1 pertemuan 21 matakuliah: i0214 / statistika multivariat tahun: 2005 versi: v1 / r1 analisis...

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1 Pertemuan 21 Matakuliah : I0214 / Statistika Multivariat Tahun : 2005 Versi : V1 / R1 Analisis Struktur Peubah Ganda (I): Analisis Komponen Utama

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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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ltltISIgtgt

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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

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

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ltltISIgtgt

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ltltISIgtgt

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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

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ltltISIgtgt

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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
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  • 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)

5

ltltISIgtgt

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ltltISIgtgt

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ltltISIgtgt

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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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ltltISIgtgt

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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
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  • Slide 18
  • Slide 19
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  • 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
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  • Slide 15
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  • Slide 23
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  • Slide 25
  • ltlt CLOSINGgtgt

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15

ltltISIgtgt

16

ltltISIgtgt

17

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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
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  • ltlt CLOSINGgtgt

9

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10

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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
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  • ltlt CLOSINGgtgt

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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
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  • ltlt CLOSINGgtgt

11

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13

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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
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  • ltlt CLOSINGgtgt

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22

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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
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  • ltlt CLOSINGgtgt

13

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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
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  • ltlt CLOSINGgtgt

14

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16

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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
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  • Slide 19
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  • Slide 25
  • ltlt CLOSINGgtgt

15

ltltISIgtgt

16

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18

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20

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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
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  • Slide 15
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  • ltlt CLOSINGgtgt

16

ltltISIgtgt

17

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18

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19

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20

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21

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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
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  • 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
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  • 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
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  • 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
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  • 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
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  • 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
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  • Slide 21
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  • 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
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  • Slide 15
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  • Slide 18
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  • 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
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  • 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
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  • 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
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  • 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
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  • ltlt CLOSINGgtgt