Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:01 PM

INPUT INSTRUCTIONS

  TITLE:
      this is an example of EFA using ESEM
      with residual variances restricted to
      be greater than zero
  MONTECARLO:
      NAMES = y1-y10;
      NOBSERVATIONS = 50;
      NREPS = 1;
      SAVE = ex5.28.dat;
  MODEL POPULATION:
      f1 BY y1-y8*0.8;
      f2 BY y9-y10*0.9;
      f1-f2@1;
      f1 WITH f2*0;
      y1-y8*0.36 y9-y10*0.1;
  ANALYSIS:
      ROTATION = GEOMIN;
  MODEL:
      f1 BY y1-y8*0.8 y9-y10*0 (*1);
      f2 BY y1-y8*0 y9-y10*0.9 (*1);
      y1-y8*0.36 y9-y10*0.1;




*** WARNING in MODEL command
  Values given in the MODEL command for EFA factors are used only as
  population values in computing coverage.  EFA factors cannot be given
  starting values.
   1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS




this is an example of EFA using ESEM
with residual variances restricted to
be greater than zero

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                          50

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                   10
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6
   Y7          Y8          Y9          Y10

Continuous latent variables

  EFA factors
  *1:   F1          F2


Estimator                                                       ML
Rotation                                                    GEOMIN
Row standardization                                    CORRELATION
Type of rotation                                           OBLIQUE
Epsilon value                                               Varies
Information matrix                                        OBSERVED
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



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        -0.191         0.041        -0.072        -0.041         0.052


           Means
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1         0.095         0.058         0.046        -0.142        -0.196


           Covariances
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.950
 Y2             0.629         0.872
 Y3             0.705         0.632         1.080
 Y4             0.646         0.586         0.716         0.979
 Y5             0.690         0.641         0.805         0.688         1.381
 Y6             0.651         0.538         0.739         0.568         0.719
 Y7             0.637         0.603         0.640         0.729         0.726
 Y8             0.637         0.565         0.641         0.687         0.839
 Y9            -0.097        -0.068        -0.099        -0.116        -0.300
 Y10           -0.093        -0.061        -0.078        -0.146        -0.315


           Covariances
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             0.853
 Y7             0.545         1.135
 Y8             0.586         0.638         1.190
 Y9             0.056        -0.156        -0.094         0.979
 Y10            0.014        -0.161        -0.192         0.885         1.020


           Correlations
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.691         1.000
 Y3             0.696         0.651         1.000
 Y4             0.670         0.634         0.696         1.000
 Y5             0.603         0.584         0.659         0.592         1.000
 Y6             0.724         0.623         0.770         0.622         0.663
 Y7             0.614         0.606         0.578         0.691         0.580
 Y8             0.600         0.555         0.566         0.636         0.655
 Y9            -0.101        -0.073        -0.096        -0.119        -0.258
 Y10           -0.094        -0.064        -0.074        -0.146        -0.265


           Correlations
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.554         1.000
 Y8             0.581         0.549         1.000
 Y9             0.061        -0.148        -0.087         1.000
 Y10            0.014        -0.149        -0.174         0.885         1.000


MODEL FIT INFORMATION

Number of Free Parameters                       39

Loglikelihood

    H0 Value

        Mean                              -540.346
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         -540.346       -540.346
           0.980       0.000         -540.346       -540.346
           0.950       0.000         -540.346       -540.346
           0.900       0.000         -540.346       -540.346
           0.800       0.000         -540.346       -540.346
           0.700       0.000         -540.346       -540.346
           0.500       0.000         -540.346       -540.346
           0.300       0.000         -540.346       -540.346
           0.200       0.000         -540.346       -540.346
           0.100       0.000         -540.346       -540.346
           0.050       0.000         -540.346       -540.346
           0.020       0.000         -540.346       -540.346
           0.010       0.000         -540.346       -540.346

    H1 Value

        Mean                              -528.971
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         -528.971       -528.971
           0.980       0.000         -528.971       -528.971
           0.950       0.000         -528.971       -528.971
           0.900       0.000         -528.971       -528.971
           0.800       0.000         -528.971       -528.971
           0.700       0.000         -528.971       -528.971
           0.500       0.000         -528.971       -528.971
           0.300       0.000         -528.971       -528.971
           0.200       0.000         -528.971       -528.971
           0.100       0.000         -528.971       -528.971
           0.050       0.000         -528.971       -528.971
           0.020       0.000         -528.971       -528.971
           0.010       0.000         -528.971       -528.971

Information Criteria

    Akaike (AIC)

        Mean                              1158.691
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1158.691       1158.691
           0.980       0.000         1158.691       1158.691
           0.950       0.000         1158.691       1158.691
           0.900       0.000         1158.691       1158.691
           0.800       0.000         1158.691       1158.691
           0.700       0.000         1158.691       1158.691
           0.500       0.000         1158.691       1158.691
           0.300       0.000         1158.691       1158.691
           0.200       0.000         1158.691       1158.691
           0.100       0.000         1158.691       1158.691
           0.050       0.000         1158.691       1158.691
           0.020       0.000         1158.691       1158.691
           0.010       0.000         1158.691       1158.691

    Bayesian (BIC)

        Mean                              1233.260
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1233.260       1233.260
           0.980       0.000         1233.260       1233.260
           0.950       0.000         1233.260       1233.260
           0.900       0.000         1233.260       1233.260
           0.800       0.000         1233.260       1233.260
           0.700       0.000         1233.260       1233.260
           0.500       0.000         1233.260       1233.260
           0.300       0.000         1233.260       1233.260
           0.200       0.000         1233.260       1233.260
           0.100       0.000         1233.260       1233.260
           0.050       0.000         1233.260       1233.260
           0.020       0.000         1233.260       1233.260
           0.010       0.000         1233.260       1233.260

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              1110.846
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1110.846       1110.846
           0.980       0.000         1110.846       1110.846
           0.950       0.000         1110.846       1110.846
           0.900       0.000         1110.846       1110.846
           0.800       0.000         1110.846       1110.846
           0.700       0.000         1110.846       1110.846
           0.500       0.000         1110.846       1110.846
           0.300       0.000         1110.846       1110.846
           0.200       0.000         1110.846       1110.846
           0.100       0.000         1110.846       1110.846
           0.050       0.000         1110.846       1110.846
           0.020       0.000         1110.846       1110.846
           0.010       0.000         1110.846       1110.846

Chi-Square Test of Model Fit

        Degrees of freedom                      26

        Mean                                22.749
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           12.198         22.749
           0.980       1.000           13.409         22.749
           0.950       1.000           15.379         22.749
           0.900       1.000           17.292         22.749
           0.800       1.000           19.820         22.749
           0.700       1.000           21.792         22.749
           0.500       0.000           25.336         22.749
           0.300       0.000           29.246         22.749
           0.200       0.000           31.795         22.749
           0.100       0.000           35.563         22.749
           0.050       0.000           38.885         22.749
           0.020       0.000           42.856         22.749
           0.010       0.000           45.642         22.749

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.000
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.000          0.000
           0.980       0.000            0.000          0.000
           0.950       0.000            0.000          0.000
           0.900       0.000            0.000          0.000
           0.800       0.000            0.000          0.000
           0.700       0.000            0.000          0.000
           0.500       0.000            0.000          0.000
           0.300       0.000            0.000          0.000
           0.200       0.000            0.000          0.000
           0.100       0.000            0.000          0.000
           0.050       0.000            0.000          0.000
           0.020       0.000            0.000          0.000
           0.010       0.000            0.000          0.000

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.029
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.029          0.029
           0.980       0.000            0.029          0.029
           0.950       0.000            0.029          0.029
           0.900       0.000            0.029          0.029
           0.800       0.000            0.029          0.029
           0.700       0.000            0.029          0.029
           0.500       0.000            0.029          0.029
           0.300       0.000            0.029          0.029
           0.200       0.000            0.029          0.029
           0.100       0.000            0.029          0.029
           0.050       0.000            0.029          0.029
           0.020       0.000            0.029          0.029
           0.010       0.000            0.029          0.029


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 F1       BY
  Y1               0.800     0.8127     0.0000     0.1139     0.0002 1.000 1.000
  Y2               0.800     0.7282     0.0000     0.1136     0.0052 1.000 1.000
  Y3               0.800     0.8817     0.0000     0.1208     0.0067 1.000 1.000
  Y4               0.800     0.7984     0.0000     0.1190     0.0000 1.000 1.000
  Y5               0.800     0.8891     0.0000     0.1404     0.0079 1.000 1.000
  Y6               0.800     0.7937     0.0000     0.1074     0.0000 1.000 1.000
  Y7               0.800     0.7759     0.0000     0.1330     0.0006 1.000 1.000
  Y8               0.800     0.7981     0.0000     0.1406     0.0000 1.000 1.000
  Y9               0.000     0.0085     0.0000     0.0140     0.0001 1.000 0.000
  Y10              0.000    -0.0263     0.0000     0.0978     0.0007 1.000 0.000

 F2       BY
  Y1               0.000    -0.0026     0.0000     0.0627     0.0000 1.000 0.000
  Y2               0.000     0.0175     0.0000     0.0896     0.0003 1.000 0.000
  Y3               0.000     0.0026     0.0000     0.0893     0.0000 1.000 0.000
  Y4               0.000    -0.0192     0.0000     0.1340     0.0004 1.000 0.000
  Y5               0.000    -0.1924     0.0000     0.1745     0.0370 1.000 0.000
  Y6               0.000     0.1517     0.0000     0.0834     0.0230 1.000 0.000
  Y7               0.000    -0.0627     0.0000     0.1341     0.0039 1.000 0.000
  Y8               0.000     0.0095     0.0000     0.2815     0.0001 1.000 0.000
  Y9               0.900     1.0011     0.0000     0.2940     0.0102 1.000 1.000
  Y10              0.900     0.8818     0.0000     0.2805     0.0003 1.000 1.000

 F2       WITH
  F1               0.000    -0.1277     0.0000     0.1456     0.0163 1.000 0.000

 Intercepts
  Y1               0.000    -0.1907     0.0000     0.1378     0.0364 1.000 0.000
  Y2               0.000     0.0411     0.0000     0.1321     0.0017 1.000 0.000
  Y3               0.000    -0.0720     0.0000     0.1470     0.0052 1.000 0.000
  Y4               0.000    -0.0411     0.0000     0.1400     0.0017 1.000 0.000
  Y5               0.000     0.0523     0.0000     0.1662     0.0027 1.000 0.000
  Y6               0.000     0.0952     0.0000     0.1306     0.0091 1.000 0.000
  Y7               0.000     0.0580     0.0000     0.1507     0.0034 1.000 0.000
  Y8               0.000     0.0455     0.0000     0.1543     0.0021 1.000 0.000
  Y9               0.000    -0.1421     0.0000     0.1400     0.0202 1.000 0.000
  Y10              0.000    -0.1957     0.0000     0.1428     0.0383 1.000 0.000

 Variances
  F1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  F2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y1               0.360     0.2887     0.0000     0.0687     0.0051 1.000 1.000
  Y2               0.360     0.3449     0.0000     0.0772     0.0002 1.000 1.000
  Y3               0.360     0.3036     0.0000     0.0743     0.0032 1.000 1.000
  Y4               0.360     0.3378     0.0000     0.0784     0.0005 1.000 1.000
  Y5               0.360     0.5093     0.0000     0.1212     0.0223 1.000 1.000
  Y6               0.360     0.2305     0.0000     0.0586     0.0168 0.000 1.000
  Y7               0.360     0.5166     0.0000     0.1130     0.0245 1.000 1.000
  Y8               0.360     0.5553     0.0000     0.1213     0.0381 1.000 1.000
  Y9               0.100    -0.0207     0.0000     0.5573     0.0146 1.000 0.000
  Y10              0.100     0.2360     0.0000     0.4374     0.0185 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.353E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1           1             2             3             4             5


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1           6             7             8             9            10


           LAMBDA
              F1            F2
              ________      ________
 Y1                11             0
 Y2                12            13
 Y3                14            15
 Y4                16            17
 Y5                18            19
 Y6                20            21
 Y7                22            23
 Y8                24            25
 Y9                26            27
 Y10               28            29


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                30
 Y2                 0            31
 Y3                 0             0            32
 Y4                 0             0             0            33
 Y5                 0             0             0             0            34
 Y6                 0             0             0             0             0
 Y7                 0             0             0             0             0
 Y8                 0             0             0             0             0
 Y9                 0             0             0             0             0
 Y10                0             0             0             0             0


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6                35
 Y7                 0            36
 Y8                 0             0            37
 Y9                 0             0             0            38
 Y10                0             0             0             0            39


           ALPHA
              F1            F2
              ________      ________
      1           0             0


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           PSI
              F1            F2
              ________      ________
 F1                 0
 F2                 0             0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F1            F2
              ________      ________
 Y1             0.813         0.000
 Y2             0.726         0.020
 Y3             0.881         0.005
 Y4             0.801        -0.016
 Y5             0.914        -0.188
 Y6             0.774         0.153
 Y7             0.784        -0.060
 Y8             0.797         0.012
 Y9            -0.123         0.993
 Y10           -0.142         0.874


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.289
 Y2             0.000         0.345
 Y3             0.000         0.000         0.304
 Y4             0.000         0.000         0.000         0.338
 Y5             0.000         0.000         0.000         0.000         0.509
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 Y9             0.000         0.000         0.000         0.000         0.000
 Y10            0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             0.231
 Y7             0.000         0.517
 Y8             0.000         0.000         0.555
 Y9             0.000         0.000         0.000        -0.022
 Y10            0.000         0.000         0.000         0.000         0.237


           ALPHA
              F1            F2
              ________      ________
      1         0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           PSI
              F1            F2
              ________      ________
 F1             1.000
 F2             0.000         1.000


     TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1           1             2             3             4             5


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1           6             7             8             9            10


           LAMBDA
              F1            F2
              ________      ________
 Y1                11            12
 Y2                13            14
 Y3                15            16
 Y4                17            18
 Y5                19            20
 Y6                21            22
 Y7                23            24
 Y8                25            26
 Y9                27            28
 Y10               29            30


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                31
 Y2                 0            32
 Y3                 0             0            33
 Y4                 0             0             0            34
 Y5                 0             0             0             0            35
 Y6                 0             0             0             0             0
 Y7                 0             0             0             0             0
 Y8                 0             0             0             0             0
 Y9                 0             0             0             0             0
 Y10                0             0             0             0             0


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6                36
 Y7                 0            37
 Y8                 0             0            38
 Y9                 0             0             0            39
 Y10                0             0             0             0            40


           ALPHA
              F1            F2
              ________      ________
      1           0             0


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           PSI
              F1            F2
              ________      ________
 F1                 0
 F2                41             0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F1            F2
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 Y3             0.000         0.000
 Y4             0.000         0.000
 Y5             0.000         0.000
 Y6             0.000         0.000
 Y7             0.000         0.000
 Y8             0.000         0.000
 Y9             0.000         0.000
 Y10            0.000         0.000


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.360
 Y2             0.000         0.360
 Y3             0.000         0.000         0.360
 Y4             0.000         0.000         0.000         0.360
 Y5             0.000         0.000         0.000         0.000         0.360
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 Y9             0.000         0.000         0.000         0.000         0.000
 Y10            0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             0.360
 Y7             0.000         0.360
 Y8             0.000         0.000         0.360
 Y9             0.000         0.000         0.000         0.100
 Y10            0.000         0.000         0.000         0.000         0.100


           ALPHA
              F1            F2
              ________      ________
      1         0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           PSI
              F1            F2
              ________      ________
 F1             1.000
 F2             0.000         1.000


     POPULATION VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F1            F2
              ________      ________
 Y1             0.800         0.000
 Y2             0.800         0.000
 Y3             0.800         0.000
 Y4             0.800         0.000
 Y5             0.800         0.000
 Y6             0.800         0.000
 Y7             0.800         0.000
 Y8             0.800         0.000
 Y9             0.000         0.900
 Y10            0.000         0.900


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.360
 Y2             0.000         0.360
 Y3             0.000         0.000         0.360
 Y4             0.000         0.000         0.000         0.360
 Y5             0.000         0.000         0.000         0.000         0.360
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 Y9             0.000         0.000         0.000         0.000         0.000
 Y10            0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             0.360
 Y7             0.000         0.360
 Y8             0.000         0.000         0.360
 Y9             0.000         0.000         0.000         0.100
 Y10            0.000         0.000         0.000         0.000         0.100


           ALPHA
              F1            F2
              ________      ________
 1              0.000         0.000


           BETA
              F1            F2
              ________      ________
 F1             0.000         0.000
 F2             0.000         0.000


           PSI
              F1            F2
              ________      ________
 F1             1.000
 F2             0.000         1.000


SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4
    Y5
    Y6
    Y7
    Y8
    Y9
    Y10

  Save file
    ex5.28.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:01:56
        Ending Time:  22:01:56
       Elapsed Time:  00:00:00



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