```Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 PM

INPUT INSTRUCTIONS

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

montecarlo:
names = y1-y5;
nobs = 500;
nreps = 1;
save = ex6.11.dat;

model population:

i s1 | y1@0 y2@1 y3@2 y4@2 y5@2;
i s2 | y1@0 y2@0 y3@0 y4@1 y5@2;

y1-y5*.5;
[i*.5 s1*1 s2*2];
i*1; s1-s2*.2;

model:

i s1 | y1@0 y2@1 y3@2 y4@2 y5@2;
i s2 | y1@0 y2@0 y3@0 y4@1 y5@2;

y1-y5*.5;
[i*.5 s1*1 s2*2];
i*1; s1-s2*.2;

output:
tech9;

INPUT READING TERMINATED NORMALLY

this is an example of a piecewise 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                                    5
Number of independent variables                                  0
Number of continuous latent variables                            3

Observed dependent variables

Continuous
Y1          Y2          Y3          Y4          Y5

Continuous latent variables
I           S1          S2

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
________      ________      ________      ________      ________
0.443         1.584         2.595         4.535         6.535

Covariances
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.367
Y2             0.963         1.732
Y3             0.906         1.408         2.318
Y4             0.976         1.422         1.797         2.491
Y5             1.030         1.480         1.824         2.252         3.269

Correlations
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1             1.000
Y2             0.626         1.000
Y3             0.509         0.703         1.000
Y4             0.529         0.684         0.748         1.000
Y5             0.487         0.622         0.662         0.789         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       14

Loglikelihood

H0 Value

Mean                             -3706.171
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -3706.171      -3706.171
0.980       0.000        -3706.171      -3706.171
0.950       0.000        -3706.171      -3706.171
0.900       0.000        -3706.171      -3706.171
0.800       0.000        -3706.171      -3706.171
0.700       0.000        -3706.171      -3706.171
0.500       0.000        -3706.171      -3706.171
0.300       0.000        -3706.171      -3706.171
0.200       0.000        -3706.171      -3706.171
0.100       0.000        -3706.171      -3706.171
0.050       0.000        -3706.171      -3706.171
0.020       0.000        -3706.171      -3706.171
0.010       0.000        -3706.171      -3706.171

H1 Value

Mean                             -3703.549
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -3703.549      -3703.549
0.980       0.000        -3703.549      -3703.549
0.950       0.000        -3703.549      -3703.549
0.900       0.000        -3703.549      -3703.549
0.800       0.000        -3703.549      -3703.549
0.700       0.000        -3703.549      -3703.549
0.500       0.000        -3703.549      -3703.549
0.300       0.000        -3703.549      -3703.549
0.200       0.000        -3703.549      -3703.549
0.100       0.000        -3703.549      -3703.549
0.050       0.000        -3703.549      -3703.549
0.020       0.000        -3703.549      -3703.549
0.010       0.000        -3703.549      -3703.549

Information Criteria

Akaike (AIC)

Mean                              7440.342
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7440.342       7440.342
0.980       0.000         7440.342       7440.342
0.950       0.000         7440.342       7440.342
0.900       0.000         7440.342       7440.342
0.800       0.000         7440.342       7440.342
0.700       0.000         7440.342       7440.342
0.500       0.000         7440.342       7440.342
0.300       0.000         7440.342       7440.342
0.200       0.000         7440.342       7440.342
0.100       0.000         7440.342       7440.342
0.050       0.000         7440.342       7440.342
0.020       0.000         7440.342       7440.342
0.010       0.000         7440.342       7440.342

Bayesian (BIC)

Mean                              7499.346
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7499.346       7499.346
0.980       0.000         7499.346       7499.346
0.950       0.000         7499.346       7499.346
0.900       0.000         7499.346       7499.346
0.800       0.000         7499.346       7499.346
0.700       0.000         7499.346       7499.346
0.500       0.000         7499.346       7499.346
0.300       0.000         7499.346       7499.346
0.200       0.000         7499.346       7499.346
0.100       0.000         7499.346       7499.346
0.050       0.000         7499.346       7499.346
0.020       0.000         7499.346       7499.346
0.010       0.000         7499.346       7499.346

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

Mean                              7454.909
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         7454.909       7454.909
0.980       0.000         7454.909       7454.909
0.950       0.000         7454.909       7454.909
0.900       0.000         7454.909       7454.909
0.800       0.000         7454.909       7454.909
0.700       0.000         7454.909       7454.909
0.500       0.000         7454.909       7454.909
0.300       0.000         7454.909       7454.909
0.200       0.000         7454.909       7454.909
0.100       0.000         7454.909       7454.909
0.050       0.000         7454.909       7454.909
0.020       0.000         7454.909       7454.909
0.010       0.000         7454.909       7454.909

Chi-Square Test of Model Fit

Degrees of freedom                       6

Mean                                 5.244
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       1.000            0.872          5.244
0.980       1.000            1.134          5.244
0.950       1.000            1.635          5.244
0.900       1.000            2.204          5.244
0.800       1.000            3.070          5.244
0.700       1.000            3.828          5.244
0.500       0.000            5.348          5.244
0.300       0.000            7.231          5.244
0.200       0.000            8.558          5.244
0.100       0.000           10.645          5.244
0.050       0.000           12.592          5.244
0.020       0.000           15.033          5.244
0.010       0.000           16.812          5.244

RMSEA (Root Mean Square Error Of Approximation)

Mean                                 0.000
Std Dev                              0.000
Number of successful computations        1

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       1.000
0.050       1.000
0.020       1.000
0.010       1.000

CFI/TLI

CFI

Mean                                 1.000
Std Dev                              0.000
Number of successful computations        1

Cumulative Distribution Function
Value    Function Value
0.990       0.000
0.980       0.000
0.950       0.000
0.900       0.000
0.800       0.000
0.700       0.000
0.500       0.000
0.300       0.000
0.200       0.000
0.100       0.000
0.050       0.000
0.020       0.000
0.010       0.000

TLI

Mean                                 1.000
Std Dev                              0.000
Number of successful computations        1

Cumulative Distribution Function
Value    Function Value
0.990       0.000
0.980       0.000
0.950       0.000
0.900       0.000
0.800       0.000
0.700       0.000
0.500       0.000
0.300       0.000
0.200       0.000
0.100       0.000
0.050       0.000
0.020       0.000
0.010       0.000

SRMR (Standardized Root Mean Square Residual)

Mean                                 0.010
Std Dev                              0.000
Number of successful computations        1

Cumulative Distribution Function
Value    Function Value
0.990       1.000
0.980       1.000
0.950       1.000
0.900       1.000
0.800       1.000
0.700       1.000
0.500       1.000
0.300       1.000
0.200       1.000
0.100       1.000
0.050       1.000
0.020       1.000
0.010       0.000

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
Y5                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

S1       |
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                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
Y5                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000

S2       |
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                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y5                  2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000

S1       WITH
I                   0.000    -0.0291     0.0000     0.0494     0.0008 1.000 0.000

S2       WITH
I                   0.000     0.0594     0.0000     0.0362     0.0035 1.000 0.000
S1                  0.000    -0.0309     0.0000     0.0261     0.0010 1.000 0.000

Means
I                   0.500     0.4622     0.0000     0.0516     0.0014 1.000 1.000
S1                  1.000     1.0714     0.0000     0.0298     0.0051 0.000 1.000
S2                  2.000     1.9573     0.0000     0.0304     0.0018 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
Y5                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Variances
I                   1.000     0.9846     0.0000     0.1002     0.0002 1.000 1.000
S1                  0.200     0.2396     0.0000     0.0374     0.0016 1.000 1.000
S2                  0.200     0.2191     0.0000     0.0416     0.0004 1.000 1.000

Residual Variances
Y1                  0.500     0.3944     0.0000     0.0765     0.0111 1.000 1.000
Y2                  0.500     0.5251     0.0000     0.0431     0.0006 1.000 1.000
Y3                  0.500     0.5013     0.0000     0.0682     0.0000 1.000 1.000
Y4                  0.500     0.4832     0.0000     0.0479     0.0003 1.000 1.000
Y5                  0.500     0.5587     0.0000     0.1030     0.0034 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.136E-01
(ratio of smallest to largest eigenvalue)

TECHNICAL OUTPUT

PARAMETER SPECIFICATION

NU
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
0             0             0             0             0

LAMBDA
I             S1            S2
________      ________      ________
Y1                 0             0             0
Y2                 0             0             0
Y3                 0             0             0
Y4                 0             0             0
Y5                 0             0             0

THETA
Y1            Y2            Y3            Y4            Y5
________      ________      ________      ________      ________
Y1                 1
Y2                 0             2
Y3                 0             0             3
Y4                 0             0             0             4
Y5                 0             0             0             0             5

ALPHA
I             S1            S2
________      ________      ________
6             7             8

BETA
I             S1            S2
________      ________      ________
I                  0             0             0
S1                 0             0             0
S2                 0             0             0

PSI
I             S1            S2
________      ________      ________
I                  9
S1                10            11
S2                12            13            14

STARTING VALUES

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

LAMBDA
I             S1            S2
________      ________      ________
Y1             1.000         0.000         0.000
Y2             1.000         1.000         0.000
Y3             1.000         2.000         0.000
Y4             1.000         2.000         1.000
Y5             1.000         2.000         2.000

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         0.500
Y5             0.000         0.000         0.000         0.000         0.500

ALPHA
I             S1            S2
________      ________      ________
0.500         1.000         2.000

BETA
I             S1            S2
________      ________      ________
I              0.000         0.000         0.000
S1             0.000         0.000         0.000
S2             0.000         0.000         0.000

PSI
I             S1            S2
________      ________      ________
I              1.000
S1             0.000         0.200
S2             0.000         0.000         0.200

POPULATION VALUES

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

LAMBDA
I             S1            S2
________      ________      ________
Y1             1.000         0.000         0.000
Y2             1.000         1.000         0.000
Y3             1.000         2.000         0.000
Y4             1.000         2.000         1.000
Y5             1.000         2.000         2.000

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         0.500
Y5             0.000         0.000         0.000         0.000         0.500

ALPHA
I             S1            S2
________      ________      ________
0.500         1.000         2.000

BETA
I             S1            S2
________      ________      ________
I              0.000         0.000         0.000
S1             0.000         0.000         0.000
S2             0.000         0.000         0.000

PSI
I             S1            S2
________      ________      ________
I              1.000
S1             0.000         0.200
S2             0.000         0.000         0.200

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

Y1
Y2
Y3
Y4
Y5

Save file
ex6.11.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:24:14
Ending Time:  22:24:14
Elapsed Time:  00:00:00

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