(Stock Data): Principal Factor Method with Varimax Rotation

 

The FACTOR Procedure

Initial Factor Method: Principal Components

 

Prior Communality Estimates: ONE

Eigenvalues of the Correlation Matrix: Total
= 5 Average = 1

 

Eigenvalue

Difference

Proportion

Cumulative

1

2.43761478

1.03135359

0.4875

0.4875

2

1.40626120

0.90607546

0.2813

0.7688

3

0.50018573

0.10015292

0.1000

0.8688

4

0.40003281

0.14412732

0.0800

0.9488

5

0.25590548

 

0.0512

1.0000

 

2 factors will be retained by the NFACTOR criterion.

Factor Pattern

 

Factor1

Factor2

x1

0.73258

-0.43614

x2

0.83096

-0.28039

x3

0.72635

-0.37403

x4

0.60474

0.69375

x5

0.56317

0.71850

 

Variance Explained by Each
Factor

Factor1

Factor2

2.4376148

1.4062612

 

Final Communality Estimates: Total = 3.843876

x1

x2

x3

x4

x5

0.72689087

0.76910539

0.66748055

0.84699821

0.83340095

 

Residual Correlations With Uniqueness on the Diagonal

 

x1

x2

x3

x4

x5

x1

0.27311

-0.09903

-0.18424

-0.02545

0.05580

x2

-0.09903

0.23089

-0.13444

0.01401

-0.05352

x3

-0.18424

-0.13444

0.33252

0.00323

0.00568

x4

-0.02545

0.01401

0.00323

0.15300

-0.15603

x5

0.05580

-0.05352

0.00568

-0.15603

0.16660

 

Root Mean Square Off-Diagonal Residuals: Overall = 0.09645329

x1

x2

x3

x4

x5

0.10898520

0.08794901

0.11408265

0.07937147

0.08711316

 

Partial Correlations Controlling Factors

 

x1

x2

x3

x4

x5

x1

1.00000

-0.39436

-0.61137

-0.12448

0.26158

x2

-0.39436

1.00000

-0.48518

0.07452

-0.27286

x3

-0.61137

-0.48518

1.00000

0.01434

0.02414

x4

-0.12448

0.07452

0.01434

1.00000

-0.97729

x5

0.26158

-0.27286

0.02414

-0.97729

1.00000

 

Root Mean Square Off-Diagonal Partials: Overall = 0.43410706

x1

x2

x3

x4

x5

0.39153754

0.34311832

0.39049831

0.49405058

0.52405910

 


(Stock Data): Principal Factor Method with Varimax Rotation

 

The FACTOR Procedure

Initial Factor Method: Principal Components

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                       B                                                        
                                               .8                                               
                                  A C                                                           
                                               .7                                               
                                                                                                
                                               .6                   D                           
                                                                     E                          
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                                F               
                                               .1                               a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
               x1=A          x2=B          x3=C          x4=D          x5=E                     

 


(Stock Data): Principal Factor Method with Varimax Rotation

 

The FACTOR Procedure

Rotation Method: Varimax

Orthogonal Transformation Matrix

 

1

2

1

0.84070

0.54150

2

-0.54150

0.84070

 

Rotated Factor Pattern

 

Factor1

Factor2

x1

0.85205

0.03002

x2

0.85042

0.21424

x3

0.81318

0.07886

x4

0.13275

0.91070

x5

0.08440

0.90900

 

Variance Explained by Each
Factor

Factor1

Factor2

2.1352041

1.7086719

 

Final Communality Estimates: Total = 3.843876

x1

x2

x3

x4

x5

0.72689087

0.76910539

0.66748055

0.84699821

0.83340095

 


(Stock Data): Principal Factor Method with Varimax Rotation

 

The FACTOR Procedure

Rotation Method: Varimax

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                A     B                                         
                                               .8 C                                             
                                                                                                
                                               .7                                               
                                                                                                
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                           D    F               
                                               .1                          E    a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
               x1=A          x2=B          x3=C          x4=D          x5=E                     

 


#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

 

The FACTOR Procedure

Initial Factor Method: Maximum Likelihood

Prior Communality Estimates: SMC

x1

x2

x3

x4

x5

0.45156689

0.53347907

0.36655825

0.51643642

0.47767780

 

Preliminary Eigenvalues: Total = 4.52808758
Average = 0.90561752

 

Eigenvalue

Difference

Proportion

Cumulative

1

3.67372695

1.95722570

0.8113

0.8113

2

1.71650125

1.86845966

0.3791

1.1904

3

-.15195842

0.07024376

-0.0336

1.1568

4

-.22220217

0.26577786

-0.0491

1.1078

5

-.48798003

 

-0.1078

1.0000

 

2 factors will be retained by the NFACTOR criterion.

Iteration

Criterion

Ridge

Change

Communalities

1

0.0979665

0.0313

0.4836

0.52461

0.64776

0.42439

1.00000

0.23287

2

0.0195937

0.0000

0.2349

0.58313

0.72449

0.45774

1.00000

0.46775

3

0.0195920

0.0000

0.0010

0.58408

0.72379

0.45854

1.00000

0.46756

 

Convergence criterion satisfied.

 

Significance Tests Based on 10000 Observations

Test

DF

Chi-Square

Pr >
ChiSq

H0: No common factors

10

17393.6805

<.0001

HA: At least one common factor

 

 

 

H0: 2 Factors are sufficient

1

195.8253

<.0001

HA: More factors are needed

 

 

 

 

Chi-Square without Bartlett's Correction

195.90039

Akaike's Information Criterion

193.90039

Schwarz's Bayesian Criterion

186.69005

Tucker and Lewis's Reliability Coefficient

0.88793

 

Squared Canonical Correlations

Factor1

Factor2

1.0000000

0.8149733

 

Eigenvalues of the Weighted Reduced Correlation Matrix: Total = 4.40462521 Average = 1.1011563

 

Eigenvalue

Difference

Proportion

Cumulative

1

Infty

Infty

 

 

2

4.40462638

4.26529969

1.0000

1.0000

3

0.13932669

0.13939470

0.0316

1.0316

4

-.00006801

0.13919184

-0.0000

1.0316

5

-.13925985

 

-0.0316

1.0000

 

Factor Pattern

 

Factor1

Factor2

x1

0.11500

0.75555

x2

0.32200

0.78747

x3

0.18300

0.65195

x4

1.00000

-0.00000

x5

0.68300

0.03281

 

Variance Explained by Each Factor

Factor

Weighted

Unweighted

Factor1

1.34516012

1.61688700

Factor2

4.40462638

1.61708744

 

Final Communality Estimates
and Variable Weights

Total Communality: Weighted
= 5.749786 Unweighted = 3.233974

Variable

Communality

Weight

x1

0.58408551

2.40432917

x2

0.72379091

3.62045851

x3

0.45853266

1.84686184

x4

1.00000000

Infty

x5

0.46756536

1.87813579

 

Residual Correlations With Uniqueness on the Diagonal

 

x1

x2

x3

x4

x5

x1

0.41591

-0.00000

-0.00263

0.00000

0.05167

x2

-0.00000

0.27621

0.00168

0.00000

-0.03276

x3

-0.00263

0.00168

0.54147

0.00000

-0.00038

x4

0.00000

0.00000

0.00000

0.00000

0.00000

x5

0.05167

-0.03276

-0.00038

0.00000

0.53243

 

Root Mean Square Off-Diagonal Residuals: Overall = 0.01937176

x1

x2

x3

x4

x5

0.02586691

0.01640214

0.00157232

0.00000000

0.03058965

 

Partial Correlations Controlling Factors

 

x1

x2

x3

x4

x5

x1

1.00000

-0.00001

-0.00554

0.00000

0.10979

x2

-0.00001

1.00000

0.00435

0.00000

-0.08543

x3

-0.00554

0.00435

1.00000

0.00000

-0.00070

x4

0.00000

0.00000

0.00000

0.00000

0.00000

x5

0.10979

-0.08543

-0.00070

0.00000

1.00000

 

Root Mean Square Off-Diagonal Partials: Overall = 0.04404878

x1

x2

x3

x4

x5

0.05496674

0.04276996

0.00353966

0.00000000

0.06955812

 


#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

 

The FACTOR Procedure

Initial Factor Method: Maximum Likelihood

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                D                                               
                                                                                                
                                               .9                                               
                                                                                                
                                               .8                                               
                                                                                                
                                               .E                                               
                                                                                                
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                      B                        
                                                                                                
                                               .2                  C                            
                                                                                F               
                                               .1                     A         a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
               x1=A          x2=B          x3=C          x4=D          x5=E                     

 


#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

 

The FACTOR Procedure

Rotation Method: Varimax

Orthogonal Transformation Matrix

 

1

2

1

0.11841

0.99297

2

0.99297

-0.11841

 

Rotated Factor Pattern

 

Factor1

Factor2

x1

0.76385

0.02473

x2

0.82006

0.22649

x3

0.66904

0.10452

x4

0.11841

0.99297

x5

0.11345

0.67431

 

Variance Explained by Each Factor

Factor

Weighted

Unweighted

Factor1

4.68843713

1.73046567

Factor2

1.06134937

1.50350876

 

Final Communality Estimates
and Variable Weights

Total Communality: Weighted
= 5.749786 Unweighted = 3.233974

Variable

Communality

Weight

x1

0.58408551

2.40432917

x2

0.72379091

3.62045851

x3

0.45853266

1.84686184

x4

1.00000000

Infty

x5

0.46756536

1.87813579

 


#3b (Stock Data): Maximum Likelihood Method (k=2 factor)

 

The FACTOR Procedure

Rotation Method: Varimax

Plot of Factor Pattern for Factor1 and Factor2                                                  
                                                                                                
                                             Factor1                                            
                                                1                                               
                                                                                                
                                               .9                                               
                                                                                                
                                               .8     B                                         
                                                A                                               
                                               .7                                               
                                                   C                                            
                                               .6                                               
                                                                                                
                                               .5                                               
                                                                                                
                                               .4                                               
                                                                                                
                                               .3                                               
                                                                                                
                                               .2                                               
                                                                                F               
                                               .1                   E        D  a               
                                                                                c               
                -1 -.9-.8-.7-.6-.5-.4-.3-.2-.1  0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0t               
                                                                                o               
                                              -.1                               r               
                                                                                2               
                                              -.2                                               
                                                                                                
                                              -.3                                               
                                                                                                
                                              -.4                                               
                                                                                                
                                              -.5                                               
                                                                                                
                                              -.6                                               
                                                                                                
                                              -.7                                               
                                                                                                
                                              -.8                                               
                                                                                                
                                              -.9                                               
                                                                                                
                                               -1                                               
                                                                                                
               x1=A          x2=B          x3=C          x4=D          x5=E