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

INPUT INSTRUCTIONS

title:	this is an example of a linear growth
model for a censored outcome using a
censored-inflated model

montecarlo:
names = y11-y14;
generate = y11-y14(cbi 0);
censored = y11-y14(bi);
nobs = 1000;
nreps = 1;
save = ex6.3.dat;

model population:

i s | y11@0 y12@1 y13@2 y14@3;
[y11-y14@0];
y11-y14*1.5;
[i*3.5 s*1.5];
! censored below at zero gives many zeros at time 1
i*1; s*.3; i with s*.1;

ii si | y11#1@0 y12#1@1 y13#1@2 y14#1@3;
[y11#1-y14#1*-1.5] (1);
! parameterization 2 with equal logit intercepts
[ii@0 si*.1];
ii*1 si@0;
! for simplicity, use only 3 dimensions of integration:
! i, s, and ii
si with i-ii@0;

analysis:
integration = 7;

model:

i s | y11@0 y12@1 y13@2 y14@3;
[y11-y14@0];
y11-y14*1.5;
[i*3.5 s*1.5];

i*1; s*.3; i with s*.1;

ii si | y11#1@0 y12#1@1 y13#1@2 y14#1@3;
[y11#1-y14#1*-1.5] (1);

[ii@0 si*.1];
ii*1 si@0;
si with i-ii@0;

output:
tech8 tech9;

this is an example of a linear growth
model for a censored outcome using a
censored-inflated model

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                            4

Observed dependent variables

Censored
Y11         Y12         Y13         Y14

Continuous latent variables
I           S           II          SI

Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                 100
Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations                                 500
Convergence criteria
Loglikelihood change                                 0.100D-02
Relative loglikelihood change                        0.100D-05
Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            15
Minimum value for logit thresholds                           -15
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                   7
Dimensions of numerical integration                            3
Cholesky                                                        ON

SUMMARY OF CENSORED LIMITS

Y11                0.000
Y12                0.000
Y13                0.000
Y14                0.000

MODEL FIT INFORMATION

Number of Free Parameters                       14

Loglikelihood

H0 Value

Mean                             -8014.919
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -8014.919      -8014.919
0.980       0.000        -8014.919      -8014.919
0.950       0.000        -8014.919      -8014.919
0.900       0.000        -8014.919      -8014.919
0.800       0.000        -8014.919      -8014.919
0.700       0.000        -8014.919      -8014.919
0.500       0.000        -8014.919      -8014.919
0.300       0.000        -8014.919      -8014.919
0.200       0.000        -8014.919      -8014.919
0.100       0.000        -8014.919      -8014.919
0.050       0.000        -8014.919      -8014.919
0.020       0.000        -8014.919      -8014.919
0.010       0.000        -8014.919      -8014.919

Information Criteria

Akaike (AIC)

Mean                             16057.838
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        16057.838      16057.838
0.980       0.000        16057.838      16057.838
0.950       0.000        16057.838      16057.838
0.900       0.000        16057.838      16057.838
0.800       0.000        16057.838      16057.838
0.700       0.000        16057.838      16057.838
0.500       0.000        16057.838      16057.838
0.300       0.000        16057.838      16057.838
0.200       0.000        16057.838      16057.838
0.100       0.000        16057.838      16057.838
0.050       0.000        16057.838      16057.838
0.020       0.000        16057.838      16057.838
0.010       0.000        16057.838      16057.838

Bayesian (BIC)

Mean                             16126.547
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        16126.547      16126.547
0.980       0.000        16126.547      16126.547
0.950       0.000        16126.547      16126.547
0.900       0.000        16126.547      16126.547
0.800       0.000        16126.547      16126.547
0.700       0.000        16126.547      16126.547
0.500       0.000        16126.547      16126.547
0.300       0.000        16126.547      16126.547
0.200       0.000        16126.547      16126.547
0.100       0.000        16126.547      16126.547
0.050       0.000        16126.547      16126.547
0.020       0.000        16126.547      16126.547
0.010       0.000        16126.547      16126.547

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

Mean                             16082.082
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        16082.082      16082.082
0.980       0.000        16082.082      16082.082
0.950       0.000        16082.082      16082.082
0.900       0.000        16082.082      16082.082
0.800       0.000        16082.082      16082.082
0.700       0.000        16082.082      16082.082
0.500       0.000        16082.082      16082.082
0.300       0.000        16082.082      16082.082
0.200       0.000        16082.082      16082.082
0.100       0.000        16082.082      16082.082
0.050       0.000        16082.082      16082.082
0.020       0.000        16082.082      16082.082
0.010       0.000        16082.082      16082.082

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

II       |
Y11#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y12#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y13#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y14#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

SI       |
Y11#1               0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y12#1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
Y13#1               2.000     2.0000     0.0000     0.0000     0.0000 1.000 0.000
Y14#1               3.000     3.0000     0.0000     0.0000     0.0000 1.000 0.000

I        WITH
S                   0.100     0.1053     0.0000     0.0530     0.0000 1.000 1.000
SI                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

SI       WITH
S                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
II                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

II       WITH
I                   0.000     0.0209     0.0000     0.0974     0.0004 1.000 0.000
S                   0.000     0.0361     0.0000     0.0567     0.0013 1.000 0.000

Means
I                   3.500     3.6083     0.0000     0.0550     0.0117 0.000 1.000
S                   1.500     1.5188     0.0000     0.0296     0.0004 1.000 1.000
II                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
SI                  0.100     0.0175     0.0000     0.0353     0.0068 0.000 0.000

Intercepts
Y11#1              -1.500    -1.3967     0.0000     0.0800     0.0107 1.000 1.000
Y11                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y12#1              -1.500    -1.3967     0.0000     0.0800     0.0107 1.000 1.000
Y12                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y13#1              -1.500    -1.3967     0.0000     0.0800     0.0107 1.000 1.000
Y13                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y14#1              -1.500    -1.3967     0.0000     0.0800     0.0107 1.000 1.000
Y14                 0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Variances
I                   1.000     1.0904     0.0000     0.1332     0.0082 1.000 1.000
S                   0.300     0.3351     0.0000     0.0399     0.0012 1.000 1.000
II                  1.000     0.9825     0.0000     0.1457     0.0003 1.000 1.000
SI                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Residual Variances
Y11                 1.500     1.4297     0.0000     0.1392     0.0049 1.000 1.000
Y12                 1.500     1.5181     0.0000     0.1004     0.0003 1.000 1.000
Y13                 1.500     1.6431     0.0000     0.1223     0.0205 1.000 1.000
Y14                 1.500     1.2278     0.0000     0.2109     0.0741 1.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.101E-01
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
Y11#1         Y11           Y12#1         Y12           Y13#1
________      ________      ________      ________      ________
1             0             1             0             1

NU
Y13           Y14#1         Y14
________      ________      ________
0             1             0

LAMBDA
I             S             II            SI
________      ________      ________      ________
Y11#1              0             0             0             0
Y11                0             0             0             0
Y12#1              0             0             0             0
Y12                0             0             0             0
Y13#1              0             0             0             0
Y13                0             0             0             0
Y14#1              0             0             0             0
Y14                0             0             0             0

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

THETA
Y13           Y14#1         Y14
________      ________      ________
Y13                4
Y14#1              0             0
Y14                0             0             5

ALPHA
I             S             II            SI
________      ________      ________      ________
6             7             0             8

BETA
I             S             II            SI
________      ________      ________      ________
I                  0             0             0             0
S                  0             0             0             0
II                 0             0             0             0
SI                 0             0             0             0

PSI
I             S             II            SI
________      ________      ________      ________
I                  9
S                 10            11
II                12            13            14
SI                 0             0             0             0

STARTING VALUES

NU
Y11#1         Y11           Y12#1         Y12           Y13#1
________      ________      ________      ________      ________
-1.500         0.000        -1.500         0.000        -1.500

NU
Y13           Y14#1         Y14
________      ________      ________
0.000        -1.500         0.000

LAMBDA
I             S             II            SI
________      ________      ________      ________
Y11#1          0.000         0.000         1.000         0.000
Y11            1.000         0.000         0.000         0.000
Y12#1          0.000         0.000         1.000         1.000
Y12            1.000         1.000         0.000         0.000
Y13#1          0.000         0.000         1.000         2.000
Y13            1.000         2.000         0.000         0.000
Y14#1          0.000         0.000         1.000         3.000
Y14            1.000         3.000         0.000         0.000

THETA
Y11#1         Y11           Y12#1         Y12           Y13#1
________      ________      ________      ________      ________
Y11#1          0.000
Y11            0.000         1.500
Y12#1          0.000         0.000         0.000
Y12            0.000         0.000         0.000         1.500
Y13#1          0.000         0.000         0.000         0.000         0.000
Y13            0.000         0.000         0.000         0.000         0.000
Y14#1          0.000         0.000         0.000         0.000         0.000
Y14            0.000         0.000         0.000         0.000         0.000

THETA
Y13           Y14#1         Y14
________      ________      ________
Y13            1.500
Y14#1          0.000         0.000
Y14            0.000         0.000         1.500

ALPHA
I             S             II            SI
________      ________      ________      ________
3.500         1.500         0.000         0.100

BETA
I             S             II            SI
________      ________      ________      ________
I              0.000         0.000         0.000         0.000
S              0.000         0.000         0.000         0.000
II             0.000         0.000         0.000         0.000
SI             0.000         0.000         0.000         0.000

PSI
I             S             II            SI
________      ________      ________      ________
I              1.000
S              0.100         0.300
II             0.000         0.000         1.000
SI             0.000         0.000         0.000         0.000

POPULATION VALUES

NU
Y11#1         Y11           Y12#1         Y12           Y13#1
________      ________      ________      ________      ________
-1.500         0.000        -1.500         0.000        -1.500

NU
Y13           Y14#1         Y14
________      ________      ________
0.000        -1.500         0.000

LAMBDA
I             S             II            SI
________      ________      ________      ________
Y11#1          0.000         0.000         1.000         0.000
Y11            1.000         0.000         0.000         0.000
Y12#1          0.000         0.000         1.000         1.000
Y12            1.000         1.000         0.000         0.000
Y13#1          0.000         0.000         1.000         2.000
Y13            1.000         2.000         0.000         0.000
Y14#1          0.000         0.000         1.000         3.000
Y14            1.000         3.000         0.000         0.000

THETA
Y11#1         Y11           Y12#1         Y12           Y13#1
________      ________      ________      ________      ________
Y11#1          0.000
Y11            0.000         1.500
Y12#1          0.000         0.000         0.000
Y12            0.000         0.000         0.000         1.500
Y13#1          0.000         0.000         0.000         0.000         0.000
Y13            0.000         0.000         0.000         0.000         0.000
Y14#1          0.000         0.000         0.000         0.000         0.000
Y14            0.000         0.000         0.000         0.000         0.000

THETA
Y13           Y14#1         Y14
________      ________      ________
Y13            1.500
Y14#1          0.000         0.000
Y14            0.000         0.000         1.500

ALPHA
I             S             II            SI
________      ________      ________      ________
3.500         1.500         0.000         0.100

BETA
I             S             II            SI
________      ________      ________      ________
I              0.000         0.000         0.000         0.000
S              0.000         0.000         0.000         0.000
II             0.000         0.000         0.000         0.000
SI             0.000         0.000         0.000         0.000

PSI
I             S             II            SI
________      ________      ________      ________
I              1.000
S              0.100         0.300
II             0.000         0.000         1.000
SI             0.000         0.000         0.000         0.000

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.80238800D+04    0.0000000    0.0000000  EM
2 -0.80152174D+04    8.6625922    0.0010796  FS
3 -0.80148971D+04    0.3203561    0.0000400  FS
4 -0.80149191D+04   -0.0220337   -0.0000027  EM

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

Y11
Y12
Y13
Y14

Save file
ex6.3.dat

Save file format           Free
Save file record length    10000

Beginning Time:  22:24:23
Ending Time:  22:24:25
Elapsed Time:  00:00:02

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