chapter19.ppt 285KB Dec 31 1997 01:53:00 PM
Chapter XIX
Factor Analysis
Chapter Outline
1) Overview
2) Basic Concept
3) Factor Analysis Model
4) Statistics Associated with Factor Analysis
5) Conducting Factor Analysis
i. Problem Formulation
ii. Construction of the Correlation Matrix
iii. Method of Factor Analysis
iv. Number of of Factors
v. Rotation of Factors
vi. Interpretation of Factors
vii. Factor Scores
viii.Selection of Surrogate Variables
ix. Model Fit
6) Applications of Common Factor Analysis
7) Internet and Computer Applications
8) Focus on Burke
9) Summary
10) Key Terms and Concepts
11) Acronyms
Fig 19.1
Conducting Factor Analysis
Problem formulation
Construction of the Correlation Matrix
Method of Factor Analysis
Determination of Number of Factors
Rotation of Factors
Interpretation of Factors
Selection of
Surrogate variables
Calculation of
Factor Scores
Determination of Model Fit
Table 19-1
RESPONDENT
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
V1
7.00
1.00
6.00
4.00
1.00
6.00
5.00
6.00
3.00
2.00
6.00
2.00
7.00
4.00
1.00
6.00
5.00
7.00
2.00
3.00
1.00
5.00
2.00
4.00
6.00
3.00
4.00
3.00
4.00
2.00
V2
3.00
3.00
2.00
5.00
2.00
3.00
3.00
4.00
4.00
6.00
4.00
3.00
2.00
6.00
3.00
4.00
3.00
3.00
4.00
5.00
3.00
4.00
2.00
6.00
5.00
5.00
4.00
7.00
6.00
3.00
V3
6.00
2.00
7.00
4.00
2.00
6.00
6.00
7.00
2.00
2.00
7.00
1.00
6.00
4.00
2.00
6.00
6.00
7.00
3.00
3.00
2.00
5.00
1.00
4.00
4.00
4.00
7.00
2.00
3.00
2.00
V4
4.00
4.00
4.00
6.00
3.00
4.00
3.00
4.00
3.00
6.00
3.00
4.00
4.00
5.00
2.00
3.00
3.00
4.00
3.00
6.00
3.00
4.00
5.00
6.00
2.00
6.00
2.00
6.00
7.00
4.00
V5
2.00
5.00
1.00
2.00
6.00
2.00
4.00
1.00
6.00
7.00
2.00
5.00
1.00
3.00
6.00
3.00
3.00
1.00
6.00
4.00
5.00
2.00
4.00
4.00
1.00
4.00
2.00
4.00
2.00
7.00
V6
4.00
4.00
3.00
5.00
2.00
4.00
3.00
4.00
3.00
6.00
3.00
4.00
3.00
6.00
4.00
4.00
4.00
4.00
3.00
6.00
3.00
4.00
4.00
7.00
4.00
7.00
5.00
3.00
7.00
2.00
Correlation Matrix
Table 19.2
Variables
V1
V2
V3
V4
V5
V6
V1
1.00
0.53
.873
.086
.858
.004
V2
V3
V4
V5
V6
1.00
.155
.572
.020
.640
1.00
.248
.778
.018
1.00
.007
.640
1.00
.136
1.00
Results of Principal Components Analysis
Table 19.3
Communalities
Variables
V1
V2
V3
V4
V5
V6
Initial
1.000
1.000
1.000
1.000
1.000
1.000
Extraction
.926
.723
.894
.739
.878
.790
Factor
1
2
3
4
5
6
Eigenvalue % of variance
2.731
45.520
2.218
36.969
0.442
7.360
0.341
5.688
0.183
3.044
0.085
1.420
Initial Eigenvalues
Barlett test of sphericity
• Approx. ChiSquare = 111.314
• df = 15
• Significance = .00000
• KaiserMeyerOlkin measure of
sampling adequacy = .660
Cumulat. %
45.520
82.488
89.848
95.536
98.580
100.000
Table 19.2 Contd.
Extraction Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.731
45.520
2.218
36.969
Cumulat. %
45.520
82.488
Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.928
.301
.936
.342
.869
.177
Factor 2
.253
.795
.131
.789
.351
.871
Rotation Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.688
44.802
2.261
37.687
Cumulat. %
44.802
82.488
Table 19.2 Contd.
Rotated Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.962
.057
.934
.098
.933
.083
Factor 2
.027
.848
.146
.845
.084
.885
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.358
.001
.345
.017
.350
.052
Factor 2
.011
.375
.043
.377
.059
.395
Table 19.2 Contd. The lower left triangle contains the reproduced
correlation matrix; the diagonal, the communities; the
upper right triangle, the residuals between the
observed
correlations
and
the
reproduced
correlations.
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
V1
.926
.078
.902
.117
.895
.057
V2
.024
.723
.177
.730
.018
.746
V3
.029
.022
.894
.217
.859
.051
V4
.031
.158
.031
.739
.020
.748
V5
.038
.038
.081
.027
.878
.152
V6
.053
.105
.033
.107
.016
.790
Screen Plot
Fig. 19.2
3.0
Eigenvalue
2.5
2.0
1.5
1.0
0.5
0.0
1
2
3
4
5
6
Component Number
Factor Loading Plot
Fig. 19.3
Rotated Component Matrix
Component
Variable 1 2
V1
0.962 2.66E02
V2
5.72E02 .848
Component 1
V3
0.934 .146
V4
V4
9.83E02 .854
V5
.933 8.40E02
V6
8.337E02 0.885
Component Plot in Rotated Space
1.0
V6
V2
0.0
.5
1.0
V5
Component 2
0.5
V1
V3
Table 19.4
Results of Common Factor Analysis
Communalities
Variables
V1
V2
V3
V4
V5
V6
Initial
.859
.480
.814
.543
.763
.587
Extraction
.928
.562
.836
.600
.789
.723
Factor
1
2
3
4
5
6
Eigenvalue % of variance
2.731
45.520
2.218
36.969
0.442
7.360
0.341
5.688
0.183
3.044
0.085
1.420
Initial Eigenvalues
Barlett test of sphericity
• Approx. ChiSquare = 111.314
• df = 15
• Significance = .00000
• KaiserMeyerOlkin measure of
sampling adequacy = .660
Cumulat. %
45.520
82.488
89.848
95.536
98.580
100.000
Table 19.4 Contd.
Extraction Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.570
42.837
1.868
31.126
Cumulat. %
42.837
73.964
Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.949
.206
.914
.246
.850
.101
Factor 2
.168
.720
.038
.734
.259
.844
Rotation Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.541
42.343
1.897
31.621
Cumulat. %
42.343
73.964
Table 19.4 Contd.
Rotated Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.963
.054
.902
.090
.885
.075
Factor 2
.030
.747
.150
.769
.079
.847
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.628
.024
.217
.023
.166
.083
Factor 2
.101
.253
.169
.271
.059
.500
Table 19.4 Contd.
The lower left triangle contains the reproduced
correlation matrix; the diagonal, the communities; the
upper right triangle, the residuals between the
observed
correlations
and
the
reproduced
correlations.
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
V1
.928
.075
.873
.110
.850
.046
V2
.022
.562
.161
.580
.012
.629
V3
.000
.006
.836
.197
.786
.060
V4
.024
.008
.005
.600
.019
.645
V5
.008
.031
.008
.025
.789
.133
V6
.042
.012
.042
.004
.003
.723
RIP 19.1
Driving Nuts For Beetles
Generally, with time, consumer needs and tastes change.
Consumer preferences for automobiles need to be continually
tracked to identify changing demands and specifications.
However, there is one car that is quite an exception the
Volkswagen Beetle. More than 21 million have been built
since it was introduced in 1938. Surveys have been
conducted in different countries to determine the reasons why
people purchase Beetles. Principal components analyses of
the variables measuring the reasons for owning Beetles have
consistently revealed one dominant factor fanatical loyalty.
The company has long wished its natural death but without
any effect. This noisy and cramped "bug" has inspired
devotion in drivers.
RIP 19.1 Contd.
Now old bugs are being sought everywhere. "The Japanese
are going absolutely nuts for Beetles," says Jack Finn, a
recycler of old Beetles in West Palm Beach, Florida.
Beetles are still made in Mexico, but they cannot be exported
to US or Europe because of safety and emission standards.
Because of faithful loyalty for the "bug", VW has repositioned
the beetle as a new shiny VW Passat, a premium quality car
which gives an image of sophistication and class as opposed
to the old one which symbolized lowpriced brand.
Factors Predicting Unethical
Marketing Research
Practices
survey of 420 marketing
professionals was conducted to
RIP 19.2
A
identify organizational variables that determine the incidence of
unethical marketing research practices.
These marketing
professionals were asked to provide evaluations of the incidence
of fifteen marketing research practices that have been found to
pose ethical problems. They also provided responses on several
other scales, including an 11 item scale pertaining to the extent
to which ethical problems plagued the organization, and what
top management's actions were toward ethical situations. The
commonly used method of principal components analysis with
varimax rotation indicated that these 11 items could be
represented by two factors.
Contd.
RIP 19.1 Contd.
Factor Analysis of Ethical Problems and Top Management Action Scale
Extent of Ethical
Problems within Top Management
the organization actions on ethics
(factor 1)
(factor 2)
1. Successful executives in my company
make rivals look bad in the eyes of
important people in my company.
0.66
2. Peer executives in my company often
engage in behaviors that I consider unethical.
0.68
3. There are opportunities for peer executives
in my
company to engage in unethical behavior. 0.43
4. Successful executives in my company take
credit for the ideas & accomplishment of others. 0.81
5. In order to succeed in my company, it is
often necessary to compromise one's ethics.
0.66
6. Successful executives in my company are
generally more unethical than unsuccessful
executives.
0.64
7. Successful executives in my company
look for a "scapegoat" when they feel they
may by associated with failure.
0.78
Factor Analysis of Ethical Problems and Top Management Action Scale
Extent of Ethical
Problems within Top Management
the organization actions on ethics
(factor 1)
(factor 2)
8. Successful executives in my company
withhold information that is detrimental
to their self-interest.
0.68
9. Top management in my company has
let it be known in no uncertain terms that
unethical behaviors will not be tolerated.
0.73
10. If an executive in my company engages
in
unethical behavior resulting in personal
gain
(rather than corporate gain), he/she
will be
promptly reprimanded.
0.80
11. If an executive in my company engages
in
unethical behavior resulting in corporate
gain, he/she will be promptly reprimanded.
0.78
Eigenvalue
5.06
1.17
% of Variance Explained
46%
11%
Coefficient Alpha
0.87
0.75
To simplify the table, only varimax-rotated loading of .40 or greater are
reported. Each was rated on a five-point scale with 1 = "strongly agree" and 5
= "strongly disagree”
RIP 19.1 Contd.
RIP 19.1 Contd.
Factor Analysis of Ethical Problems and Top Management Action Scale
The first factor could be interpreted as the incidence of unethical
practices, while the second factor denotes top management
actions related to unethical practices. The two factors together
account for more than half the variation in the data with the first
factor being dominant. These two factors were then used along
with four other variables as predictors in a multiple regression.
The results indicated that they were the two best predictors of
unethical marketing research practices.
Factor Analysis
Chapter Outline
1) Overview
2) Basic Concept
3) Factor Analysis Model
4) Statistics Associated with Factor Analysis
5) Conducting Factor Analysis
i. Problem Formulation
ii. Construction of the Correlation Matrix
iii. Method of Factor Analysis
iv. Number of of Factors
v. Rotation of Factors
vi. Interpretation of Factors
vii. Factor Scores
viii.Selection of Surrogate Variables
ix. Model Fit
6) Applications of Common Factor Analysis
7) Internet and Computer Applications
8) Focus on Burke
9) Summary
10) Key Terms and Concepts
11) Acronyms
Fig 19.1
Conducting Factor Analysis
Problem formulation
Construction of the Correlation Matrix
Method of Factor Analysis
Determination of Number of Factors
Rotation of Factors
Interpretation of Factors
Selection of
Surrogate variables
Calculation of
Factor Scores
Determination of Model Fit
Table 19-1
RESPONDENT
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
V1
7.00
1.00
6.00
4.00
1.00
6.00
5.00
6.00
3.00
2.00
6.00
2.00
7.00
4.00
1.00
6.00
5.00
7.00
2.00
3.00
1.00
5.00
2.00
4.00
6.00
3.00
4.00
3.00
4.00
2.00
V2
3.00
3.00
2.00
5.00
2.00
3.00
3.00
4.00
4.00
6.00
4.00
3.00
2.00
6.00
3.00
4.00
3.00
3.00
4.00
5.00
3.00
4.00
2.00
6.00
5.00
5.00
4.00
7.00
6.00
3.00
V3
6.00
2.00
7.00
4.00
2.00
6.00
6.00
7.00
2.00
2.00
7.00
1.00
6.00
4.00
2.00
6.00
6.00
7.00
3.00
3.00
2.00
5.00
1.00
4.00
4.00
4.00
7.00
2.00
3.00
2.00
V4
4.00
4.00
4.00
6.00
3.00
4.00
3.00
4.00
3.00
6.00
3.00
4.00
4.00
5.00
2.00
3.00
3.00
4.00
3.00
6.00
3.00
4.00
5.00
6.00
2.00
6.00
2.00
6.00
7.00
4.00
V5
2.00
5.00
1.00
2.00
6.00
2.00
4.00
1.00
6.00
7.00
2.00
5.00
1.00
3.00
6.00
3.00
3.00
1.00
6.00
4.00
5.00
2.00
4.00
4.00
1.00
4.00
2.00
4.00
2.00
7.00
V6
4.00
4.00
3.00
5.00
2.00
4.00
3.00
4.00
3.00
6.00
3.00
4.00
3.00
6.00
4.00
4.00
4.00
4.00
3.00
6.00
3.00
4.00
4.00
7.00
4.00
7.00
5.00
3.00
7.00
2.00
Correlation Matrix
Table 19.2
Variables
V1
V2
V3
V4
V5
V6
V1
1.00
0.53
.873
.086
.858
.004
V2
V3
V4
V5
V6
1.00
.155
.572
.020
.640
1.00
.248
.778
.018
1.00
.007
.640
1.00
.136
1.00
Results of Principal Components Analysis
Table 19.3
Communalities
Variables
V1
V2
V3
V4
V5
V6
Initial
1.000
1.000
1.000
1.000
1.000
1.000
Extraction
.926
.723
.894
.739
.878
.790
Factor
1
2
3
4
5
6
Eigenvalue % of variance
2.731
45.520
2.218
36.969
0.442
7.360
0.341
5.688
0.183
3.044
0.085
1.420
Initial Eigenvalues
Barlett test of sphericity
• Approx. ChiSquare = 111.314
• df = 15
• Significance = .00000
• KaiserMeyerOlkin measure of
sampling adequacy = .660
Cumulat. %
45.520
82.488
89.848
95.536
98.580
100.000
Table 19.2 Contd.
Extraction Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.731
45.520
2.218
36.969
Cumulat. %
45.520
82.488
Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.928
.301
.936
.342
.869
.177
Factor 2
.253
.795
.131
.789
.351
.871
Rotation Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.688
44.802
2.261
37.687
Cumulat. %
44.802
82.488
Table 19.2 Contd.
Rotated Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.962
.057
.934
.098
.933
.083
Factor 2
.027
.848
.146
.845
.084
.885
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.358
.001
.345
.017
.350
.052
Factor 2
.011
.375
.043
.377
.059
.395
Table 19.2 Contd. The lower left triangle contains the reproduced
correlation matrix; the diagonal, the communities; the
upper right triangle, the residuals between the
observed
correlations
and
the
reproduced
correlations.
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
V1
.926
.078
.902
.117
.895
.057
V2
.024
.723
.177
.730
.018
.746
V3
.029
.022
.894
.217
.859
.051
V4
.031
.158
.031
.739
.020
.748
V5
.038
.038
.081
.027
.878
.152
V6
.053
.105
.033
.107
.016
.790
Screen Plot
Fig. 19.2
3.0
Eigenvalue
2.5
2.0
1.5
1.0
0.5
0.0
1
2
3
4
5
6
Component Number
Factor Loading Plot
Fig. 19.3
Rotated Component Matrix
Component
Variable 1 2
V1
0.962 2.66E02
V2
5.72E02 .848
Component 1
V3
0.934 .146
V4
V4
9.83E02 .854
V5
.933 8.40E02
V6
8.337E02 0.885
Component Plot in Rotated Space
1.0
V6
V2
0.0
.5
1.0
V5
Component 2
0.5
V1
V3
Table 19.4
Results of Common Factor Analysis
Communalities
Variables
V1
V2
V3
V4
V5
V6
Initial
.859
.480
.814
.543
.763
.587
Extraction
.928
.562
.836
.600
.789
.723
Factor
1
2
3
4
5
6
Eigenvalue % of variance
2.731
45.520
2.218
36.969
0.442
7.360
0.341
5.688
0.183
3.044
0.085
1.420
Initial Eigenvalues
Barlett test of sphericity
• Approx. ChiSquare = 111.314
• df = 15
• Significance = .00000
• KaiserMeyerOlkin measure of
sampling adequacy = .660
Cumulat. %
45.520
82.488
89.848
95.536
98.580
100.000
Table 19.4 Contd.
Extraction Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.570
42.837
1.868
31.126
Cumulat. %
42.837
73.964
Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.949
.206
.914
.246
.850
.101
Factor 2
.168
.720
.038
.734
.259
.844
Rotation Sums of Squared Loadings
Factor
1
2
Eigenvalue % of variance
2.541
42.343
1.897
31.621
Cumulat. %
42.343
73.964
Table 19.4 Contd.
Rotated Factor Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.963
.054
.902
.090
.885
.075
Factor 2
.030
.747
.150
.769
.079
.847
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
Factor 1
.628
.024
.217
.023
.166
.083
Factor 2
.101
.253
.169
.271
.059
.500
Table 19.4 Contd.
The lower left triangle contains the reproduced
correlation matrix; the diagonal, the communities; the
upper right triangle, the residuals between the
observed
correlations
and
the
reproduced
correlations.
Factor Score Coefficient Matrix
Variables
V1
V2
V3
V4
V5
V6
V1
.928
.075
.873
.110
.850
.046
V2
.022
.562
.161
.580
.012
.629
V3
.000
.006
.836
.197
.786
.060
V4
.024
.008
.005
.600
.019
.645
V5
.008
.031
.008
.025
.789
.133
V6
.042
.012
.042
.004
.003
.723
RIP 19.1
Driving Nuts For Beetles
Generally, with time, consumer needs and tastes change.
Consumer preferences for automobiles need to be continually
tracked to identify changing demands and specifications.
However, there is one car that is quite an exception the
Volkswagen Beetle. More than 21 million have been built
since it was introduced in 1938. Surveys have been
conducted in different countries to determine the reasons why
people purchase Beetles. Principal components analyses of
the variables measuring the reasons for owning Beetles have
consistently revealed one dominant factor fanatical loyalty.
The company has long wished its natural death but without
any effect. This noisy and cramped "bug" has inspired
devotion in drivers.
RIP 19.1 Contd.
Now old bugs are being sought everywhere. "The Japanese
are going absolutely nuts for Beetles," says Jack Finn, a
recycler of old Beetles in West Palm Beach, Florida.
Beetles are still made in Mexico, but they cannot be exported
to US or Europe because of safety and emission standards.
Because of faithful loyalty for the "bug", VW has repositioned
the beetle as a new shiny VW Passat, a premium quality car
which gives an image of sophistication and class as opposed
to the old one which symbolized lowpriced brand.
Factors Predicting Unethical
Marketing Research
Practices
survey of 420 marketing
professionals was conducted to
RIP 19.2
A
identify organizational variables that determine the incidence of
unethical marketing research practices.
These marketing
professionals were asked to provide evaluations of the incidence
of fifteen marketing research practices that have been found to
pose ethical problems. They also provided responses on several
other scales, including an 11 item scale pertaining to the extent
to which ethical problems plagued the organization, and what
top management's actions were toward ethical situations. The
commonly used method of principal components analysis with
varimax rotation indicated that these 11 items could be
represented by two factors.
Contd.
RIP 19.1 Contd.
Factor Analysis of Ethical Problems and Top Management Action Scale
Extent of Ethical
Problems within Top Management
the organization actions on ethics
(factor 1)
(factor 2)
1. Successful executives in my company
make rivals look bad in the eyes of
important people in my company.
0.66
2. Peer executives in my company often
engage in behaviors that I consider unethical.
0.68
3. There are opportunities for peer executives
in my
company to engage in unethical behavior. 0.43
4. Successful executives in my company take
credit for the ideas & accomplishment of others. 0.81
5. In order to succeed in my company, it is
often necessary to compromise one's ethics.
0.66
6. Successful executives in my company are
generally more unethical than unsuccessful
executives.
0.64
7. Successful executives in my company
look for a "scapegoat" when they feel they
may by associated with failure.
0.78
Factor Analysis of Ethical Problems and Top Management Action Scale
Extent of Ethical
Problems within Top Management
the organization actions on ethics
(factor 1)
(factor 2)
8. Successful executives in my company
withhold information that is detrimental
to their self-interest.
0.68
9. Top management in my company has
let it be known in no uncertain terms that
unethical behaviors will not be tolerated.
0.73
10. If an executive in my company engages
in
unethical behavior resulting in personal
gain
(rather than corporate gain), he/she
will be
promptly reprimanded.
0.80
11. If an executive in my company engages
in
unethical behavior resulting in corporate
gain, he/she will be promptly reprimanded.
0.78
Eigenvalue
5.06
1.17
% of Variance Explained
46%
11%
Coefficient Alpha
0.87
0.75
To simplify the table, only varimax-rotated loading of .40 or greater are
reported. Each was rated on a five-point scale with 1 = "strongly agree" and 5
= "strongly disagree”
RIP 19.1 Contd.
RIP 19.1 Contd.
Factor Analysis of Ethical Problems and Top Management Action Scale
The first factor could be interpreted as the incidence of unethical
practices, while the second factor denotes top management
actions related to unethical practices. The two factors together
account for more than half the variation in the data with the first
factor being dominant. These two factors were then used along
with four other variables as predictors in a multiple regression.
The results indicated that they were the two best predictors of
unethical marketing research practices.