Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:03 PM

INPUT INSTRUCTIONS

  title:	this is an example of a quadratic growth
  	model for a continuous outcome

  montecarlo:
  	names = y11-y14;
  	nobs = 500;
  	nreps = 1;
  	save = ex6.9.dat;

  model population:

  	i s q | y11@0 y12@1 y13@2 y14@3;
  	[y11-y14@0];
  	y11-y14*1;
  	[i*.5 s*1 q*.5];
  	i*1; s*.4; q*.2; i with s*.1;
  	! i and s with q defaults to zero (free)

  	! this model gives many replications with
  	! non-pos def cov matrices, with low
  	! power (see last column) for the s and y14
  	! variances, suggesting that more time points
  	! may be needed for this quadratic model

  model:
  	
  	i s q | y11@0 y12@1 y13@2 y14@3;
  	[y11-y14@0];
  	y11-y14*1;
  	[i*.5 s*1 q*.5];
  	i*1; s*.4; q*.2; i with s*.1;

  output:
  	tech9;




INPUT READING TERMINATED NORMALLY



this is an example of a quadratic growth
model for a continuous outcome

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                                    4
Number of independent variables                                  0
Number of continuous latent variables                            3

Observed dependent variables

  Continuous
   Y11         Y12         Y13         Y14

Continuous latent variables
   I           S           Q


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
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
      1         0.516         2.088         4.618         8.240


           Covariances
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 Y11            1.932
 Y12            1.174         2.906
 Y13            1.303         3.282         7.944
 Y14            1.635         4.946        12.455        24.897


           Correlations
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 Y11            1.000
 Y12            0.495         1.000
 Y13            0.333         0.683         1.000
 Y14            0.236         0.582         0.886         1.000


MODEL FIT INFORMATION

Number of Free Parameters                       13

Loglikelihood

    H0 Value

        Mean                             -3975.519
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -3975.519      -3975.519
           0.980       0.000        -3975.519      -3975.519
           0.950       0.000        -3975.519      -3975.519
           0.900       0.000        -3975.519      -3975.519
           0.800       0.000        -3975.519      -3975.519
           0.700       0.000        -3975.519      -3975.519
           0.500       0.000        -3975.519      -3975.519
           0.300       0.000        -3975.519      -3975.519
           0.200       0.000        -3975.519      -3975.519
           0.100       0.000        -3975.519      -3975.519
           0.050       0.000        -3975.519      -3975.519
           0.020       0.000        -3975.519      -3975.519
           0.010       0.000        -3975.519      -3975.519

    H1 Value

        Mean                             -3975.281
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -3975.281      -3975.281
           0.980       0.000        -3975.281      -3975.281
           0.950       0.000        -3975.281      -3975.281
           0.900       0.000        -3975.281      -3975.281
           0.800       0.000        -3975.281      -3975.281
           0.700       0.000        -3975.281      -3975.281
           0.500       0.000        -3975.281      -3975.281
           0.300       0.000        -3975.281      -3975.281
           0.200       0.000        -3975.281      -3975.281
           0.100       0.000        -3975.281      -3975.281
           0.050       0.000        -3975.281      -3975.281
           0.020       0.000        -3975.281      -3975.281
           0.010       0.000        -3975.281      -3975.281

Information Criteria

    Akaike (AIC)

        Mean                              7977.038
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         7977.038       7977.038
           0.980       0.000         7977.038       7977.038
           0.950       0.000         7977.038       7977.038
           0.900       0.000         7977.038       7977.038
           0.800       0.000         7977.038       7977.038
           0.700       0.000         7977.038       7977.038
           0.500       0.000         7977.038       7977.038
           0.300       0.000         7977.038       7977.038
           0.200       0.000         7977.038       7977.038
           0.100       0.000         7977.038       7977.038
           0.050       0.000         7977.038       7977.038
           0.020       0.000         7977.038       7977.038
           0.010       0.000         7977.038       7977.038

    Bayesian (BIC)

        Mean                              8031.828
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         8031.828       8031.828
           0.980       0.000         8031.828       8031.828
           0.950       0.000         8031.828       8031.828
           0.900       0.000         8031.828       8031.828
           0.800       0.000         8031.828       8031.828
           0.700       0.000         8031.828       8031.828
           0.500       0.000         8031.828       8031.828
           0.300       0.000         8031.828       8031.828
           0.200       0.000         8031.828       8031.828
           0.100       0.000         8031.828       8031.828
           0.050       0.000         8031.828       8031.828
           0.020       0.000         8031.828       8031.828
           0.010       0.000         8031.828       8031.828

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

        Mean                              7990.565
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         7990.565       7990.565
           0.980       0.000         7990.565       7990.565
           0.950       0.000         7990.565       7990.565
           0.900       0.000         7990.565       7990.565
           0.800       0.000         7990.565       7990.565
           0.700       0.000         7990.565       7990.565
           0.500       0.000         7990.565       7990.565
           0.300       0.000         7990.565       7990.565
           0.200       0.000         7990.565       7990.565
           0.100       0.000         7990.565       7990.565
           0.050       0.000         7990.565       7990.565
           0.020       0.000         7990.565       7990.565
           0.010       0.000         7990.565       7990.565

Chi-Square Test of Model Fit

        Degrees of freedom                       1

        Mean                                 0.475
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.000          0.475
           0.980       1.000            0.001          0.475
           0.950       1.000            0.004          0.475
           0.900       1.000            0.016          0.475
           0.800       1.000            0.064          0.475
           0.700       1.000            0.148          0.475
           0.500       1.000            0.455          0.475
           0.300       0.000            1.074          0.475
           0.200       0.000            1.642          0.475
           0.100       0.000            2.706          0.475
           0.050       0.000            3.841          0.475
           0.020       0.000            5.412          0.475
           0.010       0.000            6.635          0.475

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                                 0.004
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000            0.004          0.004
           0.980       0.000            0.004          0.004
           0.950       0.000            0.004          0.004
           0.900       0.000            0.004          0.004
           0.800       0.000            0.004          0.004
           0.700       0.000            0.004          0.004
           0.500       0.000            0.004          0.004
           0.300       0.000            0.004          0.004
           0.200       0.000            0.004          0.004
           0.100       0.000            0.004          0.004
           0.050       0.000            0.004          0.004
           0.020       0.000            0.004          0.004
           0.010       0.000            0.004          0.004


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
 I        |
  Y11              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y12              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y13              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y14              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

 S        |
  Y11              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y12              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y13              2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y14              3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

 Q        |
  Y11              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y12              1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y13              4.000     4.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y14              9.000     9.0000     0.0000     0.0000     0.0000 1.000 0.000

 I        WITH
  S                0.100    -0.1734     0.0000     0.3003     0.0747 1.000 0.000

 Q        WITH
  I                0.000     0.1010     0.0000     0.0796     0.0102 1.000 0.000
  S                0.000    -0.1787     0.0000     0.1172     0.0319 1.000 0.000

 Means
  I                0.500     0.5214     0.0000     0.0618     0.0005 1.000 1.000
  S                1.000     1.0348     0.0000     0.0769     0.0012 1.000 1.000
  Q                0.500     0.5121     0.0000     0.0311     0.0001 1.000 1.000

 Intercepts
  Y11              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y12              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y13              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y14              0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Variances
  I                1.000     1.2462     0.0000     0.2728     0.0606 1.000 1.000
  S                0.400     0.9982     0.0000     0.3581     0.3579 1.000 1.000
  Q                0.200     0.2815     0.0000     0.0603     0.0066 1.000 1.000

 Residual Variances
  Y11              1.000     0.6855     0.0000     0.2647     0.0989 1.000 1.000
  Y12              1.000     0.8822     0.0000     0.1145     0.0139 1.000 1.000
  Y13              1.000     0.9460     0.0000     0.1827     0.0029 1.000 1.000
  Y14              1.000     0.7379     0.0000     0.9445     0.0687 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.241E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
      1           0             0             0             0


           LAMBDA
              I             S             Q
              ________      ________      ________
 Y11                0             0             0
 Y12                0             0             0
 Y13                0             0             0
 Y14                0             0             0


           THETA
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 Y11                1
 Y12                0             2
 Y13                0             0             3
 Y14                0             0             0             4


           ALPHA
              I             S             Q
              ________      ________      ________
      1           5             6             7


           BETA
              I             S             Q
              ________      ________      ________
 I                  0             0             0
 S                  0             0             0
 Q                  0             0             0


           PSI
              I             S             Q
              ________      ________      ________
 I                  8
 S                  9            10
 Q                 11            12            13


     STARTING VALUES


           NU
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
      1         0.000         0.000         0.000         0.000


           LAMBDA
              I             S             Q
              ________      ________      ________
 Y11            1.000         0.000         0.000
 Y12            1.000         1.000         1.000
 Y13            1.000         2.000         4.000
 Y14            1.000         3.000         9.000


           THETA
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 Y11            1.000
 Y12            0.000         1.000
 Y13            0.000         0.000         1.000
 Y14            0.000         0.000         0.000         1.000


           ALPHA
              I             S             Q
              ________      ________      ________
      1         0.500         1.000         0.500


           BETA
              I             S             Q
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         0.000
 Q              0.000         0.000         0.000


           PSI
              I             S             Q
              ________      ________      ________
 I              1.000
 S              0.100         0.400
 Q              0.000         0.000         0.200


     POPULATION VALUES


           NU
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              I             S             Q
              ________      ________      ________
 Y11            1.000         0.000         0.000
 Y12            1.000         1.000         1.000
 Y13            1.000         2.000         4.000
 Y14            1.000         3.000         9.000


           THETA
              Y11           Y12           Y13           Y14
              ________      ________      ________      ________
 Y11            1.000
 Y12            0.000         1.000
 Y13            0.000         0.000         1.000
 Y14            0.000         0.000         0.000         1.000


           ALPHA
              I             S             Q
              ________      ________      ________
 1              0.500         1.000         0.500


           BETA
              I             S             Q
              ________      ________      ________
 I              0.000         0.000         0.000
 S              0.000         0.000         0.000
 Q              0.000         0.000         0.000


           PSI
              I             S             Q
              ________      ________      ________
 I              1.000
 S              0.100         0.400
 Q              0.000         0.000         0.200


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y11
    Y12
    Y13
    Y14

  Save file
    ex6.9.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:03:03
        Ending Time:  22:03:03
       Elapsed Time:  00:00:00



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