Mplus VERSION 5.1

MUTHEN & MUTHEN

06/18/2009 10:14 AM

INPUT INSTRUCTIONS

TITLE: ex4.2.inp

This is an example of an exploratory

factor analysis with categorical factor

indicators

It uses weighted least squares estimation

It computes tetrachoric correlations and does the

Factor analysis on them. The RMSEA and chi-square

Values are reported.

DATA:

FILE IS ex4.2.dat;

VARIABLE:

NAMES ARE u1-u12;

CATEGORICAL ARE u1-u12;

ANALYSIS:

TYPE = EFA 1 4;

! ESTIMATOR = MLR;

PROCESSORS = 4 ;

INPUT READING TERMINATED NORMALLY

ex4.2.inp

This is an example of an exploratory

factor analysis with categorical factor

indicators

It uses weighted least squares estimation

It computes tetrachoric correlations and does the

Factor analysis on them. The RMSEA and chi-square

Values are reported.

SUMMARY OF ANALYSIS

Number of groups 1

Number of observations 500

Number of dependent variables 12

Number of independent variables 0

Number of continuous latent variables 0

Observed dependent variables

Binary and ordered categorical (ordinal)

U1 U2 U3 U4 U5 U6

U7 U8 U9 U10 U11 U12

Estimator WLSM

Rotation GEOMIN

Row standardization CORRELATION

Type of rotation OBLIQUE

Epsilon value Varies

Maximum number of iterations 1000

Convergence criterion 0.500D-04

Maximum number of steepest descent iterations 20

Optimization Specifications for the Exploratory Factor Analysis

Rotation Algorithm

Number of random starts 30

Maximum number of iterations 10000

Derivative convergence criterion 0.100D-04

Input data file(s)

ex4.2.dat

Input data format FREE

SUMMARY OF CATEGORICAL DATA PROPORTIONS

Category 1 0.494

Category 2 0.506

Category 1 0.484

Category 2 0.516

Category 1 0.528

Category 2 0.472

Category 1 0.504

Category 2 0.496

Category 1 0.486

Category 2 0.514

Category 1 0.504

Category 2 0.496

Category 1 0.496

Category 2 0.504

Category 1 0.492

Category 2 0.508

Category 1 0.514

Category 2 0.486

U10

Category 1 0.496

Category 2 0.504

U11

Category 1 0.490

Category 2 0.510

U12

Category 1 0.502

Category 2 0.498

RESULTS FOR EXPLORATORY FACTOR ANALYSIS

EIGENVALUES FOR SAMPLE CORRELATION MATRIX

1 2 3 4 5

______

1 2.326 2.230 2.009 1.710 0.659

EIGENVALUES FOR SAMPLE CORRELATION MATRIX

6 7 8 9 10

______

1 0.655 0.524 0.496 0.471 0.350

EIGENVALUES FOR SAMPLE CORRELATION MATRIX

11 12

______

1 0.320 0.248

EXPLORATORY FACTOR ANALYSIS WITH 1 FACTOR(S):

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 898.350*

Degrees of Freedom 54

P-Value 0.0000

Scaling Correction Factor 0.874

for MLR

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference tests. MLM, MLR and WLSM chi-square difference

testing is described in the Mplus Technical Appendices at

See chi-square difference testing in the index of the Mplus User's Guide.

Chi-Square Test of Model Fit for the Baseline Model

Value 1179.976

Degrees of Freedom 66

P-Value 0.0000

CFI/TLI

CFI 0.242

TLI 0.074

Number of Free Parameters 12

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.177

SRMR (Standardized Root Mean Square Residual)

Value 0.189

MINIMUM ROTATION FUNCTION VALUE 1.89944

GEOMIN ROTATED LOADINGS

______

U1 0.608

U2 0.689

U3 0.596

U4 0.038

U5 -0.019

U6 0.099

U7 0.460

U8 0.398

U9 0.390

U10 -0.249

U11 -0.286

U12 -0.143

GEOMIN FACTOR CORRELATIONS

______

1 1.000

ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.630 0.526 0.645 0.999 1.000

ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.990 0.788 0.841 0.848 0.938

ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.918 0.980

S.E. GEOMIN ROTATED LOADINGS

______

U1 0.057

U2 0.056

U3 0.055

U4 0.069

U5 0.069

U6 0.068

U7 0.060

U8 0.062

U9 0.061

U10 0.066

U11 0.065

U12 0.067

S.E. GEOMIN FACTOR CORRELATIONS

______

1 0.000

S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.069 0.078 0.065 0.005 0.003

S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.013 0.055 0.050 0.048 0.033

S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.037 0.019

Est./S.E. GEOMIN ROTATED LOADINGS

______

U1 10.660

U2 12.217

U3 10.939

U4 0.549

U5 -0.275

U6 1.447

U7 7.711

U8 6.403

U9 6.358

U10 -3.784

U11 -4.375

U12 -2.125

Est./S.E. GEOMIN FACTOR CORRELATIONS

______

1 0.000

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 9.078 6.767 9.916 192.224 386.069

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 73.504 14.351 16.992 17.690 28.600

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 24.571 50.953

FACTOR DETERMINACIES

______

1 0.861

EXPLORATORY FACTOR ANALYSIS WITH 2 FACTOR(S):

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 589.635*

Degrees of Freedom 43

P-Value 0.0000

Scaling Correction Factor 0.724

for MLR

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference tests. MLM, MLR and WLSM chi-square difference

testing is described in the Mplus Technical Appendices at

See chi-square difference testing in the index of the Mplus User's Guide.

Chi-Square Test of Model Fit for the Baseline Model

Value 1179.976

Degrees of Freedom 66

P-Value 0.0000

CFI/TLI

CFI 0.509

TLI 0.247

Number of Free Parameters 23

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.159

SRMR (Standardized Root Mean Square Residual)

Value 0.147

MINIMUM ROTATION FUNCTION VALUE 0.76516

GEOMIN ROTATED LOADINGS

1 2

______

U1 0.630 0.109

U2 0.793 -0.004

U3 0.670 -0.008

U4 -0.171 0.361

U5 -0.290 0.452

U6 -0.126 0.438

U7 0.326 0.431

U8 0.256 0.422

U9 0.267 0.382

U10 -0.012 -0.475

U11 -0.001 -0.599

U12 0.132 -0.499

GEOMIN FACTOR CORRELATIONS

1 2

______

1 1.000

2 -0.053 1.000

ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.599 0.371 0.551 0.834 0.697

ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.786 0.723 0.768 0.793 0.775

ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.642 0.726

S.E. GEOMIN ROTATED LOADINGS

1 2

______

U1 0.057 0.071

U2 0.055 0.020

U3 0.055 0.048

U4 0.079 0.066

U5 0.080 0.067

U6 0.079 0.064

U7 0.078 0.067

U8 0.080 0.066

U9 0.075 0.066

U10 0.063 0.062

U11 0.012 0.057

U12 0.070 0.062

S.E. GEOMIN FACTOR CORRELATIONS

1 2

______

1 0.000

2 0.108 0.000

S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.071 0.088 0.074 0.052 0.067

S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.057 0.062 0.059 0.055 0.059

S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.069 0.064

Est./S.E. GEOMIN ROTATED LOADINGS

1 2

______

U1 11.113 1.522

U2 14.296 -0.212

U3 12.127 -0.175

U4 -2.172 5.459

U5 -3.636 6.732

U6 -1.592 6.828

U7 4.151 6.414

U8 3.219 6.352

U9 3.588 5.769

U10 -0.195 -7.658

U11 -0.084 -10.459

U12 1.891 -8.109

Est./S.E. GEOMIN FACTOR CORRELATIONS

1 2

______

1 0.000

2 -0.493 0.000

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 8.482 4.215 7.464 16.092 10.417

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 13.705 11.622 13.116 14.531 13.165

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 9.361 11.424

FACTOR STRUCTURE

1 2

______

U1 0.624 0.075

U2 0.793 -0.047

U3 0.670 -0.044

U4 -0.190 0.370

U5 -0.314 0.468

U6 -0.149 0.445

U7 0.303 0.413

U8 0.234 0.409

U9 0.247 0.368

U10 0.013 -0.474

U11 0.031 -0.599

U12 0.159 -0.506

FACTOR DETERMINACIES

1 2

______

1 0.887 0.849

EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 308.143*

Degrees of Freedom 33

P-Value 0.0000

Scaling Correction Factor 0.557

for MLR

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference tests. MLM, MLR and WLSM chi-square difference

testing is described in the Mplus Technical Appendices at

See chi-square difference testing in the index of the Mplus User's Guide.

Chi-Square Test of Model Fit for the Baseline Model

Value 1179.976

Degrees of Freedom 66

P-Value 0.0000

CFI/TLI

CFI 0.753

TLI 0.506

Number of Free Parameters 33

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.129

SRMR (Standardized Root Mean Square Residual)

Value 0.095

MINIMUM ROTATION FUNCTION VALUE 0.20246

GEOMIN ROTATED LOADINGS

1 2 3

______

U1 0.646 0.105 -0.047

U2 0.875 -0.007 0.025

U3 0.713 -0.013 0.021

U4 -0.014 -0.115 -0.502

U5 -0.181 -0.007 -0.536

U6 -0.046 0.068 -0.468

U7 0.018 0.807 0.023

U8 -0.039 0.722 -0.016

U9 -0.002 0.667 0.002

U10 -0.181 0.029 0.566

U11 -0.145 -0.073 0.639

U12 -0.004 -0.001 0.573

GEOMIN FACTOR CORRELATIONS

1 2 3

______

1 1.000

2 0.025 1.000

3 0.064 -0.057 1.000

ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.570 0.230 0.490 0.740 0.668

ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.768 0.349 0.478 0.555 0.661

ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.571 0.672

S.E. GEOMIN ROTATED LOADINGS

1 2 3

______

U1 0.057 0.073 0.068

U2 0.057 0.035 0.043

U3 0.056 0.050 0.042

U4 0.043 0.073 0.065

U5 0.071 0.036 0.062

U6 0.073 0.074 0.063

U7 0.043 0.061 0.056

U8 0.070 0.059 0.049

U9 0.039 0.059 0.045

U10 0.085 0.070 0.063

U11 0.084 0.085 0.062

U12 0.059 0.069 0.062

S.E. GEOMIN FACTOR CORRELATIONS

1 2 3

______

1 0.000

2 0.080 0.000

3 0.096 0.092 0.000

S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.074 0.100 0.080 0.066 0.070

S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.060 0.097 0.085 0.078 0.072

S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.078 0.070

Est./S.E. GEOMIN ROTATED LOADINGS

1 2 3

______

U1 11.336 1.435 -0.684

U2 15.239 -0.210 0.591

U3 12.671 -0.268 0.501

U4 -0.324 -1.570 -7.758

U5 -2.538 -0.186 -8.591

U6 -0.625 0.917 -7.412

U7 0.412 13.267 0.407

U8 -0.563 12.195 -0.323

U9 -0.046 11.364 0.052

U10 -2.131 0.417 9.055

U11 -1.722 -0.862 10.330

U12 -0.069 -0.020 9.300

Est./S.E. GEOMIN FACTOR CORRELATIONS

1 2 3

______

1 0.000

2 0.319 0.000

3 0.662 -0.617 0.000

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 7.692 2.312 6.152 11.275 9.515

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 12.887 3.581 5.623 7.105 9.152

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 7.348 9.596

FACTOR STRUCTURE

1 2 3

______

U1 0.645 0.124 -0.011

U2 0.877 0.013 0.082

U3 0.714 0.004 0.067

U4 -0.049 -0.087 -0.496

U5 -0.216 0.019 -0.547

U6 -0.074 0.093 -0.475

U7 0.040 0.806 -0.022

U8 -0.022 0.721 -0.059

U9 0.015 0.667 -0.036

U10 -0.144 -0.008 0.553

U11 -0.106 -0.113 0.634

U12 0.032 -0.034 0.572

FACTOR DETERMINACIES

1 2 3

______

1 0.916 0.890 0.857

EXPLORATORY FACTOR ANALYSIS WITH 4 FACTOR(S):

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 22.741*

Degrees of Freedom 24

P-Value 0.5351

Scaling Correction Factor 0.402

for MLR

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference tests. MLM, MLR and WLSM chi-square difference

testing is described in the Mplus Technical Appendices at

See chi-square difference testing in the index of the Mplus User's Guide.

Chi-Square Test of Model Fit for the Baseline Model

Value 1179.976

Degrees of Freedom 66

P-Value 0.0000

CFI/TLI

CFI 1.000

TLI 1.003

Number of Free Parameters 42

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.000

SRMR (Standardized Root Mean Square Residual)

Value 0.024

MINIMUM ROTATION FUNCTION VALUE 0.38499

GEOMIN ROTATED LOADINGS

1 2 3 4

______

U1 0.628 -0.004 0.098 -0.061

U2 0.938 0.042 -0.012 0.070

U3 0.690 -0.073 -0.019 -0.036

U4 0.072 0.705 -0.120 -0.005

U5 -0.130 0.805 0.018 0.016

U6 0.015 0.602 0.089 -0.045

U7 0.026 -0.014 0.805 0.009

U8 -0.036 -0.003 0.720 -0.029

U9 0.017 0.034 0.669 0.025

U10 -0.066 -0.017 0.057 0.654

U11 -0.005 0.040 -0.056 0.872

U12 0.110 -0.069 0.022 0.624

GEOMIN FACTOR CORRELATIONS

1 2 3 4

______

1 1.000

2 -0.026 1.000

3 0.025 0.032 1.000

4 -0.029 -0.150 -0.059 1.000

ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.586 0.121 0.515 0.491 0.331

ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.615 0.352 0.479 0.550 0.563

ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.239 0.586

S.E. GEOMIN ROTATED LOADINGS

1 2 3 4

______

U1 0.057 0.049 0.066 0.062

U2 0.060 0.040 0.029 0.049

U3 0.057 0.064 0.047 0.043

U4 0.058 0.067 0.074 0.048

U5 0.077 0.072 0.017 0.043

U6 0.033 0.064 0.070 0.065

U7 0.041 0.044 0.060 0.042

U8 0.051 0.047 0.059 0.053

U9 0.048 0.056 0.059 0.052

U10 0.060 0.049 0.058 0.064

U11 0.019 0.043 0.049 0.070

U12 0.066 0.065 0.044 0.064

S.E. GEOMIN FACTOR CORRELATIONS

1 2 3 4

______

1 0.000

2 0.083 0.000

3 0.067 0.077 0.000

4 0.070 0.070 0.071 0.000

S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 0.072 0.113 0.078 0.093 0.114

S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 0.075 0.096 0.084 0.078 0.083

S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 0.120 0.078

Est./S.E. GEOMIN ROTATED LOADINGS

1 2 3 4

______

U1 11.001 -0.072 1.498 -0.979

U2 15.608 1.045 -0.412 1.423

U3 12.041 -1.140 -0.404 -0.842

U4 1.237 10.456 -1.639 -0.104

U5 -1.679 11.112 1.093 0.376

U6 0.466 9.384 1.284 -0.698

U7 0.648 -0.309 13.377 0.215

U8 -0.707 -0.056 12.204 -0.545

U9 0.363 0.599 11.404 0.493

U10 -1.112 -0.351 0.986 10.156

U11 -0.268 0.924 -1.146 12.389

U12 1.664 -1.061 0.498 9.796

Est./S.E. GEOMIN FACTOR CORRELATIONS

1 2 3 4

______

1 0.000

2 -0.309 0.000

3 0.368 0.420 0.000

4 -0.423 -2.153 -0.832 0.000

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U1 U2 U3 U4 U5

______

1 8.087 1.078 6.592 5.282 2.915

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U6 U7 U8 U9 U10

______

1 8.156 3.651 5.668 7.047 6.792

Est./S.E. ESTIMATED RESIDUAL VARIANCES

U11 U12

______

1 1.992 7.471

FACTOR STRUCTURE

1 2 3 4

______

U1 0.632 -0.007 0.117 -0.084

U2 0.934 0.007 0.008 0.037

U3 0.692 -0.086 -0.002 -0.045

U4 0.051 0.700 -0.096 -0.106

U5 -0.151 0.807 0.040 -0.102

U6 0.003 0.612 0.112 -0.141

U7 0.046 0.010 0.804 -0.037

U8 -0.017 0.026 0.721 -0.070

U9 0.032 0.051 0.669 -0.020

U10 -0.084 -0.112 0.016 0.655

U11 -0.033 -0.093 -0.107 0.869

U12 0.094 -0.164 -0.014 0.630

FACTOR DETERMINACIES

1 2 3 4

______

1 0.948 0.885 0.890 0.907

Beginning Time: 10:14:49

Ending Time: 10:14:50

Elapsed Time: 00:00:01

MUTHEN & MUTHEN

3463 Stoner Ave.

Los Angeles, CA 90066

Tel: (310) 391-9971

Fax: (310) 391-8971

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