RM FA Explained
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Transcript of 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
.747
.
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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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.componen s ex rac e ..
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 Matrixa
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Extraction Method: Principal Component Analysis.
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o a on converge n era ons..
Rotated component matrix
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Component Score Covariance Matrix
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Extraction Method: Principal Component Analysis.
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$ Identity matrix
Step 6: Component Score Covariance matrix
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Rotated Component Matrixa
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Extraction Method: Principal Component Analysis.
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o a on converge n era ons..
Total Variance Explained = 60.854 3 components
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Rotated Component Matrixa
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Extraction Method: Principal Component Analysis.
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o a on converge n era ons..
Total Variance Explained = 69.082 4 components
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Rotated Component Matrix
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Extraction Method: Principal Component Analysis.
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o a on converge n era ons..
Total Variance Explained = 76.104 5 components
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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