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Chapter Nineteen MULTIVARIATE ANALYSIS: An Overview

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Title: Chapter Nineteen MULTIVARIATE ANALYSIS: An Overview


1
Chapter NineteenMULTIVARIATE ANALYSISAn
Overview
2
Two Types of Multivariate Techniques
  • Dependency
  • dependent (criterion) variables and independent
    (predictor) variables are present
  • Interdependency
  • variables are interrelated without designating
    some dependent and others independent

3
Dependency Techniques
  • Multiple regression
  • Discriminant analysis
  • Multivariate analysis of variance (MANOVA)
  • Linear structural relationships (LISREL)
  • Conjoint analysis

4
Multiple Regression
  • Extension of bivariate linear regression to
    include more than one independent variable.
  • Y ßo ß1 X1 ß2 X2 ß3X3 .. e
  • Use of multiple regression
  • Predict values for a criterion variable
    (dependent variable) by developing a
    self-weighting estimating equation.

5
Multiple Regression
  • Control for confounding variables to better
    evaluate the contribution of other variables
  • Test and explain causal theories
  • Path analysis
  • Method of least squares (minimizing the sum of
    squared error terms) are used as in bivariate
    regression
  • Coefficients (B) vs. standardized coefficients
    (beta weights)

6
Multiple Regression
  • Estimation Method
  • Enter method
  • includes all the variables in the order of
    variables entered.
  • Forward selection
  • starts with the constant and adds variables that
    results in the largest R2.
  • Backward selection
  • include all the variables and remove variable
    that change R2 the least.

7
Multiple Regression
  • Stepwise selection
  • The variable with the greatest explanatory power
    is added first. Subsequent variables are included
    according to their marginal (or incremental)
    contribution.
  • A variable entered can be removed later if it
    becomes insignificant at a given alpha.
  • This method which combines both forward and
    backward methods is the most popular method.

8
Multiple Regression
  • Tests
  • T- test for individual coefficients
  • Ho ßi 0, d.f. for t n-k-1
  • F-test for the overall model
  • Ho R2 0 d.f. for F (k, n-k-1)
  • As R2 increases, standard error (of the estimate)
    decreases. The smaller standard error, the
    better model.

9
Multiple Regression
  • Collinearity (or Multicollinearity) problem
  • What is it?
  • Situation where two or more independent variables
    are highly correlated.
  • What is consequence?
  • Unreliable regression coefficients
  • How to detect?
  • High correlation coefficients among independent
    variables (r gt.8 requires attention)

10
Multiple Regression
  • Collinearity problem continued
  • Collinearity statistics (VIF)
  • If VIFgt10, then multicollinearity suspicion
  • How to fix?
  • Choose one and delete another when two
    independent variables are highly correlated.
  • Create a new variable that is a composite of the
    two.

11
Multiple Regression
  • Autocorrelation problem
  • Commonly found in time series data
  • What is it? Error terms are correlated
  • What is consequence? Unreliable coefficients
  • How to detect? Visual detection, DW statistics
  • How to fix?
  • Taking the first difference
  • Taking logarithm
  • Lagged dependent variable as an additional
    independent variable

12
Multiple Regression
  • Use of dummy variables
  • Dummy variables are used when a nominal scale
    variable is to be included in the regression
  • When there are two categories of the variable,
    then one dummy variable is used.
  • When there are n categories, then n-1 dummy
    variables are used.

13
Discriminant Analysis
  • Use
  • Classify persons or objects into various groups.
  • Analyze known groups to determine the relative
    influence of specific factors (or variables)
  • Model
  • Similar to the multiple regression
  • Dependent variable nominal
  • One equation for two groups, two equations for
    three groups, and so on.
  • Independent variables interval or ratio

14
MANOVA
  • Assess relationship between two or more dependent
    variables and classificatory variables (or
    factors).
  • Examples measuring differences between
  • employees
  • customers
  • manufactured items
  • production parts

15
Uses of LISREL
  • Explains causality among constructs not directly
    measured
  • Two parts
  • Measurement model
  • Structural Equation model

16
Conjoint Analysis
  • Mainly used for market research and product
    development.
  • Evaluate a set of attributes to choose the
    product that best meets their needs

17
Interdependency Techniques
  • Factor analysis techniques to reduce many
    independent variables into a few manageable
    number.
  • Cluster analysis a set of techniques for
    grouping similar objects or people
  • Multidimensional Scaling (MDS) a special
    description of a participants perception about a
    product, service, or other object of interest

18
Factor Analysis
  • Computational techniques that reduce variables to
    a manageable number of factors that are not
    correlated with each other.
  • Principal components analysis is most popular
    construction of new set of variables (which are
    called factors) based on relationships in the
    correlation matrix.

19
Factor Analysiscontinued
  • Loading and communalities(h2)
  • Loading correlation between a variable and a
    factor
  • Communalities variance in each variable
    explained by all the factors
  • Eigenvalue
  • A measure of explanatory power of each factor
  • Eignevalue/ of variables of total variance
    explained by each factor

20
Factor Analysiscontinued
  • Rotation
  • To make pure constructs of each factor by
    focusing on a few major determinants of each
    factor.
  • To improve representations of variables by
    factors and to differentiate between factors.
  • Methods Orthogonal vs. oblique

21
Steps in Cluster Analysis
  • Select sample to be clustered
  • Define measurement variables (e.g. market segment
    characteristics)
  • Compute similarities among the entities through
    correlation, Euclidean distances, and other
    techniques
  • Select mutually exclusive clusters
  • Compare and validate the clusters

22
Multidimensional Scaling
  • a special description of a participants
    perception about a product, service, or other
    object of interest
  • Used in conjunction with cluster analysis or
    conjoint analysis.
  • Used to understand difficult-to-measure constructs
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