chapter 17 overview of multivariate analysis methods
TRANSCRIPT
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Chapter 17 Overview of Multivariate
Analysis Methods
Chapter 17 Overview of Multivariate
Analysis Methods
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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.
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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.
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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
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CoefficientsCoefficients
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CLUSTER ANALYSIS COEFFICIENTS
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New New cluster cluster
variablevariable
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NEW CLUSTER VARIABLE
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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
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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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