Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:40 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level exploratory
  	factor analysis with continuous factor indicators
  DATA:	FILE IS ex4.5.dat;
  VARIABLE:	NAMES ARE y1-y6 x1 x2 w clus;
  	USEVARIABLES = y1-y6;
  	CLUSTER = clus;
  ANALYSIS:	TYPE = TWOLEVEL EFA 1 2 UW 1 1 UB;




INPUT READING TERMINATED NORMALLY



this is an example of a two-level exploratory
factor analysis with continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of dependent variables                                    6
Number of independent variables                                  0
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6

Variables with special functions

  Cluster variable      CLUS

Estimator                                                       ML
Rotation                                                    GEOMIN
Row standardization                                    CORRELATION
Type of rotation                                           OBLIQUE
Epsilon value                                               Varies
Information matrix                                        OBSERVED
Maximum number of iterations                                   100
Convergence criterion                                    0.100D-05
Maximum number of EM iterations                                500
Convergence criteria for the EM algorithm
  Loglikelihood change                                   0.100D-02
  Relative loglikelihood change                          0.100D-05
  Derivative                                             0.100D-03
Minimum variance                                         0.100D-03
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
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
Optimization algorithm                                         EMA

Input data file(s)
  ex4.5.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                        110

     Average cluster size        9.091

     Estimated Intraclass Correlations for the Y Variables

                Intraclass              Intraclass              Intraclass
     Variable  Correlation   Variable  Correlation   Variable  Correlation

     Y1           0.399      Y2           0.407      Y3           0.369
     Y4           0.371      Y5           0.424      Y6           0.445




RESULTS FOR EXPLORATORY FACTOR ANALYSIS


           EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
                  1             2             3             4             5
              ________      ________      ________      ________      ________
      1         2.960         1.522         0.424         0.382         0.364


           EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
                  6
              ________
      1         0.348


           EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
                  1             2             3             4             5
              ________      ________      ________      ________      ________
      1         5.178         0.249         0.188         0.168         0.122


           EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
                  6
              ________
      1         0.096


EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):


MODEL FIT INFORMATION

Number of Free Parameters                       30

Loglikelihood

          H0 Value                      -11160.512
          H1 Value                      -10754.176

Information Criteria

          Akaike (AIC)                   22381.023
          Bayesian (BIC)                 22528.256
          Sample-Size Adjusted BIC       22432.974
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                            812.672
          Degrees of Freedom                    18
          P-Value                           0.0000

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.210

CFI/TLI

          CFI                                0.711
          TLI                                0.519

Chi-Square Test of Model Fit for the Baseline Model

          Value                           2783.122
          Degrees of Freedom                    30
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value for Within                   0.179
          Value for Between                  0.031



MINIMUM ROTATION FUNCTION VALUE       2.30287



WITHIN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1
              ________
 Y1             0.795*
 Y2             0.779*
 Y3             0.780*
 Y4             0.377*
 Y5             0.389*
 Y6             0.402*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1
              ________
      1         1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.368         0.393         0.392         0.858         0.849


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.838


           S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1             0.017
 Y2             0.018
 Y3             0.018
 Y4             0.034
 Y5             0.034
 Y6             0.033


           S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.028         0.028         0.028         0.025         0.026


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.026


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1            45.472
 Y2            43.113
 Y3            43.345
 Y4            11.207
 Y5            11.595
 Y6            12.225


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        13.259        13.952        13.951        33.827        32.507


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1        31.690


EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):



MINIMUM ROTATION FUNCTION VALUE       5.13290



BETWEEN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1
              ________
 Y1             0.910*
 Y2             0.901*
 Y3             0.912*
 Y4             0.913*
 Y5             0.977*
 Y6             0.934*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1
              ________
      1         1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.173         0.188         0.168         0.166         0.046


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.127


           S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1             0.025
 Y2             0.026
 Y3             0.026
 Y4             0.029
 Y5             0.019
 Y6             0.023


           S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.046         0.048         0.047         0.052         0.037


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.043


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1            36.211
 Y2            34.131
 Y3            35.583
 Y4            31.903
 Y5            52.100
 Y6            40.502


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         3.781         3.955         3.585         3.179         1.246


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         2.953


EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):


MODEL FIT INFORMATION

Number of Free Parameters                       35

Loglikelihood

          H0 Value                      -10759.644
          H1 Value                      -10754.176

Information Criteria

          Akaike (AIC)                   21589.288
          Bayesian (BIC)                 21761.059
          Sample-Size Adjusted BIC       21649.897
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                             10.937
          Degrees of Freedom                    13
          P-Value                           0.6161

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.000

CFI/TLI

          CFI                                1.000
          TLI                                1.002

Chi-Square Test of Model Fit for the Baseline Model

          Value                           2783.122
          Degrees of Freedom                    30
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value for Within                   0.007
          Value for Between                  0.017



MINIMUM ROTATION FUNCTION VALUE       0.06784



WITHIN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1             2
              ________      ________
 Y1             0.801*        0.006
 Y2             0.797*       -0.009
 Y3             0.788*        0.002
 Y4            -0.002         0.765*
 Y5            -0.008         0.815*
 Y6             0.027         0.758*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1             2
              ________      ________
      1         1.000
      2         0.374*        1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.354         0.371         0.378         0.415         0.340


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.410


           S.E. GEOMIN ROTATED LOADINGS
                  1             2
              ________      ________
 Y1             0.021         0.022
 Y2             0.022         0.025
 Y3             0.020         0.017
 Y4             0.014         0.021
 Y5             0.023         0.022
 Y6             0.032         0.025


           S.E. GEOMIN FACTOR CORRELATIONS
                  1             2
              ________      ________
      1         0.000
      2         0.038         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.029         0.029         0.029         0.030         0.031


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.030


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1             2
              ________      ________
 Y1            38.200         0.283
 Y2            36.324        -0.366
 Y3            38.799         0.109
 Y4            -0.138        35.786
 Y5            -0.342        36.721
 Y6             0.838        30.414


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1             2
              ________      ________
      1         0.000
      2         9.914         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        12.343        12.730        13.110        13.674        11.021


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1        13.628


           FACTOR STRUCTURE
                  1             2
              ________      ________
 Y1             0.803         0.306
 Y2             0.793         0.289
 Y3             0.789         0.297
 Y4             0.285         0.765
 Y5             0.297         0.812
 Y6             0.310         0.768


EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):



MINIMUM ROTATION FUNCTION VALUE       5.06570



BETWEEN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1
              ________
 Y1             0.931*
 Y2             0.915*
 Y3             0.928*
 Y4             0.886*
 Y5             0.949*
 Y6             0.903*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1
              ________
      1         1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.134         0.163         0.138         0.216         0.100


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.184


           S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1             0.021
 Y2             0.024
 Y3             0.023
 Y4             0.030
 Y5             0.020
 Y6             0.026


           S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.040         0.045         0.042         0.053         0.037


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.047


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1            43.365
 Y2            37.478
 Y3            40.759
 Y4            29.445
 Y5            48.228
 Y6            35.016


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         3.349         3.651         3.264         4.047         2.689


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         3.949


EXPLORATORY FACTOR ANALYSIS WITH UNRESTRICTED WITHIN COVARIANCE AND 1 BETWEEN FACTOR(S):


MODEL FIT INFORMATION

Number of Free Parameters                       18

Loglikelihood

          H0 Value                      -10757.461
          H1 Value                      -10754.176

Information Criteria

          Akaike (AIC)                   21550.922
          Bayesian (BIC)                 21639.262
          Sample-Size Adjusted BIC       21582.093
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                              6.571
          Degrees of Freedom                     9
          P-Value                           0.6817

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.000

CFI/TLI

          CFI                                1.000
          TLI                                1.003

Chi-Square Test of Model Fit for the Baseline Model

          Value                           2783.122
          Degrees of Freedom                    30
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value for Within                   0.000
          Value for Between                  0.016



MINIMUM ROTATION FUNCTION VALUE       5.06118



BETWEEN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1
              ________
 Y1             0.930*
 Y2             0.914*
 Y3             0.928*
 Y4             0.885*
 Y5             0.948*
 Y6             0.903*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1
              ________
      1         1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.134         0.164         0.139         0.216         0.102


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.185


           S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1             0.021
 Y2             0.024
 Y3             0.023
 Y4             0.030
 Y5             0.020
 Y6             0.026


           S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.040         0.045         0.042         0.053         0.037


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.047


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1            43.560
 Y2            37.450
 Y3            40.935
 Y4            29.536
 Y5            48.440
 Y6            35.038


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         3.382         3.675         3.293         4.067         2.748


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         3.964


EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:


MODEL FIT INFORMATION

Number of Free Parameters                       18

Loglikelihood

          H0 Value                      -11156.190
          H1 Value                      -10754.176

Information Criteria

          Akaike (AIC)                   22348.380
          Bayesian (BIC)                 22436.719
          Sample-Size Adjusted BIC       22379.550
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                            804.028
          Degrees of Freedom                     9
          P-Value                           0.0000

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.161

CFI/TLI

          CFI                                0.711
          TLI                                0.037

Chi-Square Test of Model Fit for the Baseline Model

          Value                           2783.122
          Degrees of Freedom                    30
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value for Within                   0.177
          Value for Between                  0.000



MINIMUM ROTATION FUNCTION VALUE       2.30369



WITHIN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1
              ________
 Y1             0.789*
 Y2             0.774*
 Y3             0.774*
 Y4             0.389*
 Y5             0.404*
 Y6             0.409*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1
              ________
      1         1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.378         0.401         0.400         0.849         0.837


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.832


           S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1             0.018
 Y2             0.018
 Y3             0.018
 Y4             0.033
 Y5             0.033
 Y6             0.033


           S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.028         0.028         0.028         0.026         0.027


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.027


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1
              ________
 Y1            44.292
 Y2            42.126
 Y3            42.282
 Y4            11.689
 Y5            12.302
 Y6            12.525


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1
              ________
      1         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        13.467        14.081        14.108        32.809        31.525


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1        31.084


EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:


MODEL FIT INFORMATION

Number of Free Parameters                       23

Loglikelihood

          H0 Value                      -10756.649
          H1 Value                      -10754.176

Information Criteria

          Akaike (AIC)                   21559.297
          Bayesian (BIC)                 21672.175
          Sample-Size Adjusted BIC       21599.126
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                              4.946
          Degrees of Freedom                     4
          P-Value                           0.2929

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.000

CFI/TLI

          CFI                                1.000
          TLI                                0.997

Chi-Square Test of Model Fit for the Baseline Model

          Value                           2783.122
          Degrees of Freedom                    30
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value for Within                   0.006
          Value for Between                  0.000



MINIMUM ROTATION FUNCTION VALUE       0.06852



WITHIN LEVEL RESULTS



           GEOMIN ROTATED LOADINGS (* significant at 5% level)
                  1             2
              ________      ________
 Y1             0.798*        0.009
 Y2             0.799*       -0.012
 Y3             0.788*        0.001
 Y4            -0.002         0.763*
 Y5            -0.008         0.814*
 Y6             0.023         0.760*


           GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
                  1             2
              ________      ________
      1         1.000
      2         0.382*        1.000


           ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.358         0.369         0.379         0.418         0.342


           ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.409


           S.E. GEOMIN ROTATED LOADINGS
                  1             2
              ________      ________
 Y1             0.022         0.025
 Y2             0.022         0.027
 Y3             0.020         0.013
 Y4             0.014         0.021
 Y5             0.023         0.023
 Y6             0.031         0.025


           S.E. GEOMIN FACTOR CORRELATIONS
                  1             2
              ________      ________
      1         0.000
      2         0.038         0.000


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.029         0.029         0.029         0.030         0.031


           S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1         0.030


           Est./S.E. GEOMIN ROTATED LOADINGS
                  1             2
              ________      ________
 Y1            36.516         0.378
 Y2            35.556        -0.456
 Y3            39.844         0.101
 Y4            -0.116        35.590
 Y5            -0.348        36.177
 Y6             0.716        30.410


           Est./S.E. GEOMIN FACTOR CORRELATIONS
                  1             2
              ________      ________
      1         0.000
      2         9.977         0.000


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        12.488        12.674        13.141        13.760        11.094


           Est./S.E. ESTIMATED RESIDUAL VARIANCES
              Y6
              ________
      1        13.586


           FACTOR STRUCTURE
                  1             2
              ________      ________
 Y1             0.801         0.314
 Y2             0.794         0.293
 Y3             0.788         0.302
 Y4             0.290         0.763
 Y5             0.303         0.811
 Y6             0.313         0.769


     Beginning Time:  14:40:23
        Ending Time:  14:40:23
       Elapsed Time:  00:00:00



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