36847multivariate Techniques

8/9/2019 36847multivariate Techniques

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Amity Business School

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MULTIVARITE TECHNIQUES




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FACTOR ANALYSIS

A type of analysis used to discern the

underlying dimensions or regularity in

phenomena.

Its general purpose is to summarise the

information contained in a large number of variables into a smaller number of factors.




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If a researcher has a set of variables and

suspects that these variables are interrelated in

a complex fashion, then

-factor analysis may be used to untangle the

linear relationships into their separate patterns.

The statistical purpose of factor analysis is todetermine linear combinations of variables that

aid in investigating the interrelationships.




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EXAMPLE ±FACTOR ANALYSIS

Suppose a researcher collects a variety of data

on intermediaries' attitudes toward their working

relationship with a manufacturer.

Numerous questions about delivery, pricing

arrange-ments, discounts, sales personnel,

repair service, and other relevant issues are

asked.

-contd




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The researcher, however, wants to reduce the largenumber of variables to certain underlying constructs, or dimensions,that will summarize the importantinformation contained in the variables.

Thus, the researcher's pur-pose is to discover the basicstructure of a domain and to add substantiveinter-pretation to the underlying dimensions.

-contd




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Factor analysis accomplishes this by

combining the questions to create new,

more abstract variablescalled factors.

In general, the goal of factor analysis is

parsimony: to reduce a large number of

variables to as few dimensions or

constructs as possible.




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CONJOINT ANALYSIS




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Conjoint analysis is a technique used to identify

the most desirable combination of features to be

offered in a new product.

Conjoint analysis is done to determine what utility

a consumer attaches to attributes such as: Price (high, low,)

After sales service (frequent, monthly, yearly, guarantee)

Product features




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Conjoint analysis ± how it works

A consumer is asked to compare different productsattribute combinations and rank them. Respondents areto indicate the combination they most prefer, the second

most preferred, etc.

Conjoint analysis is applied to categorical variables,which reflect different features or characteristics of products. For example for a new product the featuresmay be:

Color (different shades)

Size (largest vs. medium vs. small)

Shape (square vs. cylindrical)

Price (different price levels)




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Factor analysis vs. conjoint

analysis It differs from factor analysis because it is

only applied to categorical variables. It is

similar to factor analysis in that it tries to

identify interdependencies between a

number of variables where the variables

are the different features.




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CLUSTER ANALYSIS

Cluster analysis is a term given to a body of techniques used toidentify objects or individuals that are similar with respect to somecriterion

The purpose of cluster analysis is to classify individuals or objectsinto a small number of mutually exclusive and exhaustive groups.

The researcher¶s focus is to determine how objects or individualsshould be assigned to groups to ensure that there will be as muchlikeness within groups and as much difference among groups as

possible. The cluster should have high internal (within-cluster)homogeneity and high external (between-cluster) heterogeneity.




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A typical use of cluster analysis is to

facilitate market segmentation by

identifying subjects or individuals who

have similar needs, lifestyles, or

responses to marketing strategies.




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Clusters, or subgroups, of recreational

vehi-cle owners may be identified on the

basis of their similarity of usage of and

benefits sought from recreational vehicles.

Alternatively, the researcher might use

demographic variables or lifestyle

variables to group individuals into clustersidentified as market segments.




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ILLUSTRATION- CLUSTER

We will illustrate cluster analysis with a hypothetical example relating to the types of vacations taken by 12 individuals.

Vacation behavior is represented on two dimensions: number of vacation days and Rupees expenditures onvacations during a given year.

Exhibit 1 is a scatter diagram that represents the geometric distance between the 12 individuals in two-dimensionalspace.

The scatter diagram portrays three clear-cut clusters.

The first subgroup, consisting of individuals L, H, and B, suggests a group of individuals who have many vacationdays but do not spend much money on their vacations.

The second cluster, consisting of individuals A, I, K, G, and F, represents intermediate values on both variables: anaverage number of vacation days and an average dollar expenditure on vacations.

The third group consists of a cluster oft individuals who have relatively few vacation days but who spend largeamounts on these outings.




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X- axis ± Rupee spend on expenditure

Y-axis- no. of vacations

Ly

HyBy

Ay Iy Ky

Gy Fy

Cy Jy

Ey Dy




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In this hypothetical example individuals are grouped onthe basis of their similarity or proximity to other individuals.

The logic of cluster analysis is to group individuals or objects on the bases of their similarity to or distance fromeach other.

The actual mathematical procedures for deriving clusterswill not be dealt with here, as our purpose is only tointroduce the technique.

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36847multivariate Techniques