```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:42 AM

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
DATA:	FILE = ex6.17.dat;
VARIABLE:	NAMES = y1-y4;
MODEL:	i s | y1@0 y2@1 y3@2 y4@3;
y1-y4 (resvar);
y1-y3 PWITH y2-y4 (p1);
y1-y2 PWITH y3-y4 (p2);
y1 WITH y4 (p3);
MODEL CONSTRAINT:
NEW (corr);
p1 = resvar*corr;
p2 = resvar*corr**2;
p3 = resvar*corr**3;

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 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

Input data file(s)
ex6.17.dat

Input data format  FREE

UNIVARIATE SAMPLE STATISTICS

UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

Y1                    0.016      -0.084      -3.687    0.10%      -1.132     -0.303      0.040
1000.000       1.897      -0.258       3.792    0.10%       0.356      1.232
Y2                    1.027       0.027      -4.043    0.10%      -0.230      0.641      1.018
1000.000       2.295      -0.038       5.854    0.10%       1.391      2.277
Y3                    2.001       0.047      -3.213    0.10%       0.509      1.454      1.958
1000.000       2.982      -0.329       8.140    0.10%       2.467      3.566
Y4                    3.053       0.044      -3.040    0.10%       1.292      2.538      3.081
1000.000       4.006      -0.019       9.244    0.10%       3.546      4.687

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

H0 Value                       -6593.460
H1 Value                       -6592.226

Information Criteria

Akaike (AIC)                   13200.921
Bayesian (BIC)                 13235.275
(n* = (n + 2) / 24)

Chi-Square Test of Model Fit

Value                              2.469
Degrees of Freedom                     7
P-Value                           0.9294

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.000
90 Percent C.I.                    0.000  0.012
Probability RMSEA <= .05           1.000

CFI/TLI

CFI                                1.000
TLI                                1.002

Chi-Square Test of Model Fit for the Baseline Model

Value                           2118.221
Degrees of Freedom                     6
P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

Value                              0.006

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

I        |
Y1                 1.000      0.000    999.000    999.000
Y2                 1.000      0.000    999.000    999.000
Y3                 1.000      0.000    999.000    999.000
Y4                 1.000      0.000    999.000    999.000

S        |
Y1                 0.000      0.000    999.000    999.000
Y2                 1.000      0.000    999.000    999.000
Y3                 2.000      0.000    999.000    999.000
Y4                 3.000      0.000    999.000    999.000

S        WITH
I                  0.139      0.052      2.680      0.007

Y1       WITH
Y2                 0.734      0.209      3.507      0.000
Y3                 0.368      0.154      2.397      0.017
Y4                 0.185      0.102      1.820      0.069

Y2       WITH
Y3                 0.734      0.209      3.507      0.000
Y4                 0.368      0.154      2.397      0.017

Y3       WITH
Y4                 0.734      0.209      3.507      0.000

Means
I                  0.011      0.042      0.266      0.790
S                  1.011      0.021     49.078      0.000

Intercepts
Y1                 0.000      0.000    999.000    999.000
Y2                 0.000      0.000    999.000    999.000
Y3                 0.000      0.000    999.000    999.000
Y4                 0.000      0.000    999.000    999.000

Variances
I                  0.424      0.253      1.676      0.094
S                  0.142      0.034      4.135      0.000

Residual Variances
Y1                 1.462      0.225      6.490      0.000
Y2                 1.462      0.225      6.490      0.000
Y3                 1.462      0.225      6.490      0.000
Y4                 1.462      0.225      6.490      0.000

CORR               0.502      0.067      7.543      0.000

QUALITY OF NUMERICAL RESULTS

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

Beginning Time:  04:42:41
Ending Time:  04:42:41
Elapsed Time:  00:00:00

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