5682_4433_factor & cluster analysis.ppt

8/10/2019 5682_4433_Factor & Cluster Analysis.ppt

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Factor AnalysisFactor AnalysisA data reduction techniqueA data reduction technique

It is a techniqueIt is a technique applicable when there is a systematicapplicable when there is a systematic

dependence amongst a set of observed or manifestdependence amongst a set of observed or manifest

variablesvariablesand the researcher is interested in ndingand the researcher is interested in nding

outout something more fundamental (or latent) whichsomething more fundamental (or latent) whichcreates this commonalitycreates this commonality..

Epl! "everal individuals# income$ education$Epl! "everal individuals# income$ education$

occupation$ dwelling area having close correlationoccupation$ dwelling area having close correlation

could indicate that they are from one socio%economiccould indicate that they are from one socio%economicclass.class.


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&hus$ the&hus$ the substantive purpose of thesubstantive purpose of the

factor analysisfactor analysisisis

to search for and test of construct orto search for and test of construct or

dimensions assumed to underlie thedimensions assumed to underlie themanifest variablemanifest variableExample - 1:Example - 1:

"Proneness to purchase a brand" may not represent"Proneness to purchase a brand" may not represent

an observable variable directly. Rather one has toan observable variable directly. Rather one has toinfer from correlated measures.infer from correlated measures.

Statement :Statement : Strongly greeStrongly gree Strongly !isagree Strongly !isagree

1 11.1.

#.#.

$$..


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&he factor is the latent variable and&he factor is the latent variable and

summari'es the manifest variablessummari'es the manifest variables

Eple % !Eple % !e have several variables whiche have several variables which

in*uence the purchase decision of di+erentin*uence the purchase decision of di+erent

commodities in the mar,et or perception.commodities in the mar,et or perception.

"ee -uestionnaire A /"ee -uestionnaire A /

hether a group of variables or groups ofhether a group of variables or groups of

variables cluster around to eplain the buyingvariables cluster around to eplain the buying

behavior0 And what is the eplanatory power ofbehavior0 And what is the eplanatory power ofthese groups.these groups.

&hese questions necessitates a factor analysis.&hese questions necessitates a factor analysis.


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Example : %uying %ehaviour : RefrigeratorExample : %uying %ehaviour : Refrigerator

&ttributes rated in a ' point scale&ttributes rated in a ' point scale

1 2 3 4 5 6 7

Price

%rand (ame

)ultiple *emperature+ones

d,ustable racs andshelves

fter -sales service

Ease of maintenance

Refrigeration space

loor space occupied

/omputerised cooling

rost-free

!urability

Ease of cleaning


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Perception of )anagers to0ards a productPerception of )anagers to0ards a product

collected in a 1 point scalecollected in a 1 point scale

Variables 1 10

Product 2uality

E-/ommerce

*echnical Support

/omplaint Resolution

dvertising

Product 3ine

Salesforce 4mage

/ompetitive Pricing

5arranty 6 /laims

7rder 6 %illing

!elivery Speed


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1haracteristics1haracteristics

Factor Analysis see,s toFactor Analysis see,s to resolve a large set ofresolve a large set ofmeasured (manifest) variablesmeasured (manifest) variablesin terms ofin terms ofrelatively few categories ,nown asrelatively few categories ,nown as factorsfactors..

2o criterion or predictor subsets.2o criterion or predictor subsets.

Eamines theEamines the overall association amongstoverall association amongstvariablesvariables

/ased on/ased on linear correlationlinear correlationand assumesand assumes datadatain metric scale( interval or ratio)in metric scale( interval or ratio)

It serves the purpose ofIt serves the purpose of scientic parsimonyscientic parsimony.."ub3ectivity is involved in naming the factor"ub3ectivity is involved in naming the factor..


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4mportant )ethods for actor nalysis4mportant )ethods for actor nalysis

There areThere are several methodsseveral methods of factor analysisof factor analysis

The Centroid MethodThe Centroid Method

The Princial Comonent Method!The Princial Comonent Method!

Ma"im#m $i%elihood Method!Ma"im#m $i%elihood Method!&enerali'ed $east ()#are Method&enerali'ed $east ()#are Method! *tc! *tc

TheThe Princial Comonent method is +idely #sedPrincial Comonent method is +idely #sedinin

research st#dies!research st#dies!

,s the name s#--ests.,s the name s#--ests. the factors e"tracted #sin- thisthe factors e"tracted #sin- thismethod are in the order of imortance!method are in the order of imortance!


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, fe+ terms #sed in /actor ,nalysis, fe+ terms #sed in /actor ,nalysis

/actor/actort is ant is an #nderlyin- dimension that acco#nts for#nderlyin- dimension that acco#nts forseveral observed variables!several observed variables!

/actor $oadin-s/actor $oadin-s Val#es +hichVal#es +hich e"lain ho+ closely thee"lain ho+ closely thevariables are related to each one of the factor discovered!variables are related to each one of the factor discovered!,lso %no+n as,lso %no+n as factor variable correlation!factor variable correlation!

Comm#nality hComm#nality h22t sho+st sho+s ho+ m#ch each variable isho+ m#ch each variable isacco#nted for by the #nderlyin- factor ta%en intoacco#nted for by the #nderlyin- factor ta%en intoconsideration!consideration!

t is thet is the s#mmation of factor loadin- s)#ares on alls#mmation of factor loadin- s)#ares on allfactors e"tractedfactors e"tractedin case of a variable!in case of a variable!


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Few &erms (1ontd)Few &erms (1ontd)

Eigen 4alue! or latent root.Eigen 4alue! or latent root.

hen we ta,e thehen we ta,e the sum of the squaredsum of the squaredvalues of factor loadings relating to avalues of factor loadings relating to afactorfactor$ then such sum is referred to as$ then such sum is referred to as

Eigen 4alue.Eigen 4alue.

ItIt indicates the relative importance of aindicates the relative importance of afactorfactorwhen 5rincipal 1omponent 6ethodwhen 5rincipal 1omponent 6ethod

is used.is used.

Eigen value divided by the number ofEigen value divided by the number ofvariables gives the percent variation.variables gives the percent variation.


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Issues Involved in FactorIssues Involved in Factor

AnalysisAnalysis

7otation!7otation! &here are di+erent types of rotation&here are di+erent types of rotationwhich are used in factor analysis.which are used in factor analysis.

AnAn un%rotatedun%rotatedfactor matri does not give cleanfactor matri does not give clean

set of factor loadingset of factor loading i.e. iti.e. it may have large crossmay have large crossloadingloadingoror large loading on one factor.large loading on one factor.

AA rotated factor matri changes this structurerotated factor matri changes this structureand maimi'es loading of each variable on oneand maimi'es loading of each variable on one

factor.factor.

4arima rotation is widely used4arima rotation is widely used. Epl88. Epl88


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8nrotated /omponent )atrix8nrotated /omponent )atrix

Variables 1 2 3 4Prod#ct #ality !24 !501 !01 !670

*Commerce !307 !713 !306 !24

Technical (#ort !22 !36 !74 !202

Comlaint 8esol#tion !71 !031 !274 !215

,dvertisin- !340 !51 !115 !331

Prod#ct $ine !716 !455 !151 !212

(alesforce ma-e !377 !752 !314 !232

Cometitive Pricin- !21 !660 !06 !34

9arranty : Claims !34 !306 !77 !13

;rder :


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Rotated /omponent )atrixRotated /omponent )atrix

Variables 1 2 3 4

Comlaint 8esol#tion !33

=elivery (eed !31

;rder :


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4ssues involved&/ontd94ssues involved&/ontd9

9efault Eigen value and changing it.9efault Eigen value and changing it.

"electing a cut o+ point for factor loading."electing a cut o+ point for factor loading.

&wo views&wo views!! :.;; or :. 2o of4ariables used.4ariables used.


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7eporting Analysing the factor7eporting Analysing the factor

out putout putFactor ?( 2ame@@@@@@@..)Factor ?( 2ame@@@@@@@..)

4ariable ? ( :.B)4ariable ? ( :.B)

4ariable C (:.D?)4ariable C (:.D?)

4ariable D (:.


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*"le 1! (#mmary of /actors*"le 1! (#mmary of /actors

Factor ? % 5ost sale 1ustomer "erviceFactor ? % 5ost sale 1ustomer "ervice ::Complaint Resolution, Delivery Speed and OrderComplaint Resolution, Delivery Speed and Order

and Billingand Billing

Factor % 6ar,etingFactor % 6ar,eting : Salesforce Image, !: Salesforce Image, !commerce "resence and #dvertisingcommerce "resence and #dvertising

Factor ; % &echnical "upportFactor ; % &echnical "upport : $echnical: $echnical

Support and %arranty and ClaimsSupport and %arranty and Claims

Factor C % 5roduct 4alueFactor C % 5roduct 4alue : "roduct &uality and: "roduct &uality and

Competitive BiddingCompetitive Bidding


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Example #Example #

Factor ? (pmar,etness)Factor ? (pmar,etness)

Epensive (:.:)Epensive (:.:)

1elebrity endorsement (:.D)1elebrity endorsement (:.D)

Eclusive show room ( :.B)Eclusive show room ( :.B)

Factor (Goyalty)Factor (Goyalty)

/rand Goyalty ( :.?)/rand Goyalty ( :.?)

"tore Goyalty (:.


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1luster Analysis1luster Analysis

A classicatory techniqueA classicatory technique

1luster Analysis1luster Analysisclassies ob3ectsclassies ob3ects e.g.e.g.

respondents$ products or entitiesrespondents$ products or entities so that eachso that each

ob3ect is very similar to others within the clusterob3ect is very similar to others within the cluster

with respect to some predetermined selectionwith respect to some predetermined selection

criterion or variable specied.criterion or variable specied.

&he&he resulting clusters of ob3ects ehibitresulting clusters of ob3ects ehibit highhigh

internal (within the cluster) homogeneityinternal (within the cluster) homogeneityandand highhigh

eternal (between the cluster) heterogeneity.eternal (between the cluster) heterogeneity.

Hne can determine how manyHne can determine how many mutually eclusivemutually eclusive

groups or clustersgroups or clusters are there in the sample orare there in the sample or

population.population.


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"ignicant Features of 1luster"ignicant Features of 1luster

AnalysisAnalysis

1luster variate1luster variateis theis the set of variables used toset of variables used to

compare ob3ects in the cluster analysiscompare ob3ects in the cluster analysis..

It is aIt is a multivariate techniquemultivariate technique thatthat does notdoes not

estimate the variate empiricallyestimate the variate empiricallybut insteadbut insteaduses variate specied by the researcher.uses variate specied by the researcher.

1A di+ers from FA1A di+ers from FAin thatin that it groups ob3ects$it groups ob3ects$

whereas$ FA groups variables.whereas$ FA groups variables.

1A is1A is descriptive and non%inferential.descriptive and non%inferential.It is anIt is an

eploratory technique.eploratory technique.


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Features of 1A 1ontd@Features of 1A 1ontd@

&he&he solutions are not uniquesolutions are not uniqueas the clusteras the clustermembership may di+er with respect to themembership may di+er with respect to thevariables used.variables used. Addition or deletion of variablesAddition or deletion of variablescan have substantial impact on resulting solutions.can have substantial impact on resulting solutions.

&he&he Euclidian distanceEuclidian distancein thein the9endogram9endogram is usedis usedto nd clustersto nd clusters. It is. It is done manuallydone manuallyand severaland severaltrial error method is applied.trial error method is applied.

In general$ it isIn general$ it is3udgmental3udgmentalandand devoid ofdevoid of

statistical inference from sample to populationstatistical inference from sample to populationusing probability measures. owever$ theusing probability measures. owever$ the resultsresultsof a representative sample may be used forof a representative sample may be used forarriving at conclusions about the populationarriving at conclusions about the population..


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#nalysing a Cluster #nalysis out put'#nalysing a Cluster #nalysis out put'

9endogram is used to identify clusters9endogram is used to identify clusters

6ore the distance more the dissimilarities and6ore the distance more the dissimilarities andvice versavice versa..

7espondents in a particular cluster are ta,en7espondents in a particular cluster are ta,enout and the characteristics are tabulated.out and the characteristics are tabulated.

&he cluster characteristics could be di+erent.&he cluster characteristics could be di+erent.owever$owever$ sub3ective assessment has to be madesub3ective assessment has to be made

in identifying clustersin identifying clusters

&he clusters could become target groups for&he clusters could become target groups forintervention in the mar,et.intervention in the mar,et.


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#n e(ample using demographic#n e(ample using demographic

variables for clustering:variables for clustering:

#ge,Occupation,Income,(pdr#ge,Occupation,Income,(pdr..1luster ?1luster ?"tudents (5ost JraduateK6anagement)$ Age :%;:"tudents (5ost JraduateK6anagement)$ Age :%;:

yrs$yrs$

Annual spending on clothes 7s ;:::K%$.income


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Presentation of actor andPresentation of actor and

/luster nalysis/luster nalysis

*he groups are advised to use the data*he groups are advised to use the data

collected by them for actor and /lustercollected by them for actor and /luster

nalysis.nalysis.

!emographic or other variables may be!emographic or other variables may be

taen as clustering variables.taen as clustering variables.

*he summary of output 0ill be presented*he summary of output 0ill be presented

in the class for discussion.in the class for discussion.

5682_4433_factor & cluster analysis.ppt

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