Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:48 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a Monte Carlo
  	simulation study for an exploratory factor
  	analysis with continuous factor indicators
  MONTECARLO:
  	NAMES ARE y1-y10;
  	NOBSERVATIONS = 500;
  	NREPS = 500;
  MODEL POPULATION:
  	f1 BY y1-y7*.5;
  	f2 BY y4-y5*.25 y6-y10*.8;
  	f1-f2@1;
  	f1 WITH f2*.5;
  	y1-y10*.36;
  MODEL:
  	f1 BY y1-y7*.5 y8-y10*0 (*1);
  	f2 BY y1-y3*.0 y4-y5*.25 y6-y10*.8 (*1);
  	f1 WITH f2*.5;
  	y1-y10*.36;
  OUTPUT:	TECH9;



*** 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 a Monte Carlo
simulation study for an exploratory factor
analysis with continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                  500
    Completed                                                  500
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        -0.057         0.067         0.023        -0.033         0.021


           Means
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
      1        -0.033         0.010         0.047        -0.013        -0.001


           Covariances
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.604
 Y2             0.286         0.613
 Y3             0.251         0.266         0.572
 Y4             0.327         0.344         0.342         0.848
 Y5             0.327         0.389         0.354         0.511         0.860
 Y6             0.459         0.455         0.474         0.759         0.799
 Y7             0.483         0.495         0.451         0.787         0.771
 Y8             0.223         0.199         0.241         0.452         0.489
 Y9             0.181         0.211         0.251         0.427         0.446
 Y10            0.173         0.156         0.213         0.397         0.378


           Covariances
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.643
 Y7             1.322         1.715
 Y8             0.856         0.888         1.104
 Y9             0.848         0.832         0.662         0.987
 Y10            0.786         0.751         0.586         0.593         0.943


           Correlations
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.471         1.000
 Y3             0.427         0.449         1.000
 Y4             0.457         0.477         0.491         1.000
 Y5             0.454         0.535         0.505         0.598         1.000
 Y6             0.461         0.454         0.489         0.643         0.673
 Y7             0.475         0.483         0.456         0.652         0.635
 Y8             0.273         0.242         0.303         0.467         0.502
 Y9             0.234         0.271         0.334         0.466         0.484
 Y10            0.229         0.205         0.290         0.444         0.420


           Correlations
              Y6            Y7            Y8            Y9            Y10
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.787         1.000
 Y8             0.636         0.645         1.000
 Y9             0.666         0.640         0.634         1.000
 Y10            0.632         0.590         0.575         0.614         1.000


MODEL FIT INFORMATION

Number of Free Parameters                       39

Loglikelihood

    H0 Value

        Mean                             -5475.366
        Std Dev                             48.491
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994        -5588.171      -5586.155
           0.980       0.982        -5574.953      -5567.199
           0.950       0.960        -5555.129      -5553.799
           0.900       0.894        -5537.512      -5539.458
           0.800       0.786        -5516.176      -5519.058
           0.700       0.690        -5500.795      -5501.706
           0.500       0.492        -5475.366      -5476.087
           0.300       0.298        -5449.937      -5450.482
           0.200       0.198        -5434.556      -5435.323
           0.100       0.104        -5413.219      -5412.413
           0.050       0.054        -5395.603      -5394.122
           0.020       0.016        -5375.779      -5377.226
           0.010       0.008        -5362.561      -5363.708

    H1 Value

        Mean                             -5462.274
        Std Dev                             48.668
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994        -5575.491      -5573.248
           0.980       0.984        -5562.224      -5557.150
           0.950       0.956        -5542.328      -5541.496
           0.900       0.886        -5524.647      -5527.580
           0.800       0.788        -5503.233      -5506.013
           0.700       0.696        -5487.796      -5488.916
           0.500       0.500        -5462.274      -5462.526
           0.300       0.308        -5436.752      -5436.250
           0.200       0.200        -5421.315      -5421.664
           0.100       0.106        -5399.901      -5397.939
           0.050       0.052        -5382.219      -5380.525
           0.020       0.020        -5362.324      -5362.533
           0.010       0.010        -5349.057      -5353.842

Information Criteria

    Akaike (AIC)

        Mean                             11028.732
        Std Dev                             96.983
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992        10803.121      10804.444
           0.980       0.984        10829.559      10831.682
           0.950       0.946        10869.205      10865.296
           0.900       0.896        10904.439      10901.446
           0.800       0.802        10947.111      10945.795
           0.700       0.702        10977.874      10978.741
           0.500       0.508        11028.732      11030.063
           0.300       0.310        11079.590      11081.081
           0.200       0.214        11110.353      11116.113
           0.100       0.106        11153.025      11156.274
           0.050       0.040        11188.259      11185.271
           0.020       0.018        11227.905      11208.758
           0.010       0.006        11254.343      11246.986

    Bayesian (BIC)

        Mean                             11193.102
        Std Dev                             96.983
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992        10967.491      10968.814
           0.980       0.984        10993.928      10996.052
           0.950       0.946        11033.575      11029.666
           0.900       0.896        11068.809      11065.815
           0.800       0.802        11111.481      11110.165
           0.700       0.702        11142.244      11143.111
           0.500       0.508        11193.102      11194.433
           0.300       0.310        11243.959      11245.451
           0.200       0.214        11274.722      11280.483
           0.100       0.106        11317.395      11320.644
           0.050       0.040        11352.628      11349.641
           0.020       0.018        11392.275      11373.128
           0.010       0.006        11418.712      11411.356

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

        Mean                             11069.313
        Std Dev                             96.983
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.992        10843.702      10845.025
           0.980       0.984        10870.140      10872.264
           0.950       0.946        10909.786      10905.877
           0.900       0.896        10945.020      10942.027
           0.800       0.802        10987.693      10986.376
           0.700       0.702        11018.456      11019.322
           0.500       0.508        11069.313      11070.644
           0.300       0.310        11120.171      11121.662
           0.200       0.214        11150.934      11156.694
           0.100       0.106        11193.606      11196.856
           0.050       0.040        11228.840      11225.853
           0.020       0.018        11268.486      11249.339
           0.010       0.006        11294.924      11287.567

Chi-Square Test of Model Fit

        Degrees of freedom                      26

        Mean                                26.184
        Std Dev                              7.621
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.982           12.198         10.892
           0.980       0.980           13.409         13.069
           0.950       0.940           15.379         14.829
           0.900       0.892           17.292         16.854
           0.800       0.806           19.820         19.854
           0.700       0.698           21.792         21.763
           0.500       0.514           25.336         25.506
           0.300       0.318           29.246         29.899
           0.200       0.202           31.795         31.824
           0.100       0.110           35.563         36.299
           0.050       0.056           38.885         39.490
           0.020       0.032           42.856         43.812
           0.010       0.010           45.642         45.552

RMSEA (Root Mean Square Error Of Approximation)

        Mean                                 0.010
        Std Dev                              0.012
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           -0.018          0.000
           0.980       1.000           -0.015          0.000
           0.950       1.000           -0.010          0.000
           0.900       1.000           -0.006          0.000
           0.800       1.000           -0.001          0.000
           0.700       0.456            0.003          0.000
           0.500       0.410            0.010          0.000
           0.300       0.316            0.016          0.017
           0.200       0.236            0.020          0.021
           0.100       0.148            0.025          0.028
           0.050       0.080            0.029          0.032
           0.020       0.040            0.034          0.037
           0.010       0.016            0.038          0.039

SRMR (Standardized Root Mean Square Residual)

        Mean                                 0.012
        Std Dev                              0.002
        Number of successful computations      500

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.994            0.007          0.008
           0.980       0.982            0.008          0.008
           0.950       0.962            0.009          0.009
           0.900       0.910            0.009          0.009
           0.800       0.798            0.010          0.010
           0.700       0.696            0.011          0.011
           0.500       0.490            0.012          0.012
           0.300       0.270            0.013          0.013
           0.200       0.180            0.013          0.013
           0.100       0.106            0.014          0.014
           0.050       0.066            0.015          0.015
           0.020       0.034            0.016          0.016
           0.010       0.018            0.016          0.017


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 F1       BY
  Y1               0.500     0.5062     0.0436     0.0437     0.0019 0.948 1.000
  Y2               0.500     0.5056     0.0403     0.0437     0.0016 0.968 1.000
  Y3               0.500     0.5082     0.0427     0.0437     0.0019 0.952 1.000
  Y4               0.500     0.5060     0.0466     0.0516     0.0022 0.964 1.000
  Y5               0.500     0.5088     0.0472     0.0516     0.0023 0.964 1.000
  Y6               0.500     0.5055     0.0498     0.0615     0.0025 0.984 1.000
  Y7               0.500     0.5058     0.0550     0.0618     0.0030 0.960 1.000
  Y8               0.000    -0.0086     0.0367     0.0377     0.0014 0.982 0.018
  Y9               0.000    -0.0052     0.0368     0.0370     0.0014 0.988 0.012
  Y10              0.000    -0.0050     0.0358     0.0391     0.0013 0.990 0.010

 F2       BY
  Y1               0.000    -0.0131     0.0354     0.0392     0.0014 0.980 0.020
  Y2               0.000    -0.0132     0.0355     0.0390     0.0014 0.990 0.010
  Y3               0.000    -0.0145     0.0373     0.0392     0.0016 0.980 0.020
  Y4               0.250     0.2359     0.0516     0.0572     0.0029 0.964 0.964
  Y5               0.250     0.2327     0.0490     0.0573     0.0027 0.966 0.966
  Y6               0.800     0.7824     0.0558     0.0654     0.0034 0.974 1.000
  Y7               0.800     0.7838     0.0567     0.0658     0.0035 0.974 1.000
  Y8               0.800     0.8029     0.0451     0.0468     0.0020 0.964 1.000
  Y9               0.800     0.8008     0.0459     0.0466     0.0021 0.956 1.000
  Y10              0.800     0.8009     0.0472     0.0472     0.0022 0.950 1.000

 F1       WITH
  F2               0.500     0.5295     0.0481     0.0596     0.0032 0.952 0.998

 Intercepts
  Y1               0.000    -0.0024     0.0359     0.0349     0.0013 0.944 0.056
  Y2               0.000    -0.0003     0.0357     0.0349     0.0013 0.936 0.064
  Y3               0.000     0.0006     0.0336     0.0349     0.0011 0.970 0.030
  Y4               0.000     0.0004     0.0408     0.0400     0.0017 0.946 0.054
  Y5               0.000     0.0000     0.0411     0.0399     0.0017 0.958 0.042
  Y6               0.000    -0.0002     0.0554     0.0574     0.0031 0.954 0.046
  Y7               0.000     0.0021     0.0574     0.0575     0.0033 0.950 0.050
  Y8               0.000     0.0013     0.0424     0.0446     0.0018 0.958 0.042
  Y9               0.000     0.0006     0.0439     0.0446     0.0019 0.940 0.060
  Y10              0.000     0.0010     0.0442     0.0447     0.0019 0.950 0.050

 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     0.3583     0.0269     0.0276     0.0007 0.954 1.000
  Y2               0.360     0.3584     0.0292     0.0276     0.0009 0.918 1.000
  Y3               0.360     0.3566     0.0276     0.0276     0.0008 0.936 1.000
  Y4               0.360     0.3594     0.0274     0.0266     0.0008 0.950 1.000
  Y5               0.360     0.3573     0.0272     0.0266     0.0007 0.930 1.000
  Y6               0.360     0.3562     0.0302     0.0298     0.0009 0.934 1.000
  Y7               0.360     0.3586     0.0293     0.0299     0.0009 0.956 1.000
  Y8               0.360     0.3550     0.0292     0.0300     0.0009 0.956 1.000
  Y9               0.360     0.3567     0.0292     0.0300     0.0009 0.938 1.000
  Y10              0.360     0.3587     0.0304     0.0302     0.0009 0.946 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.392E-01
       (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             0.510         0.000
 Y2             0.563         0.042
 Y3             0.480        -0.065
 Y4             0.649        -0.260
 Y5             0.683        -0.251
 Y6             0.889        -0.723
 Y7             0.912        -0.693
 Y8             0.425        -0.695
 Y9             0.395        -0.693
 Y10            0.334        -0.657


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.344
 Y2             0.000         0.295
 Y3             0.000         0.000         0.337
 Y4             0.000         0.000         0.000         0.359
 Y5             0.000         0.000         0.000         0.000         0.330
 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             0.331
 Y7             0.000         0.402
 Y8             0.000         0.000         0.441
 Y9             0.000         0.000         0.000         0.350
 Y10            0.000         0.000         0.000         0.000         0.399


           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         0.360
 Y10            0.000         0.000         0.000         0.000         0.360


           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             0.500         0.000
 Y2             0.500         0.000
 Y3             0.500         0.000
 Y4             0.500         0.250
 Y5             0.500         0.250
 Y6             0.500         0.800
 Y7             0.500         0.800
 Y8             0.000         0.800
 Y9             0.000         0.800
 Y10            0.000         0.800


           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         0.360
 Y10            0.000         0.000         0.000         0.000         0.360


           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             0.500         1.000


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



     Beginning Time:  22:48:46
        Ending Time:  22:48:53
       Elapsed Time:  00:00:07



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