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;
INPUT READING TERMINATED NORMALLY
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
Adaptive quadrature ON
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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