster analysisInterdependence Techniques

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Cluster analysisExhibit 17.11

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Statistical Procedures for Cluster Analysis

Degree of similarity between objectsdetermined through a distance measure

Distance between any pair of points is positively related to how similar the corresponding individuals are when the two variables are considered together

Cluster analysisInterdependence Techniques

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Clustersdeveloped from scatter plots

This is a very complex, trial and error process

Requires the use of computer algorithmsCluster analysis Scatter PlotsInterdependence Techniques

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Applications in Marketing Research

New product researchto examine product offerings relative to competition

Test marketingto group test cities into homogeneous clusters for test marketing purposes

Buyer behaviorto identify similar groups of buyers who have similar choice criteria

Market segmentationto develop distinct market segments on the basis of geographic, demographic, psychographic, and behavioral variablesCluster analysisInterdependence Techniques

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Define and understand factor analysis and cluster analysisExhibit 17.12

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SPSS exercise Use the Santa Fe databaseFind different subgroups of customers with different levels of commitmentUse Variables 22, 23,24Anaylse-classify-hierarchical clusterSelect wards methodSave box select 2 This procedure takes time

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Define and understand factor analysis and cluster analysisExhibit 17.13

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Define and understand factor analysis and cluster analysisExhibit 17.14

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Define and understand factor analysis and cluster analysisExhibit 17.15

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End Here

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Discriminant Analysismultivariate procedure used for predicting group membership on the basis of two or more independent variables

Purposeto classify objects or groups by a set of independent variables

Dependent variablenonmetric or categorical

Independent variablesmetric

Define and use discriminant analysisAnalysis of Dependence

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Define and understand factor analysis and cluster analysisExhibit 17.17

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Purpose of discriminant analysisprediction of a categorical variable by studying the direction of group differences based on finding a linear combination of independent variables

Discriminant functionlinear combination of independent variables developed by discriminant analysis which will best discriminate between the categories of the dependent variable

Discriminate analysisstatistical tool for determining linear combinations of those independent variables and using this to predict group membership

Define and use discriminant analysisAnalysis of Dependence

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Discriminant score (Z-score)basis for predicting to which group the particular individual belongs and is determined by a linear functionZi=b1X1i + b2X2i + bnXni

Zi=ith individuals discriminant score

bn=Discriminant coefficient for the nth variable

Xni=Individuals value on the nth independent variable

Discriminant scorethe score of each respondent on the discriminant function

Define and use discriminant analysisAnalysis of Dependence

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Discriminant function coefficientsestimates of the discriminatory power of a particular independent variable

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

Coefficientscomputed by means of the discriminant analysis software

Define and use d