# 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

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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

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Sheet2

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Sheet3

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Sheet4

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Sheet5

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Sheet6

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Sheet7

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Sheet8

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Sheet9

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Sheet10

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Sheet11

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Sheet12

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Sheet13

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Sheet14

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Sheet15

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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.

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

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

-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.

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

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