Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:02 PM

INPUT INSTRUCTIONS

  TITLE:
  	this is an example of a linear growth
  	model for a continuous outcome with first-
  	order auto correlated residuals using non-
  	linear constraints
  MONTECARLO:
  	NAMES = y1-y4;
  	NOBS = 1000;
  	NREPS = 1;
  	SAVE = ex6.17.dat;
  MODEL POPULATION:
  	i s | y1@0 y2@1 y3@2 y4@3;
  	[i*0 s*1];
  	i*1 s*.2;
  	y1-y4*1;
  	y1-y3 PWITH y2-y4*.3;
  	y1-y2 PWITH y3-y4*.09;	
  	y1 WITH y4*.027;
  MODEL:
  	i s | y1@0 y2@1 y3@2 y4@3;
  	[i*0 s*1];
  	i*1 s*.2;
  	y1-y4*1 (resvar);
  	y1-y3 PWITH y2-y4*.3 (p1);
  	y1-y2 PWITH y3-y4*.09 (p2);
  	y1 WITH y4*.027 (p3);
  MODEL CONSTRAINT:
      NEW(corr*0.3);
      p1 = resvar*corr;
  	p2 = resvar*corr**2;
  	p3 = resvar*corr**3;
  OUTPUT:
  	TECH9;



INPUT READING TERMINATED NORMALLY




this is an example of a linear growth
model for a continuous outcome with first-
order auto correlated residuals using non-
linear constraints

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    4
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Continuous latent variables
   I           S


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
              ________      ________      ________      ________
      1         0.016         1.027         2.001         3.053


           Covariances
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.897
 Y2             1.302         2.295
 Y3             1.045         1.835         2.982
 Y4             1.039         1.772         2.698         4.006


           Correlations
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.624         1.000
 Y3             0.439         0.701         1.000
 Y4             0.377         0.584         0.781         1.000


MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

    H0 Value

        Mean                             -6593.460
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -6593.460      -6593.460
           0.980       0.000        -6593.460      -6593.460
           0.950       0.000        -6593.460      -6593.460
           0.900       0.000        -6593.460      -6593.460
           0.800       0.000        -6593.460      -6593.460
           0.700       0.000        -6593.460      -6593.460
           0.500       0.000        -6593.460      -6593.460
           0.300       0.000        -6593.460      -6593.460
           0.200       0.000        -6593.460      -6593.460
           0.100       0.000        -6593.460      -6593.460
           0.050       0.000        -6593.460      -6593.460
           0.020       0.000        -6593.460      -6593.460
           0.010       0.000        -6593.460      -6593.460

    H1 Value

        Mean                             -6592.226
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -6592.226      -6592.226
           0.980       0.000        -6592.226      -6592.226
           0.950       0.000        -6592.226      -6592.226
           0.900       0.000        -6592.226      -6592.226
           0.800       0.000        -6592.226      -6592.226
           0.700       0.000        -6592.226      -6592.226
           0.500       0.000        -6592.226      -6592.226
           0.300       0.000        -6592.226      -6592.226
           0.200       0.000        -6592.226      -6592.226
           0.100       0.000        -6592.226      -6592.226
           0.050       0.000        -6592.226      -6592.226
           0.020       0.000        -6592.226      -6592.226
           0.010       0.000        -6592.226      -6592.226

Information Criteria

    Akaike (AIC)

        Mean                             13200.921
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        13200.921      13200.921
           0.980       0.000        13200.921      13200.921
           0.950       0.000        13200.921      13200.921
           0.900       0.000        13200.921      13200.921
           0.800       0.000        13200.921      13200.921
           0.700       0.000        13200.921      13200.921
           0.500       0.000        13200.921      13200.921
           0.300       0.000        13200.921      13200.921
           0.200       0.000        13200.921      13200.921
           0.100       0.000        13200.921      13200.921
           0.050       0.000        13200.921      13200.921
           0.020       0.000        13200.921      13200.921
           0.010       0.000        13200.921      13200.921

    Bayesian (BIC)

        Mean                             13235.275
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        13235.275      13235.275
           0.980       0.000        13235.275      13235.275
           0.950       0.000        13235.275      13235.275
           0.900       0.000        13235.275      13235.275
           0.800       0.000        13235.275      13235.275
           0.700       0.000        13235.275      13235.275
           0.500       0.000        13235.275      13235.275
           0.300       0.000        13235.275      13235.275
           0.200       0.000        13235.275      13235.275
           0.100       0.000        13235.275      13235.275
           0.050       0.000        13235.275      13235.275
           0.020       0.000        13235.275      13235.275
           0.010       0.000        13235.275      13235.275

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

        Mean                             13213.043
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        13213.043      13213.043
           0.980       0.000        13213.043      13213.043
           0.950       0.000        13213.043      13213.043
           0.900       0.000        13213.043      13213.043
           0.800       0.000        13213.043      13213.043
           0.700       0.000        13213.043      13213.043
           0.500       0.000        13213.043      13213.043
           0.300       0.000        13213.043      13213.043
           0.200       0.000        13213.043      13213.043
           0.100       0.000        13213.043      13213.043
           0.050       0.000        13213.043      13213.043
           0.020       0.000        13213.043      13213.043
           0.010       0.000        13213.043      13213.043

Chi-Square Test of Model Fit

        Degrees of freedom                       7

        Mean                                 2.469
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            1.239          2.469
           0.980       1.000            1.564          2.469
           0.950       1.000            2.167          2.469
           0.900       0.000            2.833          2.469
           0.800       0.000            3.822          2.469
           0.700       0.000            4.671          2.469
           0.500       0.000            6.346          2.469
           0.300       0.000            8.383          2.469
           0.200       0.000            9.803          2.469
           0.100       0.000           12.017          2.469
           0.050       0.000           14.067          2.469
           0.020       0.000           16.622          2.469
           0.010       0.000           18.475          2.469

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                                 0.006
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.006          0.006
           0.980       0.000            0.006          0.006
           0.950       0.000            0.006          0.006
           0.900       0.000            0.006          0.006
           0.800       0.000            0.006          0.006
           0.700       0.000            0.006          0.006
           0.500       0.000            0.006          0.006
           0.300       0.000            0.006          0.006
           0.200       0.000            0.006          0.006
           0.100       0.000            0.006          0.006
           0.050       0.000            0.006          0.006
           0.020       0.000            0.006          0.006
           0.010       0.000            0.006          0.006


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 I        |
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        |
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3               2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4               3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        WITH
  I                0.000     0.1389     0.0000     0.0518     0.0193 0.000 1.000

 Y1       WITH
  Y4               0.027     0.1849     0.0000     0.1016     0.0249 1.000 0.000
  Y2               0.300     0.7337     0.0000     0.2092     0.1881 0.000 1.000
  Y3               0.090     0.3684     0.0000     0.1537     0.0775 1.000 1.000

 Y2       WITH
  Y3               0.300     0.7337     0.0000     0.2092     0.1881 0.000 1.000
  Y4               0.090     0.3684     0.0000     0.1537     0.0775 1.000 1.000

 Y3       WITH
  Y4               0.300     0.7337     0.0000     0.2092     0.1881 0.000 1.000

 Means
  I                0.000     0.0112     0.0000     0.0423     0.0001 1.000 0.000
  S                1.000     1.0111     0.0000     0.0206     0.0001 1.000 1.000

 Intercepts
  Y1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y3               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y4               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Variances
  I                1.000     0.4236     0.0000     0.2528     0.3322 0.000 0.000
  S                0.200     0.1420     0.0000     0.0343     0.0034 1.000 1.000

 Residual Variances
  Y1               1.000     1.4615     0.0000     0.2252     0.2130 0.000 1.000
  Y2               1.000     1.4615     0.0000     0.2252     0.2130 0.000 1.000
  Y3               1.000     1.4615     0.0000     0.2252     0.2130 0.000 1.000
  Y4               1.000     1.4615     0.0000     0.2252     0.2130 0.000 1.000

 New/Additional Parameters
  CORR             0.300     0.5020     0.0000     0.0666     0.0408 0.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.159E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
      1           0             0             0             0


           LAMBDA
              I             S
              ________      ________
 Y1                 0             0
 Y2                 0             0
 Y3                 0             0
 Y4                 0             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 1
 Y2                 2             1
 Y3                 3             2             1
 Y4                 4             3             2             1


           ALPHA
              I             S
              ________      ________
      1           5             6


           BETA
              I             S
              ________      ________
 I                  0             0
 S                  0             0


           PSI
              I             S
              ________      ________
 I                  7
 S                  8             9


     PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              CORR
              ________
 1                 10


     STARTING VALUES


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


           LAMBDA
              I             S
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         1.000
 Y3             1.000         2.000
 Y4             1.000         3.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.300         1.000
 Y3             0.090         0.300         1.000
 Y4             0.027         0.090         0.300         1.000


           ALPHA
              I             S
              ________      ________
      1         0.000         1.000


           BETA
              I             S
              ________      ________
 I              0.000         0.000
 S              0.000         0.000


           PSI
              I             S
              ________      ________
 I              1.000
 S              0.000         0.200


     STARTING VALUES FOR THE ADDITIONAL PARAMETERS


           New/Additional Parameters
              CORR
              ________
 1              0.300


     POPULATION VALUES


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


           LAMBDA
              I             S
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         1.000
 Y3             1.000         2.000
 Y4             1.000         3.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.300         1.000
 Y3             0.090         0.300         1.000
 Y4             0.027         0.090         0.300         1.000


           ALPHA
              I             S
              ________      ________
 1              0.000         1.000


           BETA
              I             S
              ________      ________
 I              0.000         0.000
 S              0.000         0.000


           PSI
              I             S
              ________      ________
 I              1.000
 S              0.000         0.200


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4

  Save file
    ex6.17.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:02:54
        Ending Time:  22:02:54
       Elapsed Time:  00:00:00



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