Description
It explains the factor analysis in marketing research. It covers all the basics of factor analysis.
What is Factor Analysis ?
? Collection of methods examines how underlying constructs influence response to variables.
? If large number of variables - FA used for data
reduction and summarization. ? Does not have dept and indept variables – interdependence technique – interdependence of relationships explored.
When do we use Factor Analysis ?
? To identify underlying dimensions or factors that explain correlations between set of variables.
? To identify smaller number of uncorrelated
variables to replace the original ? Used in segmentation , attitudinal studies , media consumption , product research , ad research , pricing .
Types of factor analysis
? Exploratory Factor Analysis ( EFA) – discover nature of constructs influencing a set of responses
? Confirmatory factor analysis (CFA) tests whether a
specified set of constructs is influencing responses in a predicted way. ? Both are based on the Common Factor Model
Common Factor Model
Measure 1 Factor1 Measure 2 Measure 3 Factor2 Measure 4 Measure 5
Observed response ( M1-5) influenced partly by underlying common factors and partly by unique factors Strength of Factor with measure varies – some factors influence some measures more than others. E1 E2 E3 E4 E5
FACTORA ANALYSIS AMODEL X = A F + F + A F + A F +…+ F +VU
i i1 1 i2 2 i3 3 i4 4 im m i i
X I = ith standardized variable Aij = standardized multiple regression coeff of variable i on common factor j F = common factor Vi = standardized reg coeff of variable i on unique factor i . Ui = Unique factor for variable i m = No. of common factors Unique factors are uncorrelated with each other and with common factors. THUS MATHEMATICALLY , FA IS LIKE MULTIPLE REGRESSION
CommonXFactors +…+ W X F =W X +W +W X +W X
i i1 1 i2 2 i3 3 i4 4 ik
k
Fi Wi k
= estimate of ith common factor = weight or factor score coefficient = No. of variables
We select weights such that the first factor explains the largest portion of total variance . The second set of weights then selected that the second factor accounts for most of the residual variance These Factor scores are independent – unlike the original variables
Principal Components Analysis
? Data reduction technique
? based on measured PC are A difft model resp.
EFA - measured responses based on Measure 1 underlying responses PC linear combn – contains both unique and common factors.
Measure 2 Measure 3 Component 2
EFA - unique & common factors
PC use when key task is data reduction. EFA - understanding underlying dimensions
Component 1
Measure 4 Measure 5
Background
? Measuring affinity for different music types
? Measured on a 5 pt liking scale ? 4 additional demog – age , income , gender and edu ? Objective : whether different music affinity groups exist.
Step 1 Correlation Matrix
Blues and R&B Music Classical Music Country Western Music Heavy Metal Music Jazz Music Rap Music Age of Respondent Respondent' s Income Respondent' s Sex Blues and Classical R&B Music Music 1 0.2 0.2 1 Correlation Matrix Country Western Heavy Metal Age of Respondent' Respondent' Music Music Jazz Music Rap Music Respondent s Income s Sex 0.012 0.073 0.529 0.133 0.038 -0.09 -0.01 -0.102 -0.002 0.3 0.011 -0.081 -0.104 -0.07
0.012
-0.102
1
-0.101
-0.088
-0.004
-0.118
0.103
-0.046
0.073 0.529 0.133 0.038 -0.09 -0.01
-0.002 0.3 0.011 -0.081 -0.104 -0.07
-0.101 -0.088 -0.004 -0.118 0.103 -0.046
1 0.056 0.279 0.376 0.145 0.125
0.056 1 0.152 0.087 -0.109 0.026
0.279 0.152 1 0.272 0.083 -0.047
0.376 0.087 0.272 1 0.179 0.019
0.145 -0.109 0.083 0.179 1 -0.234
0.125 0.026 -0.047 0.019 -0.234 1
Corr coeff should not be more than .9 - problem of singularity ( unique factor may not be identifiable If very low correlations – factor analysis is not suitable. In either case leave out variables KMO measure of sampling adequacy - small value means corr betwn pairs of var cant be explained by others ( >0.5) Barlett’s test of sphericity - null hyp – var are uncorrletated – should be rejected.
Communalities Blues and R&B Music Classical Music (3) Classical Music Country Western Music Heavy Metal Music Jazz Music Rap Music Initial Extraction 1.000 0.777
1.000 1.000 1.000
0.843 0.867 0.562
Communalities measure the percent of variance in a given variable explained by all the factors
Initial assumption is that all variance is common – so the communality is 1.00
After factor extraction % of variance in a variable , that is explained by all the factors Variance of Uniqueness = 1- communality
1.000 1.000 1.000
0.64 0.76 0.955
Age of Respondent
Respondent's Income Respondent's Sex
1.000
1.000 1.000
0.636
0.745 0.738
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Eigenvalue for a factor indicates the total variance attributed to that factor. The total variance accounted for by 18 components ( 18 variables ) is 18. Eigenvalues will decline – as successive components explain residual variance
% of variance for Factor 1 = 4.433 / 18
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Ignores factors with eigenvalues less than 1
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Relative importance of 6 factors is equalized .
Else , first factor pulls all variables towards it. Makes interpretation easier. Rotation can be orthogonal ( Varimax) – so that factors are uncorrelated or Oblique ( Factors are correlated)
Extraction Method: Principal Component Analysis.
How many factors ?
1 Classical Music Jazz Music Blues or R & B Music Blues and R&B Music Opera Broadway Musicals Bigband Music Rap Music 0.725 0.713 0.677 0.667 0.621 0.621 0.603 0.186
Component Matrixa Component 2 3 4 -0.295 -0.439 0.054 0.324 0.303 0.3 -0.244 -0.335 -0.343 0.704 0.188 0.449 0.444 -0.244 -0.168 0.181 -0.239 -0.286 -0.139 -0.175 0.223 0.277 0.248 0.462 -0.11
5 0.053 -0.168 -0.092 -0.123 0.115 -0.177 0.093 0.224 -0.106
6 0.237 -0.036 0.004 -0.001 0.05 -0.149 -0.062 -0.321 0.379
Unrotated matrix
Cells are corr coeff between Factors and variables These r are called Factor Loadings .
Age of -0.091 0.632 -0.248 Respondent Country -0.018 -0.152 0.506 Western Music Bluegrass 0.314 -0.188 0.468 Music Highest Year -0.343 0.057 0.446 of School Completed Respondent' -0.176 0.179 0.054 s Income Respondent' -0.074 0.094 0.136 s Sex Heavy Metal 0.02 0.505 -0.169 Music Extraction Method: Principal Component Analysis. a. 6 components extracted.
0.491
0.197
0.059
0.326 0.395
0.378 -0.13
0.229 0.128
All over the place
Eigenvalue of Component 1 = sum of squares down a column.
0.509 -0.382 0.075
-0.468 0.724 0.2
0.447 0.188 0.558
1 Classical 0.912 Music Opera 0.729 0.111 Broadway 0.672 0.17 Musicals Bigband Music 0.53 0.263 Blues and R&B 0.089 0.866 Music Blues or R & B 0.104 0.858 Music Jazz Music 0.203 0.834 Rap Music 0.024 0.094 Bluegrass 0.221 0.159 Music Country -0.064 -0.041 Western Music Highest Year -0.391 -0.105 of School Completed Heavy Metal 0.035 0.035 Music Age of -0.161 0.11 Respondent Respondent's -0.129 0 Sex Respondent's -0.079 -0.103 Income Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 6 iterations.
Rotated Component Matrixa Component 2 3 4 0.133 -0.056 -0.083 0.103 0.077 -0.005 0.038 0.063 0.074 0.956 -0.05 0.039 -0.023 0.107 0.051 0.382 0.135 0.172 -0.124 0.009 0.743 0.732 0.478
5 0.079 -0.072 -0.327 -0.304 0.004 0.012 0.033 0.174 0.006 -0.114 0.056
6 -0.034 -0.013 0.246 0.004 -0.013 -0.021 -0.033 0.027 -0.161 0.079 0.335
0.17 0.173 -0.079 -0.015
0.052 -0.291 0.148 0.233
0.775 0.69 0.251 0.415
-0.075 0.086 -0.794 0.708
Classical Music A Classical Music B Opera Broadway Musicals Bigband Music Blues and R&B Music Blues or R & B Music Jazz Music A Jazz Music B Rap Music A Rap Music B Bluegrass Music Country Western Music Heavy Metal Music Age of Respondent Respondent's Sex Respondent's Income
1 0.912 0.895 0.729 0.672 0.53
Rotated Component Matrixa Component 2 3 4
5
6
0.866 0.858 0.837 0.834 0.956 0.953 0.743 0.732 0.775 0.69 -0.794 0.708
1 Bigband Music Blues and R&B Music Bluegrass Music Classical Music Country Western Music Heavy Metal Music Jazz Music Broadway Musicals Opera Rap Music Age of Respondent Respondent's Income Respondent's Sex 0.13 -0.087 0.066 0.328 -0.027 0.088 -0.039 0.19 0.247 0.004 -0.007 0.027 -0.017
Component Score Coefficient Matrix Component 2 3 4 0.025 0.028 0.194 0.316 -0.003 -0.073 -0.03 -0.037 0.293 -0.011 -0.069 -0.047 0.045 -0.01 -0.035 -0.045 -0.026 -0.065 0.05 -0.032 -0.03 0.065 0.059 0.519 -0.035 -0.117 -0.034 0.05 0.452 -0.041 0.425 0.108 -0.099 -0.018 0.06 0.027 -0.121 0.133 0.164
5 -0.136 -0.011 0.099 0.149 -0.027 0.535 -0.007 -0.18 0.012 -0.041 0.418 0.314 0.198
6 -0.008 0.028 -0.161 -0.013 0.006 -0.074 0.026 0.187 -0.019 -0.04 0.077 0.514 -0.607
If we use PCA as a data reduction technique – we now have 6 new variables instead of original 18. Each respondent would have 6 new scores on each Factor . F i = Wi1X1 + Wi2X2 + Wi3X3 + Wi4X4 +…+ WikXk
Example Factor Matrix: Orientation towards Technology
Factor Matrix Factor 1 .654 .530 -.392 -.394 -.422 .656 .694 -.693 .680 .620 -.568 2 .221 .241 .279 .372 .257 .275 .254 .455 .212 .283 .472
I think new technology is fascinating Using a computer saves me time and work I feel very negative about technology in general Computers control too much of our world today. The Internet negatively effects my life. Using computers makes learning more fun for me Using the Internet is enjoyable. Technology is being forced on us, making us lose control of our lives. Using the Internet helps improve my life I like to be the first one to try out new technology and gadgets The Internet is having negative effects on our society. Extraction Method: Principal Axis Factoring. a 2 factors extracted. 8 iterations required.
Rotated Factor Loading Matrix
Rotated Factor Matrix Factor 1 .655 .568 -.144 -.535 -.181 .689 .706 -.277 2 -.219 -.128 .459 .535 .460 -.177 -.217 .782
I think new technology is fascinating Using a computer saves me time and work I feel very negative about technology in general Computers control too much of our world today. The Internet negatively effects my life. Using computers makes learning more fun for me Using the Internet is enjoyable. Technology is being forced on us, making us lose control of our lives. Using the Internet helps improve my life .670 -.242 I like to be the first one to try out new technology and .665 -.149 gadgets The Internet is having negative effects on our society. -.167 .720 Extraction Method: Principal Axis Factoring. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.
Rotated Matrix with Sorting and Suppression<.30)
Rotated Factor Matrix Factor 1 .706 .689 .670 .665 2
Using the Internet is enjoyable. Using computers makes learning more fun for me Using the Internet helps improve my life I like to be the first one to try out new technology and gadgets I think new technology is fascinating .655 Using a computer saves me time and work .568 Technology is being forced on us, making us lose .782 control of our lives. The Internet is having negative effects on our society. .720 Computers control too much of our world today. .535 The Internet negatively effects my life. .460 I feel very negative about technology in general .459 Extraction Method: Principal Axis Factoring. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.
Tech Savvy
Tech Averse
You need at least 300 cases to run FA
doc_955131609.pptx
It explains the factor analysis in marketing research. It covers all the basics of factor analysis.
What is Factor Analysis ?
? Collection of methods examines how underlying constructs influence response to variables.
? If large number of variables - FA used for data
reduction and summarization. ? Does not have dept and indept variables – interdependence technique – interdependence of relationships explored.
When do we use Factor Analysis ?
? To identify underlying dimensions or factors that explain correlations between set of variables.
? To identify smaller number of uncorrelated
variables to replace the original ? Used in segmentation , attitudinal studies , media consumption , product research , ad research , pricing .
Types of factor analysis
? Exploratory Factor Analysis ( EFA) – discover nature of constructs influencing a set of responses
? Confirmatory factor analysis (CFA) tests whether a
specified set of constructs is influencing responses in a predicted way. ? Both are based on the Common Factor Model
Common Factor Model
Measure 1 Factor1 Measure 2 Measure 3 Factor2 Measure 4 Measure 5
Observed response ( M1-5) influenced partly by underlying common factors and partly by unique factors Strength of Factor with measure varies – some factors influence some measures more than others. E1 E2 E3 E4 E5
FACTORA ANALYSIS AMODEL X = A F + F + A F + A F +…+ F +VU
i i1 1 i2 2 i3 3 i4 4 im m i i
X I = ith standardized variable Aij = standardized multiple regression coeff of variable i on common factor j F = common factor Vi = standardized reg coeff of variable i on unique factor i . Ui = Unique factor for variable i m = No. of common factors Unique factors are uncorrelated with each other and with common factors. THUS MATHEMATICALLY , FA IS LIKE MULTIPLE REGRESSION
CommonXFactors +…+ W X F =W X +W +W X +W X
i i1 1 i2 2 i3 3 i4 4 ik
k
Fi Wi k
= estimate of ith common factor = weight or factor score coefficient = No. of variables
We select weights such that the first factor explains the largest portion of total variance . The second set of weights then selected that the second factor accounts for most of the residual variance These Factor scores are independent – unlike the original variables
Principal Components Analysis
? Data reduction technique
? based on measured PC are A difft model resp.
EFA - measured responses based on Measure 1 underlying responses PC linear combn – contains both unique and common factors.
Measure 2 Measure 3 Component 2
EFA - unique & common factors
PC use when key task is data reduction. EFA - understanding underlying dimensions
Component 1
Measure 4 Measure 5
Background
? Measuring affinity for different music types
? Measured on a 5 pt liking scale ? 4 additional demog – age , income , gender and edu ? Objective : whether different music affinity groups exist.
Step 1 Correlation Matrix
Blues and R&B Music Classical Music Country Western Music Heavy Metal Music Jazz Music Rap Music Age of Respondent Respondent' s Income Respondent' s Sex Blues and Classical R&B Music Music 1 0.2 0.2 1 Correlation Matrix Country Western Heavy Metal Age of Respondent' Respondent' Music Music Jazz Music Rap Music Respondent s Income s Sex 0.012 0.073 0.529 0.133 0.038 -0.09 -0.01 -0.102 -0.002 0.3 0.011 -0.081 -0.104 -0.07
0.012
-0.102
1
-0.101
-0.088
-0.004
-0.118
0.103
-0.046
0.073 0.529 0.133 0.038 -0.09 -0.01
-0.002 0.3 0.011 -0.081 -0.104 -0.07
-0.101 -0.088 -0.004 -0.118 0.103 -0.046
1 0.056 0.279 0.376 0.145 0.125
0.056 1 0.152 0.087 -0.109 0.026
0.279 0.152 1 0.272 0.083 -0.047
0.376 0.087 0.272 1 0.179 0.019
0.145 -0.109 0.083 0.179 1 -0.234
0.125 0.026 -0.047 0.019 -0.234 1
Corr coeff should not be more than .9 - problem of singularity ( unique factor may not be identifiable If very low correlations – factor analysis is not suitable. In either case leave out variables KMO measure of sampling adequacy - small value means corr betwn pairs of var cant be explained by others ( >0.5) Barlett’s test of sphericity - null hyp – var are uncorrletated – should be rejected.
Communalities Blues and R&B Music Classical Music (3) Classical Music Country Western Music Heavy Metal Music Jazz Music Rap Music Initial Extraction 1.000 0.777
1.000 1.000 1.000
0.843 0.867 0.562
Communalities measure the percent of variance in a given variable explained by all the factors
Initial assumption is that all variance is common – so the communality is 1.00
After factor extraction % of variance in a variable , that is explained by all the factors Variance of Uniqueness = 1- communality
1.000 1.000 1.000
0.64 0.76 0.955
Age of Respondent
Respondent's Income Respondent's Sex
1.000
1.000 1.000
0.636
0.745 0.738
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Eigenvalue for a factor indicates the total variance attributed to that factor. The total variance accounted for by 18 components ( 18 variables ) is 18. Eigenvalues will decline – as successive components explain residual variance
% of variance for Factor 1 = 4.433 / 18
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Ignores factors with eigenvalues less than 1
Extraction Method: Principal Component Analysis.
Componen t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Total Variance Explained Extraction Sums of Squared Initial Eigenvalues Loadings Rotation Sums of Squared Loadings % of Cumulative % of Cumulative % of Cumulative Total Variance % Total Variance % Total Variance % 4.433 24.629 24.629 4.433 24.629 24.629 3.252 18.069 18.069 2.595 1.863 1.738 1.215 1.143 0.885 0.791 0.673 0.562 0.524 0.5 0.417 0.381 0.092 0.078 0.06 0.05 14.415 10.348 9.656 6.749 6.351 4.915 4.396 3.739 3.121 2.912 2.777 2.319 2.115 0.513 0.432 0.335 0.278 39.044 49.392 59.048 65.797 72.148 77.063 81.459 85.198 88.32 91.231 94.008 96.327 98.442 98.955 99.387 99.722 100 2.595 1.863 1.738 1.215 1.143 14.415 10.348 9.656 6.749 6.351 39.044 49.392 59.048 65.797 72.148 3.114 1.933 1.727 1.603 1.358 17.299 10.74 9.596 8.903 7.542 35.368 46.108 55.703 64.606 72.148
Relative importance of 6 factors is equalized .
Else , first factor pulls all variables towards it. Makes interpretation easier. Rotation can be orthogonal ( Varimax) – so that factors are uncorrelated or Oblique ( Factors are correlated)
Extraction Method: Principal Component Analysis.
How many factors ?
1 Classical Music Jazz Music Blues or R & B Music Blues and R&B Music Opera Broadway Musicals Bigband Music Rap Music 0.725 0.713 0.677 0.667 0.621 0.621 0.603 0.186
Component Matrixa Component 2 3 4 -0.295 -0.439 0.054 0.324 0.303 0.3 -0.244 -0.335 -0.343 0.704 0.188 0.449 0.444 -0.244 -0.168 0.181 -0.239 -0.286 -0.139 -0.175 0.223 0.277 0.248 0.462 -0.11
5 0.053 -0.168 -0.092 -0.123 0.115 -0.177 0.093 0.224 -0.106
6 0.237 -0.036 0.004 -0.001 0.05 -0.149 -0.062 -0.321 0.379
Unrotated matrix
Cells are corr coeff between Factors and variables These r are called Factor Loadings .
Age of -0.091 0.632 -0.248 Respondent Country -0.018 -0.152 0.506 Western Music Bluegrass 0.314 -0.188 0.468 Music Highest Year -0.343 0.057 0.446 of School Completed Respondent' -0.176 0.179 0.054 s Income Respondent' -0.074 0.094 0.136 s Sex Heavy Metal 0.02 0.505 -0.169 Music Extraction Method: Principal Component Analysis. a. 6 components extracted.
0.491
0.197
0.059
0.326 0.395
0.378 -0.13
0.229 0.128
All over the place
Eigenvalue of Component 1 = sum of squares down a column.
0.509 -0.382 0.075
-0.468 0.724 0.2
0.447 0.188 0.558
1 Classical 0.912 Music Opera 0.729 0.111 Broadway 0.672 0.17 Musicals Bigband Music 0.53 0.263 Blues and R&B 0.089 0.866 Music Blues or R & B 0.104 0.858 Music Jazz Music 0.203 0.834 Rap Music 0.024 0.094 Bluegrass 0.221 0.159 Music Country -0.064 -0.041 Western Music Highest Year -0.391 -0.105 of School Completed Heavy Metal 0.035 0.035 Music Age of -0.161 0.11 Respondent Respondent's -0.129 0 Sex Respondent's -0.079 -0.103 Income Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 6 iterations.
Rotated Component Matrixa Component 2 3 4 0.133 -0.056 -0.083 0.103 0.077 -0.005 0.038 0.063 0.074 0.956 -0.05 0.039 -0.023 0.107 0.051 0.382 0.135 0.172 -0.124 0.009 0.743 0.732 0.478
5 0.079 -0.072 -0.327 -0.304 0.004 0.012 0.033 0.174 0.006 -0.114 0.056
6 -0.034 -0.013 0.246 0.004 -0.013 -0.021 -0.033 0.027 -0.161 0.079 0.335
0.17 0.173 -0.079 -0.015
0.052 -0.291 0.148 0.233
0.775 0.69 0.251 0.415
-0.075 0.086 -0.794 0.708
Classical Music A Classical Music B Opera Broadway Musicals Bigband Music Blues and R&B Music Blues or R & B Music Jazz Music A Jazz Music B Rap Music A Rap Music B Bluegrass Music Country Western Music Heavy Metal Music Age of Respondent Respondent's Sex Respondent's Income
1 0.912 0.895 0.729 0.672 0.53
Rotated Component Matrixa Component 2 3 4
5
6
0.866 0.858 0.837 0.834 0.956 0.953 0.743 0.732 0.775 0.69 -0.794 0.708
1 Bigband Music Blues and R&B Music Bluegrass Music Classical Music Country Western Music Heavy Metal Music Jazz Music Broadway Musicals Opera Rap Music Age of Respondent Respondent's Income Respondent's Sex 0.13 -0.087 0.066 0.328 -0.027 0.088 -0.039 0.19 0.247 0.004 -0.007 0.027 -0.017
Component Score Coefficient Matrix Component 2 3 4 0.025 0.028 0.194 0.316 -0.003 -0.073 -0.03 -0.037 0.293 -0.011 -0.069 -0.047 0.045 -0.01 -0.035 -0.045 -0.026 -0.065 0.05 -0.032 -0.03 0.065 0.059 0.519 -0.035 -0.117 -0.034 0.05 0.452 -0.041 0.425 0.108 -0.099 -0.018 0.06 0.027 -0.121 0.133 0.164
5 -0.136 -0.011 0.099 0.149 -0.027 0.535 -0.007 -0.18 0.012 -0.041 0.418 0.314 0.198
6 -0.008 0.028 -0.161 -0.013 0.006 -0.074 0.026 0.187 -0.019 -0.04 0.077 0.514 -0.607
If we use PCA as a data reduction technique – we now have 6 new variables instead of original 18. Each respondent would have 6 new scores on each Factor . F i = Wi1X1 + Wi2X2 + Wi3X3 + Wi4X4 +…+ WikXk
Example Factor Matrix: Orientation towards Technology
Factor Matrix Factor 1 .654 .530 -.392 -.394 -.422 .656 .694 -.693 .680 .620 -.568 2 .221 .241 .279 .372 .257 .275 .254 .455 .212 .283 .472
I think new technology is fascinating Using a computer saves me time and work I feel very negative about technology in general Computers control too much of our world today. The Internet negatively effects my life. Using computers makes learning more fun for me Using the Internet is enjoyable. Technology is being forced on us, making us lose control of our lives. Using the Internet helps improve my life I like to be the first one to try out new technology and gadgets The Internet is having negative effects on our society. Extraction Method: Principal Axis Factoring. a 2 factors extracted. 8 iterations required.
Rotated Factor Loading Matrix
Rotated Factor Matrix Factor 1 .655 .568 -.144 -.535 -.181 .689 .706 -.277 2 -.219 -.128 .459 .535 .460 -.177 -.217 .782
I think new technology is fascinating Using a computer saves me time and work I feel very negative about technology in general Computers control too much of our world today. The Internet negatively effects my life. Using computers makes learning more fun for me Using the Internet is enjoyable. Technology is being forced on us, making us lose control of our lives. Using the Internet helps improve my life .670 -.242 I like to be the first one to try out new technology and .665 -.149 gadgets The Internet is having negative effects on our society. -.167 .720 Extraction Method: Principal Axis Factoring. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.
Rotated Matrix with Sorting and Suppression<.30)
Rotated Factor Matrix Factor 1 .706 .689 .670 .665 2
Using the Internet is enjoyable. Using computers makes learning more fun for me Using the Internet helps improve my life I like to be the first one to try out new technology and gadgets I think new technology is fascinating .655 Using a computer saves me time and work .568 Technology is being forced on us, making us lose .782 control of our lives. The Internet is having negative effects on our society. .720 Computers control too much of our world today. .535 The Internet negatively effects my life. .460 I feel very negative about technology in general .459 Extraction Method: Principal Axis Factoring. Rotation Method: Varimax with Kaiser Normalization. a Rotation converged in 3 iterations.
Tech Savvy
Tech Averse
You need at least 300 cases to run FA
doc_955131609.pptx