rm fa explained

8/3/2019 RM FA Explained

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Factor Analysis data reduction technique

Too many variables

Correlated among

themselves

Fewer factors/PCs

Not correlated

among themselves

PC 1

F 1

PC 2

F 2


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Rate each of the following features on their importance, as

per your opinion. 1 least important, 7 most important.

ATM 1 2 3 4 5 6 7

Internet 1 2 3 4 5 6 7

Phone 1 2 3 4 5 6 7

Mobile

In-house

Forex

Retail

CRM

Parking

Approach road 1 2 3 4 5 6 7


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ATM Int Ph Mb In-hs Forex Retail CRM Park Rd

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7 2 1 6

PASW data sheet

Correlation coefficient = 0.379


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PASW output

Correlation Matrix

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proach

Step 1: data screening - using correlation matrix

Example 1 UBI Customer Services


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KMO and Bartlett's Test

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Kaiser-Meyer-Olkin Measure of Sampling

Adequacy.

pprox. - quare

g.

Bartlett's Test of

Sphericity

Step 2: Tests of the adequacy of data for FA

> 0.6 good

H0:V = I

H1:V I

Reject H0

V I

there is adequate

correlation among

variables to do an FA

V = Population

correlation

Matrix (10 X 10)

< 0.05 (= E)


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Bartlett's Test of Spericity explained

1 V12 V13 .. V1p

V21 1 V13 .. V2p

V31 V32 1 .. V3p

............................

...

...

Vp1 Vp2 Vp3 .. 1

V =

(p x p

square

matrix)

0 0 0


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1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

I =

(p x p

Identitymatrix)

Find the eigen roots of the matrix C = - 2 4

7 1


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Eigen values (latent roots, characteristic roots)

p original variables

p x p Sample correlation matrixR PI= 0, where I pxp is an identity matrix

p eigen values, P1, P2, ......... , Pp

each eigen value corresponds to a factor/PC p factors or PCs

In the table of Total Variance Explained (next slide) the eigen

values are arranged in order of magnitude

largest ... to . smallest

F1/PC1 to . F p/PC p


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Total Variance Explained

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Step 3: Extracting the Factors - Total Variance Explained

Satisfied ?

If not ask for higher

no. of components

so that total variance

explained is more

By default eigen values > 1


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Step 3: Extracting the Factors Scree plot

Screes off indicates the

no. of major components


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Component Matrixa

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Step 4: Unrotated component matrix = component leadings


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0.571, 0.516

(0,0)- 1 + 1

- 1

+ 1

PC 1

PC 3

0.683, 0.347


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Rotated Component Matrixa

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Extraction Method: Principal Component Analysis.

.o a on converge n era ons..

tep 5: Rotated component matrix


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Rotated component matrix


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Component Score Covariance Matrix

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$ Identity matrix

Step 6: Component Score Covariance matrix


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Total Variance Explained = 60.854 3 components


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Rotated Component Matrix

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I'd rather spend a

quiet evening at

home than go to aparty

1.000-.004 .628 .082 .675 -.100 -.338

I check prices even

on small items-.004 1.000 .151 -.248 .048 .582 -.251

Magazines are more

interesting than

movies

.628 .151 1.000 -.182 .480 .090 -.588

I will not buy

products advertised

on bill-boards

.082 -.248 -.182 1.000 .272 .017 .469

I am a homebody .675 .048 .480 .272 1.000 -.110 -.082

I save and cash

coupons-.100 .582 .090 .017 -.110 1.000 .014

Companies waste a

lot of time onadvertising -.338 -.251 -.588 .469 -.082 .014 1.000

Correlation Matrix Example 2 Lifestyle


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Component Initial Eigenvalues

Total % of Variance Cumulative %

1 2.485 35.505 35.505

2 1.821 26.013 61.518

3 1.339 19.131 80.6494 .508 7.258 87.907

5 .376 5.373 93.280

6 .279 3.990 97.270

7 .191 2.730 100.000


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Component 1 2 3

I'd rather spend a quiet evening at home than go to

a party.817 .378 .087

I check prices even on small items .279 -.714 .457Magazines are more interesting than movies .887 -.027 -.043

I will not buy products advertised on bill-boards -.204 .634 .597

I am a homebody.664 .505 .329

I save and cash coupons .050 -.604 .689

Companies waste a lot of time on advertising -.684 .383 .426

? ?

Unrotated Component Matrix


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Component 1 2 3

1 1.000 .000 .000

2 .000 1.000 .000

3 .000 .000 1.000

Component Score Covariance Matrix


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Rotated Component Matrix

Component 1 2 3I'd rather spend a quiet evening at home than go to

a party .897 -.082 -.076

I check prices even on small items.049 -.232 .860

Magazines are more interesting than movies .762 -.440 .125

I will not buy products advertised on bill-boards .214 .867 -.052

I am a homebody .868 .224 -.017

I save and cash coupons -.057 .091 .911

Companies waste a lot of time on advertising -.351 .817 -.073

rm fa explained

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