pertemuan 21
DESCRIPTION
Pertemuan 21. Analisis Struktur Peubah Ganda (I): Analisis Komponen Utama. Matakuliah: I0214 / Statistika Multivariat Tahun: 2005 Versi: V1 / R1. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : - PowerPoint PPT PresentationTRANSCRIPT
1
Pertemuan 21
Matakuliah I0214 Statistika MultivariatTahun 2005Versi V1 R1
Analisis Struktur Peubah Ganda (I)Analisis Komponen Utama
2
Learning Outcomes
Pada akhir pertemuan ini diharapkan mahasiswa akan mampu
bull Mahasiswa dapat menganalisis struktur peubah ganda C4
bull Mahasiswa dapat menggunakan analisis komponen utama C3
3
Outline Materi
bull Konsep dasar analisis komponen utama
bull Analisis komponen utama
4
ltltISIgtgt
Overview of PCA
One of the major objectives in exploratory data analysis ofmultivariate data is dimension reduction
1048596To screen data for obvious outliers1048596To select low-dimensional projections of the data for graphing1048596To search for ldquostructurerdquo in the data
The primary statistical tool to accomplish this is through the creationof Principal Components
A principal component is defined as a linear combination orprojection of optimally-weighted observed variables
(In appearance this linear function is similar to a multiple regressionequation except that there is no intercept term)
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PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
2
Learning Outcomes
Pada akhir pertemuan ini diharapkan mahasiswa akan mampu
bull Mahasiswa dapat menganalisis struktur peubah ganda C4
bull Mahasiswa dapat menggunakan analisis komponen utama C3
3
Outline Materi
bull Konsep dasar analisis komponen utama
bull Analisis komponen utama
4
ltltISIgtgt
Overview of PCA
One of the major objectives in exploratory data analysis ofmultivariate data is dimension reduction
1048596To screen data for obvious outliers1048596To select low-dimensional projections of the data for graphing1048596To search for ldquostructurerdquo in the data
The primary statistical tool to accomplish this is through the creationof Principal Components
A principal component is defined as a linear combination orprojection of optimally-weighted observed variables
(In appearance this linear function is similar to a multiple regressionequation except that there is no intercept term)
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ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
3
Outline Materi
bull Konsep dasar analisis komponen utama
bull Analisis komponen utama
4
ltltISIgtgt
Overview of PCA
One of the major objectives in exploratory data analysis ofmultivariate data is dimension reduction
1048596To screen data for obvious outliers1048596To select low-dimensional projections of the data for graphing1048596To search for ldquostructurerdquo in the data
The primary statistical tool to accomplish this is through the creationof Principal Components
A principal component is defined as a linear combination orprojection of optimally-weighted observed variables
(In appearance this linear function is similar to a multiple regressionequation except that there is no intercept term)
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ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
4
ltltISIgtgt
Overview of PCA
One of the major objectives in exploratory data analysis ofmultivariate data is dimension reduction
1048596To screen data for obvious outliers1048596To select low-dimensional projections of the data for graphing1048596To search for ldquostructurerdquo in the data
The primary statistical tool to accomplish this is through the creationof Principal Components
A principal component is defined as a linear combination orprojection of optimally-weighted observed variables
(In appearance this linear function is similar to a multiple regressionequation except that there is no intercept term)
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ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
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PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
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ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
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ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
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PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
9
ltltISIgtgt
10
ltltISIgtgt
11
ltltISIgtgt
12
ltltISIgtgt
13
ltltISIgtgt
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
10
ltltISIgtgt
11
ltltISIgtgt
12
ltltISIgtgt
13
ltltISIgtgt
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
11
ltltISIgtgt
12
ltltISIgtgt
13
ltltISIgtgt
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
12
ltltISIgtgt
13
ltltISIgtgt
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
13
ltltISIgtgt
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
14
ltltISIgtgt
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
15
ltltISIgtgt
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
16
ltltISIgtgt
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
17
ltltISIgtgt
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
18
ltltISIgtgt
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
19
ltltISIgtgt
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
20
ltltISIgtgt
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
21
ltltISIgtgt
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
22
ltltISIgtgt
PCA IssuesSample SizeNo less than 50 observations better to have 100 Rule of thumb is to have at least 20 observations per variable
Measurement ScalesTheory assumes continuous variables If all variables are binary use correspondence analysis
Original or Standardized VariablesPrinciple component analysis can be performed on standardized variables (ie assessing the correlation matrix) or unstandardized values (Ie using the covariance matrix) Standardized scores aid comparisons among different variables especially when those variables have quite different variances The difference in variances can be very important in the definition of components
Number or VariablesPCA can be performed on any number of variables With large numbers of variables there is a much higher chance that some of the components will have zero or very small eigenvalues indicating exact or near collinearity Variables that do not weigh highly in the more significant components may be dropped and components recomputed Removed variables can be analyzed in their own separate analysis
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
23
ltltISIgtgt
Number of Components to PlotHow many components to plot will depend on the relative values of the
eigenvalues and the analysts criteria as to how much of the total variation
must be explained Typical criteria are described below
bull Latent Root Criterion
Plot combinations of components having eigenvalues gt1 Use fewer factors if the number of variables is less than 50 and more if the number of variables greater than 50
bull Percentage of Variance Criterion
Consider components important until the fraction of explained variance exceeds some pre-specified level say 95 in the natural sciences or 60 in the social sciences or when the last component added adds less than 5
bull Scree Test Criterion
Examination of the Scree Plot to identify the number of components where the curve first begins to straighten out
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
24
ltltISIgtgt
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
25
ltltISIgtgt
PCA Summary
Principal components analysis is a powerful and useful multivariate technique for reducing the dimensions of data sets with large numbers of continuous variables
Because PCA utilizes only linear combinations the ordering of the distances between points in p-dimensional space is not changed
Can be used to develop measures capable of representing a number of observed variables (The first couple of components)
There is a high degree of subjectivity in deciding on the number of components to examine and interpretation of those components
PCA is usually applied to the correlation matrix associated with a set of variables (R-mode) or observations (Q-mode) It may also be applied to the covariance matrix of observations that have been centered but not scaled
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-
26
ltlt CLOSINGgtgt
bull Sampai dengan saat ini Anda telah mempelajari kosep dasar analisis komponen utama
bull Untuk dapat lebih memahami konsep dasar analisis komponen utama tersebut cobalah Anda pelajari materi penunjang websiteinternet dan mengerjakan latihan
- Pertemuan 21
- Learning Outcomes
- Outline Materi
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- ltlt CLOSINGgtgt
-