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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
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