Chapter XIX

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Chapter XIX. Factor Analysis. Chapter Outline 1) Overview 2) Basic Concept 3) Factor Analysis Model 4) Statistics Associated with Factor Analysis. 5) Conducting Factor Analysis i. Problem Formulation ii. Construction of the Correlation Matrix - PowerPoint PPT Presentation

Text of Chapter XIX

  • Chapter XIXFactor Analysis

  • Chapter Outline1) Overview2) Basic Concept3) Factor Analysis Model4) Statistics Associated with Factor Analysis

  • 5) Conducting Factor Analysis i. Problem Formulation ii. Construction of the Correlation Matrix iii. Method of Factor Analysis iv. Number of of Factors v. Rotation of Factors vi. Interpretation of Factors vii. Factor Scores viii.Selection of Surrogate Variables ix. Model Fit

  • 6) Applications of Common Factor Analysis 7) Internet and Computer Applications 8) Focus on Burke 9) Summary10) Key Terms and Concepts11) Acronyms

  • Conducting Factor AnalysisFig 19.1Calculation ofFactor ScoresSelection ofSurrogate variablesDetermination of Model Fit

  • Table 19-1

    Sheet17

    RESPONDENT NUMBERV1V2V3V5V6

    17.003.006.004.002.004.00

    21.003.002.004.005.004.00

    36.002.007.004.001.003.00

    44.005.004.006.002.005.00

    51.002.002.003.006.002.00

    66.003.006.004.002.004.00

    75.003.006.003.004.003.00

    86.004.007.004.001.004.00

    93.004.002.003.006.003.00

    102.006.002.006.007.006.00

    116.004.007.003.002.003.00

    122.003.001.004.005.004.00

    137.002.006.004.001.003.00

    144.006.004.005.003.006.00

    151.003.002.002.006.004.00

    166.004.006.003.003.004.00

    175.003.006.003.003.004.00

    187.003.007.004.001.004.00

    192.004.003.003.006.003.00

    203.005.003.006.004.006.00

    211.003.002.003.005.003.00

    225.004.005.004.002.004.00

    232.002.001.005.004.004.00

    244.006.004.006.004.007.00

    256.005.004.002.001.004.00

    263.005.004.006.004.007.00

    274.004.007.002.002.005.00

    283.007.002.006.004.003.00

    294.006.003.007.002.007.00

    302.003.002.004.007.002.00

    Sheet1 (2)

    RESPONDENTV1V2V3V5V6

    NUMBER

    17.003.006.004.002.004.00

    21.003.002.004.005.004.00

    36.002.007.004.001.003.00

    44.005.004.006.002.005.00

    51.002.002.003.006.002.00

    66.003.006.004.002.004.00

    75.003.006.003.004.003.00

    86.004.007.004.001.004.00

    93.004.002.003.006.003.00

    102.006.002.006.007.006.00

    116.004.007.003.002.003.00

    122.003.001.004.005.004.00

    137.002.006.004.001.003.00

    144.006.004.005.003.006.00

    151.003.002.002.006.004.00

    166.004.006.003.003.004.00

    175.003.006.003.003.004.00

    187.003.007.004.001.004.00

    192.004.003.003.006.003.00

    203.005.003.006.004.006.00

    211.003.002.003.005.003.00

    225.004.005.004.002.004.00

    232.002.001.005.004.004.00

    244.006.004.006.004.007.00

    256.005.004.002.001.004.00

    263.005.004.006.004.007.00

    274.004.007.002.002.005.00

    283.007.002.006.004.003.00

    294.006.003.007.002.007.00

    302.003.002.004.007.002.00

    &A

    Page &P

    Sheet1

    TABLE 19.1

    TOOTHPASTE ATTRIBUTE RATINGS

    RESPONDENTV1V2V3V5V6

    NUMBER

    17.003.006.004.002.004.00

    21.003.002.004.005.004.00

    36.002.007.004.001.003.00

    44.005.004.006.002.005.00

    51.002.002.003.006.002.00

    66.003.006.004.002.004.00

    75.003.006.003.004.003.00

    86.004.007.004.001.004.00

    93.004.002.003.006.003.00

    102.006.002.006.007.006.00

    116.004.007.003.002.003.00

    122.003.001.004.005.004.00

    137.002.006.004.001.003.00

    144.006.004.005.003.006.00

    151.003.002.002.006.004.00

    166.004.006.003.003.004.00

    175.003.006.003.003.004.00

    187.003.007.004.001.004.00

    192.004.003.003.006.003.00

    203.005.003.006.004.006.00

    211.003.002.003.005.003.00

    225.004.005.004.002.004.00

    232.002.001.005.004.004.00

    244.006.004.006.004.007.00

    256.005.004.002.001.004.00

    263.005.004.006.004.007.00

    274.004.007.002.002.005.00

    283.007.002.006.004.003.00

    294.006.003.007.002.007.00

    302.003.002.004.007.002.00

    &A

    Page &P

    Sheet2

    &A

    Page &P

    Sheet3

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    Page &P

    Sheet4

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    Page &P

    Sheet5

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    Sheet6

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    Page &P

    Sheet7

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    Sheet8

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    Page &P

    Sheet9

    &A

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    Sheet10

    &A

    Page &P

    Sheet11

    &A

    Page &P

    Sheet12

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    Sheet13

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    Sheet14

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    Sheet15

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    Sheet16

    &A

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  • Correlation MatrixTable 19.2

    Variables

    V1

    V2

    V3

    V4

    V5

    V6

    V1

    1.00

    V2

    -0.53

    1.00

    V3

    .873

    -.155

    1.00

    V4

    -.086

    .572

    -.248

    1.00

    V5

    -.858

    .020

    -.778

    -.007

    1.00

    V6

    .004

    .640

    -.018

    .640

    -.136

    1.00

  • Results of Principal Components AnalysisTable 19.3Barlett test of sphericity Approx. Chi-Square = 111.314 df = 15 Significance = .00000 Kaiser-Meyer-Olkin measure of sampling adequacy = .660

    Communalities

    Variables

    Initial

    Extraction

    V1

    1.000

    .926

    V2

    1.000

    .723

    V3

    1.000

    .894

    V4

    1.000

    .739

    V5

    1.000

    .878

    V6

    1.000

    .790

    Initial Eigenvalues

    Factor

    Eigenvalue

    % of variance

    Cumulat. %

    1

    2.731

    45.520

    45.520

    2

    2.218

    36.969

    82.488

    3

    0.442

    7.360

    89.848

    4

    0.341

    5.688

    95.536

    5

    0.183

    3.044

    98.580

    6

    0.085

    1.420

    100.000

  • Table 19.2 Contd.

    Extraction Sums of Squared Loadings

    Factor

    Eigenvalue

    % of variance

    Cumulat. %

    1

    2.731

    45.520

    45.520

    2

    2.218

    36.969

    82.488

    Factor Matrix

    Variables

    Factor 1

    Factor 2

    V1

    .928

    .253

    V2

    -.301

    .795

    V3

    .936

    .131

    V4

    -.342

    .789

    V5

    -.869

    -.351

    V6

    -.177

    .871

    Rotation Sums of Squared Loadings

    Factor

    Eigenvalue

    % of variance

    Cumulat. %

    1

    2.688

    44.802

    44.802

    2

    2.261

    37.687

    82.488

  • Table 19.2 Contd.

    Rotated Factor Matrix

    Variables

    Factor 1

    Factor 2

    V1

    .962

    -.027

    V2

    -.057

    .848

    V3

    .934

    -.146

    V4

    -.098

    .845

    V5

    -.933

    -.084

    V6

    .083

    .885

    Factor Score Coefficient Matrix

    Variables

    Factor 1

    Factor 2

    V1

    .358

    .011

    V2

    -.001

    .375

    V3

    .345

    -.043

    V4

    -.017

    .377

    V5

    -.350

    -.059

    V6

    .052

    .395

  • The lower left triangle contains the reproduced correlation matrix; the diagonal, the communities; the upper right triangle, the residuals between the observed correlations and the reproduced correlations.Table 19.2 Contd.

    Factor Score Coefficient Matrix

    Variables

    V1

    V2

    V3

    V4

    V5

    V6

    V1

    .926

    .024

    -.029

    .031

    .038

    -.053

    V2

    -.078

    .723

    .022

    -.158

    .038

    -.105

    V3

    .902

    -.177

    .894

    -.031

    .081

    .033

    V4

    -.117

    .730

    -.217

    .739

    -.027

    -.107

    V5

    -.895

    -.018

    -.859

    .020

    .878

    .016

    V6

    .057

    .746

    -.051

    .748

    -.152

    .790

  • Screen Plot Fig. 19.2 0.5 2 5 4 3 6 Component Number 0.0 2.0 3.0 Eigenvalue 1.0 1.5 2.5 1

  • Factor Loading Plot Fig. 19.3 1.0 0.5 0.0 -.5

    -1.0Component 2 Component 1 Component Variable 1 2 V1 0.962 -2.66E-02V2 -5.72E-02 .848V3 0.934 -.146V4 -9.83E-02 .854V5 -.933 -8.40E-02V6 8.337E-02 0.885Component Plot in Rotated Space 1.00.50.0-.5-1.0 V1 V3 V6 V2 V5 V4Rotated Component Matrix

  • Results of Common Factor AnalysisTable 19.4Barlett test of sphericity Approx. Chi-Square = 111.314 df = 15 Significance = .00000 Kaiser-Meyer-Olkin measure of sampling adequacy = .660

    Communalities

    Variables

    Initial

    Extraction

    V1

    .859

    .928

    V2

    .480

    .562

    V3

    .814

    .836

    V4

    .543

    .600

    V5

    .763

    .789

    V6

    .587

    .723

    Initial Eigenvalues

    Factor

    Eigenvalue

    % of variance

    Cumulat. %

    1

    2.731

    45.520

    45.520

    2

    2.218

    36.969

    82.488

    3

    0.442

    7.360

    89.848

    4

    0.341

    5.688

    95.536

    5

    0.183

    3.044

    98.580

    6

    0.085

    1.420

    100.000

  • Table 19.4 Contd.

    Extraction Sums of Squared Loadings

    Factor

    Eigenvalue

    % of variance

    Cumulat. %

    1

    2.570

    42.837

    42.837

    2

    1.868

    31.126

    73.964

    Factor Matrix

    Variables

    Factor 1

    Factor 2

    V1

    .949

    .168

    V2

    -.206

    .720

    V3

    .914

    .038

    V4

    -.246

    .734

    V5

    -.850

    -.259

    V6

    -.101

    .844

    Rotation Sums of Squared Loadings