class factor analysis

8/14/2019 Class Factor Analysis

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Presentation on Factor Analysis


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1) Factor Analysis

2) Use and application

3) Statistics Associated with Factor Analysis

4) Conducting Factor Analysis

5)Applications of Common Factor Analysis

6) Example: Life Insurance

Content


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Factor Analysis

Factor analysis:For data reduction and summarization.

Factor analysis:Interdependence technique: No distinction between dependent andindependent variables.

Factor analysis is used in the following circumstances:

To identify underlying dimensions or factors.

To identify a new, smaller, set of uncorrelated variables to replace. (Reg. &DA)

For MA:a smaller set of salient variables from a larger set.


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Application in Market Research

Market segmentation : Economy , Performance,Comfort.

Product design:Brand attributes.

Pricing studies: Characteristics of price sensitivecustomer.

i i i d i h


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19-5Statistics Associated with FactorAnalysis

Bartlett's test of sphericity: Identity matirx Correlation matrix.

Communality. Eigenvalue. Factor loadings.. Factor loading plot. A factor loading plot is a plot

of the original variables using the factor loadings ascoordinates.

Factor matrix. Loadings of all the variables on all thefactors extracted.

Factor scores:Composite scores-- on derived factors.

S i i A i d i h F


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Kaiser-Meyer-Olkin (KMO) measure ofsampling adequacy. An index used toexamine the appropriateness of factoranalysis.

Percentage of variance. Thepercentage of the total variance attributedto each factor.

Residuals .

Scree plot. Eigenvalues Vs. number offactors in order of extraction.

Statistics Associated with FactorAnalysis


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Conducting Factor Analysis

Construction of the Correlation Matrix

After 2 tests-Method of Factor Analysis

Determination of Number of Factors

Determination of Model Fit

Problem formulation

Calculation ofFactor Scores

Interpretation of Factors

Rotation of Factors

Selection ofSurrogate Variables

Varia.&SS


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In principal components analysis,

(1)The total variance in the data is considered.

(2) PCA is recommended .

when the primary concern is to determine the minimumnumber of factors that will account for maximum variancein the data for use in subsequent multivariate analysis.

In common factor analysis:

(1)The factors are estimated based only on thecommon variance.

(2) Communalities are inserted in the diagonal of the

correlation matrix.(3) This method is appropriate when the primary

concern is to identify the underlying dimensions and thecommon variance is of interest.

Conducting Factor AnalysisDetermine the Method of Factor Analysis


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19-9Factors

Smaller no of factors : To Summarize theinformation.

How many

1. A priori: researcher knowledge.

2. Determination based on eigenvalue:- More than1.

3. Determination based on % of variance:at least60%

4. Determination based on Split-HalfReliability:Only factors with highcorrespondence of factor loading across the twosub sample are retained.


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19-10Factors

5. Determination based on scree plot :.

1 532 4 60

3

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Component number

E

I

G

E

N

V

A

L

U

E

Factors Eigenvalue

1 2.731

2 2.218

3 .442

4 .341

5 .183

6 .085

R lt f P i i l C t


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19-11Results of Principal ComponentsAnalysis

Communalities

Variables Ini

V1 1.V2 1.

V3 1.

Initial Eigen value

Amount of variance a variable shares.

Total variance associated with the factor

R lt f P i i l C t


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Extraction Sums o

Factor Eigen valu

1 2.732 2.21

Factor Matrix

Variables F

V1

Contains F Ls of all the variables on all the factors

extracted

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Rotate factor

Rotation: Factor matrix is transformed into simple one thatis easier to interpret

Rotation does not effect communalities and % of totalvariance.

Types of rotation:

Orthogonal:

Varimax- minimize no of variables with high loading ona factor

Oblique:

Rotation changes % of variance accounted by eachfactor.

Rotation Sums of S


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Conducting Factor AnalysisInterpret Factors

(1) A factor can then be interpreted interms of the variables that load high

on it.

(2)Another useful aid in interpretationis to plot the variables

19 15R lt f P i i l C t


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Rotated Facto

Variables F

V1V2

V3

Factor Score

Variables

V1-Prevents cavityV2-Shiny teeth

V3-Strengthen gums

V4-Freshens breath

V5-Prevention of tooth

decay is not animportant thing.

V6-Attractive teeth

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(1)A factor can then be interpreted in terms ofthe variables that load high on it.

(2)Another useful aid in interpretation is to plot

the variables

Conducting Factor AnalysisInterpret Factors

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Plot

1.0

0.5

0.0

-0.5

-1.0

Compo

nent

2

Component 1

Component Plot in RotatedSpace

1.0 0.5 0.0 -0.5 -1.0

V1

V3

V6

V2

V5

V4

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C d i l i


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The factor scores for the i th factor may beestimated

as follows:

F

i= W

i1X

1+ W

i2X

2+ W

i3X

3+ . . . + W

ikX

k

Fi = estimate of ith factor

Wi = factor score coefficient

Xi = ith standard variable.

Conducting Factor AnalysisCalculate Factor Scores

19 19Results of Principal Components


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The lower left triangle contains the reproducedcorrelation matrix; the diagonal, the communalities;the upper right triangle, the residuals between theobserved correlations and the reproducedcorrelations.

The lower left triangle contains the reproducedcorrelation matrix; the diagonal, the communalities;the upper right triangle, the residuals between theobserved correlations and the reproducedcorrelations.

Fact

Variables V1 19 20C d ti F t A l i


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Selection of S/S variable, involves singling out someof the original variables for use in subsequent analysis& interpret the result in terms of original variablesrather than factor scores.

By examining the factor matrix, one could select foreach factor the variable with the highest loading onthat factor. That variable could then be used as asurrogate variable for the associated factor.

However, the choice is not as easy if two or morevariables have similarly high loadings. In such a case,

the choice between these variables should be basedon theoretical and measurement considerations.

Conducting Factor AnalysisSelect Surrogate Variables

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C d ti F t A l i


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If there are many large residuals, the factormodel dies not provide a good fit to the dataand the model should be reconsidered .

Conducting Factor AnalysisDetermine the Model Fit

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