```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:29 AM

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;

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
________      ________      ________      ________
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
________      ________      ________      ________
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
________      ________      ________
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
________      ________      ________      ________
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
________      ________      ________
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
________      ________      ________      ________
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
________      ________      ________
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:  03:29:19
Ending Time:  03:29:19
Elapsed Time:  00:00:00

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