Chapter 17 Overview of Multivariate

Analysis Methods

Chapter 17 Overview of Multivariate

Analysis Methods

MULTIVARIATE ANALYSIS

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

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

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

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

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

variables are analyzed simultaneously.

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

variables are analyzed simultaneously.

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Classification of Multivariate Methods

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We’ve already discussed ANOVA, MANOVA, Correlation, Multiple Regression, and Perceptual Mapping.

We’ve already discussed ANOVA, MANOVA, Correlation, Multiple Regression, and Perceptual Mapping.

Summary of Multivariate Methods

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DEPENDENCE VS INTERDEPENDENCE METHODS

Examples: multiple regression analysis,

discriminant analysis, ANOVA and MANOVA

Examples: multiple regression analysis,

discriminant analysis, ANOVA and MANOVA

Dependence – multivariate techniques appropriate when one or more of the variables

can be identified as dependent variables and the

remaining as independent variables.

Dependence – multivariate techniques appropriate when one or more of the variables

can be identified as dependent variables and the

remaining as independent variables.

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Examples: factor analysis, cluster analysis, and

multidimensional scaling.

Examples: factor analysis, cluster analysis, and

multidimensional scaling.

Interdependence – multivariate statistical techniques in which a

set of interdependent relationships is examined – The

goal is grouping variables in some way.

Interdependence – multivariate statistical techniques in which a

set of interdependent relationships is examined – The

goal is grouping variables in some way.

FACTOR ANALYSIS

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

separately, not together.

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

separately, not together.

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

factors.

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

factors.

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

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

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FACTOR ANALYSIS PROCESS

Steps

Examine factor loadings & percentage of

variance

Examine factor loadings & percentage of

variance

Interpret & name factorsInterpret & name factors

Decide on number of factors

Decide on number of factors

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

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

These are the starting point for interpreting factor analysis.

These are the starting point for interpreting factor analysis.

Factor Loadings are correlations between the variables and the new composite factor.

Factor Loadings are correlations between the variables and the new composite factor.

They measure the importance of each variable relative to each composite factor.

They measure the importance of each variable relative to each composite factor.

Like correlations, factor loadings range from +1.0 to –1.0

Like correlations, factor loadings range from +1.0 to –1.0

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CLUSTER ANALYSIS

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

possible across groups.

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

possible across groups.

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

identifies natural groupings orsegments among many variables,

does NOT include a dependent variable.

identifies natural groupings orsegments among many variables,

does NOT include a dependent variable.17-9

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CLUSTER ANALYSIS

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SPSS DIALOG BOX FOR CLUSTER ANALYSIS

CoefficientsCoefficients

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CLUSTER ANALYSIS COEFFICIENTS

New New cluster cluster

variablevariable

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NEW CLUSTER VARIABLE

DISCRIMINANT ANALYSIS

Dependent variable – nonmetric or categorical (nominal or ordinal).

Dependent variable – nonmetric or categorical (nominal or ordinal).

It’s a dependence technique used for predicting group membership on the basis

of two or more independent variables.

It’s a dependence technique used for predicting group membership on the basis

of two or more independent variables.

Independent variables – metric (interval or ratio), but non-metric (nominal) dummy

variables are possible.

Independent variables – metric (interval or ratio), but non-metric (nominal) dummy

variables are possible.17-14

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DISCRIMINANT ANALYSIS

Characteristics Characteristics

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

dependent variable groups.

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

dependent variable groups.

Develops a linear combination of independent variables and uses it to

predict group membership.

Develops a linear combination of independent variables and uses it to

predict group membership.

Predicts categorical dependent variable based on group differences using a combination of independent

variables.

Predicts categorical dependent variable based on group differences using a combination of independent

variables.

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DISCRIMINANT ANALYSIS

Multipliers of variables in the

discriminant function when variables are in the original units of

measurement.

Multipliers of variables in the

discriminant function when variables are in the original units of

measurement.

Estimates of the discriminatory power

of a particular independent

variable.

Estimates of the discriminatory power

of a particular independent

variable.Discriminant

FunctionCoefficients

DiscriminantFunction

Coefficients

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DISCRIMINANT ANALYSIS

..

..

Classification (Prediction) Matrix – shows whether the estimated discriminant

function is a good predictor.

Shows the number of correctly and incorrectly classified cases .

The prediction is referred to as the hit ratio.

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DISCRIMINANT ANALYSIS SCATTER PLOT

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SPSS DIALOG BOX FOR DISCRIMINANT ANALYSIS

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SPSS DISCRIMINANT ANALYSIS OUTPUT

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SPSS DISCRIMINANT ANALYSIS OUTPUT

CONTINUED

Sample Conjoint Survey Profiles

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Importance Calculations for Restaurant Data

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Conjoint Part-Worth Estimates for Restaurant Survey

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