Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:04 PM

INPUT INSTRUCTIONS

  title:	this is an example of a CFA with continuous factor indicators

  montecarlo:
  	names = y1-y6;
  	nobs = 500;
  	nreps = 1;
  	save = ex5.20.dat;

  model montecarlo:
      f1 by y1@1 y2-y3*1;
  	f2 by y4@1 y5-y6*.8;
  	y1-y3*.5; ! reliability 0.67
      y4-y6*.32; ! reliability 0.67
  	f1-f2*1;

  model:	
      f1 by y1
      y2-y3(lam2-lam3);
      f2 by y4
      y5-y6*.8 (lam5-lam6);
      f1*1 (vf1);
      f2*1 (vf2);
      y1-y3*.5 (ve1-ve3); ! reliability 0.67
      y4-y6*.32 (ve4-ve6); ! reliability 0.67

  model constraint:
      new(rel2*.67 rel5*.67 stan3*.82 stan6*.82);
      rel2 = lam2**2*vf1/(lam2**2*vf1 + ve2);
      rel5 = lam5**2*vf2/(lam5**2*vf2 + ve5);
      rel5 = rel2;
      stan3 = lam3*sqrt(vf1)/sqrt(lam3**2*vf1 + ve3);
      stan6 = lam6*sqrt(vf2)/sqrt(lam6**2*vf2 + ve6);
      0 = stan6 - stan3;
      ve2 > ve5;
      ve4 > 0;

  output:
  	tech9;




INPUT READING TERMINATED NORMALLY



this is an example of a CFA with continuous factor indicators

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    6
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6

Continuous latent variables
   F1          F2


Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20



SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1        -0.019         0.015         0.022        -0.018        -0.015


           Means
              Y6
              ________
      1         0.022


           Covariances
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.478
 Y2             1.009         1.477
 Y3             0.950         1.011         1.458
 Y4            -0.001        -0.042        -0.015         1.353
 Y5            -0.025        -0.049        -0.044         0.812         0.988
 Y6             0.014        -0.024         0.024         0.755         0.657


           Covariances
              Y6
              ________
 Y6             0.949


           Correlations
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.683         1.000
 Y3             0.647         0.689         1.000
 Y4            -0.001        -0.030        -0.011         1.000
 Y5            -0.021        -0.040        -0.037         0.702         1.000
 Y6             0.012        -0.020         0.021         0.666         0.679


           Correlations
              Y6
              ________
 Y6             1.000


MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

    H0 Value

        Mean                             -3898.949
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -3898.949      -3898.949
           0.980       0.000        -3898.949      -3898.949
           0.950       0.000        -3898.949      -3898.949
           0.900       0.000        -3898.949      -3898.949
           0.800       0.000        -3898.949      -3898.949
           0.700       0.000        -3898.949      -3898.949
           0.500       0.000        -3898.949      -3898.949
           0.300       0.000        -3898.949      -3898.949
           0.200       0.000        -3898.949      -3898.949
           0.100       0.000        -3898.949      -3898.949
           0.050       0.000        -3898.949      -3898.949
           0.020       0.000        -3898.949      -3898.949
           0.010       0.000        -3898.949      -3898.949

    H1 Value

        Mean                             -3896.904
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -3896.904      -3896.904
           0.980       0.000        -3896.904      -3896.904
           0.950       0.000        -3896.904      -3896.904
           0.900       0.000        -3896.904      -3896.904
           0.800       0.000        -3896.904      -3896.904
           0.700       0.000        -3896.904      -3896.904
           0.500       0.000        -3896.904      -3896.904
           0.300       0.000        -3896.904      -3896.904
           0.200       0.000        -3896.904      -3896.904
           0.100       0.000        -3896.904      -3896.904
           0.050       0.000        -3896.904      -3896.904
           0.020       0.000        -3896.904      -3896.904
           0.010       0.000        -3896.904      -3896.904

Information Criteria

    Akaike (AIC)

        Mean                              7831.898
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         7831.898       7831.898
           0.980       0.000         7831.898       7831.898
           0.950       0.000         7831.898       7831.898
           0.900       0.000         7831.898       7831.898
           0.800       0.000         7831.898       7831.898
           0.700       0.000         7831.898       7831.898
           0.500       0.000         7831.898       7831.898
           0.300       0.000         7831.898       7831.898
           0.200       0.000         7831.898       7831.898
           0.100       0.000         7831.898       7831.898
           0.050       0.000         7831.898       7831.898
           0.020       0.000         7831.898       7831.898
           0.010       0.000         7831.898       7831.898

    Bayesian (BIC)

        Mean                              7903.547
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         7903.547       7903.547
           0.980       0.000         7903.547       7903.547
           0.950       0.000         7903.547       7903.547
           0.900       0.000         7903.547       7903.547
           0.800       0.000         7903.547       7903.547
           0.700       0.000         7903.547       7903.547
           0.500       0.000         7903.547       7903.547
           0.300       0.000         7903.547       7903.547
           0.200       0.000         7903.547       7903.547
           0.100       0.000         7903.547       7903.547
           0.050       0.000         7903.547       7903.547
           0.020       0.000         7903.547       7903.547
           0.010       0.000         7903.547       7903.547

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

        Mean                              7849.588
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         7849.588       7849.588
           0.980       0.000         7849.588       7849.588
           0.950       0.000         7849.588       7849.588
           0.900       0.000         7849.588       7849.588
           0.800       0.000         7849.588       7849.588
           0.700       0.000         7849.588       7849.588
           0.500       0.000         7849.588       7849.588
           0.300       0.000         7849.588       7849.588
           0.200       0.000         7849.588       7849.588
           0.100       0.000         7849.588       7849.588
           0.050       0.000         7849.588       7849.588
           0.020       0.000         7849.588       7849.588
           0.010       0.000         7849.588       7849.588

Chi-Square Test of Model Fit

        Degrees of freedom                      10

        Mean                                 4.090
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            2.558          4.090
           0.980       1.000            3.059          4.090
           0.950       1.000            3.940          4.090
           0.900       0.000            4.865          4.090
           0.800       0.000            6.179          4.090
           0.700       0.000            7.267          4.090
           0.500       0.000            9.342          4.090
           0.300       0.000           11.781          4.090
           0.200       0.000           13.442          4.090
           0.100       0.000           15.987          4.090
           0.050       0.000           18.307          4.090
           0.020       0.000           21.161          4.090
           0.010       0.000           23.209          4.090

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                                 0.012
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.012          0.012
           0.980       0.000            0.012          0.012
           0.950       0.000            0.012          0.012
           0.900       0.000            0.012          0.012
           0.800       0.000            0.012          0.012
           0.700       0.000            0.012          0.012
           0.500       0.000            0.012          0.012
           0.300       0.000            0.012          0.012
           0.200       0.000            0.012          0.012
           0.100       0.000            0.012          0.012
           0.050       0.000            0.012          0.012
           0.020       0.000            0.012          0.012
           0.010       0.000            0.012          0.012


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 F1       BY
  Y1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2                  1.000     1.0602     0.0000     0.0521     0.0036 1.000 1.000
  Y3                  1.000     0.9983     0.0000     0.0507     0.0000 1.000 1.000

 F2       BY
  Y4                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y5                  0.800     0.8756     0.0000     0.0411     0.0057 1.000 1.000
  Y6                  0.800     0.8132     0.0000     0.0395     0.0002 1.000 1.000

 F2       WITH
  F1                  0.000    -0.0241     0.0000     0.0486     0.0006 1.000 0.000

 Intercepts
  Y1                  0.000    -0.0193     0.0000     0.0542     0.0004 1.000 0.000
  Y2                  0.000     0.0145     0.0000     0.0542     0.0002 1.000 0.000
  Y3                  0.000     0.0224     0.0000     0.0538     0.0005 1.000 0.000
  Y4                  0.000    -0.0182     0.0000     0.0522     0.0003 1.000 0.000
  Y5                  0.000    -0.0152     0.0000     0.0446     0.0002 1.000 0.000
  Y6                  0.000     0.0217     0.0000     0.0437     0.0005 1.000 0.000

 Variances
  F1                  1.000     0.9421     0.0000     0.0921     0.0033 1.000 1.000
  F2                  1.000     0.9370     0.0000     0.0871     0.0040 1.000 1.000

 Residual Variances
  Y1                  0.500     0.5287     0.0000     0.0483     0.0008 1.000 1.000
  Y2                  0.500     0.4078     0.0000     0.0368     0.0085 0.000 1.000
  Y3                  0.500     0.5093     0.0000     0.0390     0.0001 1.000 1.000
  Y4                  0.320     0.4237     0.0000     0.0418     0.0107 0.000 1.000
  Y5                  0.320     0.2767     0.0000     0.0248     0.0019 1.000 1.000
  Y6                  0.320     0.3361     0.0000     0.0255     0.0003 1.000 1.000

New/Additional Parameters
  REL2                0.670     0.7220     0.0000     0.0240     0.0027 0.000 1.000
  REL5                0.670     0.7220     0.0000     0.0240     0.0027 0.000 1.000
  STAN3               0.820     0.8052     0.0000     0.0153     0.0002 1.000 1.000
  STAN6               0.820     0.8052     0.0000     0.0153     0.0002 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.205E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


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


           NU
              Y6
              ________
      1           6


           LAMBDA
              F1            F2
              ________      ________
 Y1                 0             0
 Y2                 7             0
 Y3                 8             0
 Y4                 0             0
 Y5                 0             9
 Y6                 0            10


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                11
 Y2                 0            12
 Y3                 0             0            13
 Y4                 0             0             0            14
 Y5                 0             0             0             0            15
 Y6                 0             0             0             0             0


           THETA
              Y6
              ________
 Y6                16


           ALPHA
              F1            F2
              ________      ________
      1           0             0


           BETA
              F1            F2
              ________      ________
 F1                 0             0
 F2                 0             0


           PSI
              F1            F2
              ________      ________
 F1                17
 F2                18            19


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              REL2          REL5          STAN3         STAN6
              ________      ________      ________      ________
 1                 20            21            22            23


     STARTING VALUES


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


           NU
              Y6
              ________
      1         0.000


           LAMBDA
              F1            F2
              ________      ________
 Y1             1.000         0.000
 Y2             1.065         0.000
 Y3             1.003         0.000
 Y4             0.000         1.000
 Y5             0.000         0.800
 Y6             0.000         0.800


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         0.320
 Y5             0.000         0.000         0.000         0.000         0.320
 Y6             0.000         0.000         0.000         0.000         0.000


           THETA
              Y6
              ________
 Y6             0.320


           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


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              REL2          REL5          STAN3         STAN6
              ________      ________      ________      ________
 1              0.670         0.670         0.820         0.820


     POPULATION VALUES


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


           NU
              Y6
              ________
 1              0.000


           LAMBDA
              F1            F2
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         0.000
 Y3             1.000         0.000
 Y4             0.000         1.000
 Y5             0.000         0.800
 Y6             0.000         0.800


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.500
 Y2             0.000         0.500
 Y3             0.000         0.000         0.500
 Y4             0.000         0.000         0.000         0.320
 Y5             0.000         0.000         0.000         0.000         0.320
 Y6             0.000         0.000         0.000         0.000         0.000


           THETA
              Y6
              ________
 Y6             0.320


           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 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4
    Y5
    Y6

  Save file
    ex5.20.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  14:04:08
        Ending Time:  14:04:08
       Elapsed Time:  00:00:00



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