Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a Monte Carlo
simulation study this is an example of a path analysis
with a combination of censored, categorical,
and unordered categorical dependent variables
MONTECARLO:
NAMES = y1 u1 u2 x1-x3;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
GENERATE = y1(ca 1) u1(1) u2(n 2);
CENSORED = y1(a);
CATEGORICAL = u1;
NOMINAL = u2;
SAVE = ex3.15.dat;
MODEL POPULATION:
[x1-x3@0];
x1-x3@1;
y1 ON x1*-1 x2*.5 x3*1;
y1*1;
[y1*.5];
u1 ON x1*1 x2*-.5 x3*-1;
u2#1 ON y1*.5 u1*1 x2*-1;
u2#2 ON y1*.-5 u1*-1 x2*1;
MODEL:
y1 ON x1*-1 x2*.5 x3*1;
y1*1;
[y1*.5];
u1 ON x1*1 x2*-.5 x3*-1;
u2#1 ON y1*.5 u1*1 x2*-1;
u2#2 ON y1*.-5 u1*-1 x2*1;
OUTPUT: TECH8 TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a Monte Carlo
simulation study this is an example of a path analysis
with a combination of censored, categorical,
and unordered categorical dependent variables
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 53487
Number of dependent variables 3
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Censored
Y1
Binary and ordered categorical (ordinal)
U1
Unordered categorical (nominal)
U2
Observed independent variables
X1 X2 X3
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 15
Dimensions of numerical integration 0
Adaptive quadrature ON
Link LOGIT
Cholesky OFF
SUMMARY OF CENSORED LIMITS
Y1 1.000
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
X1 X2 X3
________ ________ ________
-0.009 -0.014 -0.029
Covariances
X1 X2 X3
________ ________ ________
X1 1.026
X2 0.013 0.972
X3 -0.086 0.020 1.047
Correlations
X1 X2 X3
________ ________ ________
X1 1.000
X2 0.013 1.000
X3 -0.083 0.020 1.000
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -1181.376
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1181.376 -1181.376
0.980 0.000 -1181.376 -1181.376
0.950 0.000 -1181.376 -1181.376
0.900 0.000 -1181.376 -1181.376
0.800 0.000 -1181.376 -1181.376
0.700 0.000 -1181.376 -1181.376
0.500 0.000 -1181.376 -1181.376
0.300 0.000 -1181.376 -1181.376
0.200 0.000 -1181.376 -1181.376
0.100 0.000 -1181.376 -1181.376
0.050 0.000 -1181.376 -1181.376
0.020 0.000 -1181.376 -1181.376
0.010 0.000 -1181.376 -1181.376
Information Criteria
Akaike (AIC)
Mean 2396.751
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2396.751 2396.751
0.980 0.000 2396.751 2396.751
0.950 0.000 2396.751 2396.751
0.900 0.000 2396.751 2396.751
0.800 0.000 2396.751 2396.751
0.700 0.000 2396.751 2396.751
0.500 0.000 2396.751 2396.751
0.300 0.000 2396.751 2396.751
0.200 0.000 2396.751 2396.751
0.100 0.000 2396.751 2396.751
0.050 0.000 2396.751 2396.751
0.020 0.000 2396.751 2396.751
0.010 0.000 2396.751 2396.751
Bayesian (BIC)
Mean 2468.399
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2468.399 2468.399
0.980 0.000 2468.399 2468.399
0.950 0.000 2468.399 2468.399
0.900 0.000 2468.399 2468.399
0.800 0.000 2468.399 2468.399
0.700 0.000 2468.399 2468.399
0.500 0.000 2468.399 2468.399
0.300 0.000 2468.399 2468.399
0.200 0.000 2468.399 2468.399
0.100 0.000 2468.399 2468.399
0.050 0.000 2468.399 2468.399
0.020 0.000 2468.399 2468.399
0.010 0.000 2468.399 2468.399
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 2414.440
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2414.440 2414.440
0.980 0.000 2414.440 2414.440
0.950 0.000 2414.440 2414.440
0.900 0.000 2414.440 2414.440
0.800 0.000 2414.440 2414.440
0.700 0.000 2414.440 2414.440
0.500 0.000 2414.440 2414.440
0.300 0.000 2414.440 2414.440
0.200 0.000 2414.440 2414.440
0.100 0.000 2414.440 2414.440
0.050 0.000 2414.440 2414.440
0.020 0.000 2414.440 2414.440
0.010 0.000 2414.440 2414.440
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Y1 ON
X1 -1.000 -0.9916 0.0000 0.0542 0.0001 1.000 1.000
X2 0.500 0.4883 0.0000 0.0483 0.0001 1.000 1.000
X3 1.000 0.9200 0.0000 0.0489 0.0064 1.000 1.000
U1 ON
X1 1.000 1.0306 0.0000 0.1210 0.0009 1.000 1.000
X2 -0.500 -0.5988 0.0000 0.1241 0.0098 1.000 1.000
X3 -1.000 -0.9251 0.0000 0.1165 0.0056 1.000 1.000
U2#1 ON
Y1 0.500 0.4504 0.0000 0.0965 0.0025 1.000 1.000
U1 1.000 1.5030 0.0000 0.2577 0.2530 1.000 1.000
X2 -1.000 -0.6650 0.0000 0.1645 0.1122 0.000 1.000
U2#2 ON
Y1 0.000 -0.0203 0.0000 0.1535 0.0004 1.000 0.000
U1 -1.000 -0.8865 0.0000 0.3595 0.0129 1.000 1.000
X2 1.000 1.7306 0.0000 0.2189 0.5337 0.000 1.000
Intercepts
Y1 0.500 0.4168 0.0000 0.0535 0.0069 1.000 1.000
U2#1 0.000 -0.4963 0.0000 0.1757 0.2463 0.000 1.000
U2#2 0.000 -0.5441 0.0000 0.2005 0.2961 0.000 1.000
Thresholds
U1$1 0.000 0.0941 0.0000 0.1086 0.0089 1.000 0.000
Residual Variances
Y1 1.000 0.9042 0.0000 0.0726 0.0092 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.100E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1
________
17
NU
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
0 0 0 0 0
NU
X1 X2 X3
________ ________ ________
0 0 0
LAMBDA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0 0 0 0 0
Y1 0 0 0 0 0
U2#1 0 0 0 0 0
U2#2 0 0 0 0 0
U1 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
LAMBDA
X1 X2 X3
________ ________ ________
Y1#1 0 0 0
Y1 0 0 0
U2#1 0 0 0
U2#2 0 0 0
U1 0 0 0
X1 0 0 0
X2 0 0 0
X3 0 0 0
THETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0
Y1 0 0
U2#1 0 0 0
U2#2 0 0 0 0
U1 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
THETA
X1 X2 X3
________ ________ ________
X1 0
X2 0 0
X3 0 0 0
ALPHA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
0 1 2 3 0
ALPHA
X1 X2 X3
________ ________ ________
0 0 0
BETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0 0 0 0 0
Y1 0 0 0 0 0
U2#1 0 7 0 0 8
U2#2 0 10 0 0 11
U1 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
BETA
X1 X2 X3
________ ________ ________
Y1#1 0 0 0
Y1 4 5 6
U2#1 0 9 0
U2#2 0 12 0
U1 13 14 15
X1 0 0 0
X2 0 0 0
X3 0 0 0
PSI
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0
Y1 0 16
U2#1 0 0 0
U2#2 0 0 0 0
U1 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
PSI
X1 X2 X3
________ ________ ________
X1 0
X2 0 0
X3 0 0 0
STARTING VALUES
TAU
U1$1
________
0.000
NU
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X1 X2 X3
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 1.000 0.000 0.000 0.000 0.000
Y1 0.000 1.000 0.000 0.000 0.000
U2#1 0.000 0.000 1.000 0.000 0.000
U2#2 0.000 0.000 0.000 1.000 0.000
U1 0.000 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
LAMBDA
X1 X2 X3
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 0.000 0.000 0.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000
U1 0.000 0.000 0.000
X1 1.000 0.000 0.000
X2 0.000 1.000 0.000
X3 0.000 0.000 1.000
THETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
THETA
X1 X2 X3
________ ________ ________
X1 0.000
X2 0.000 0.000
X3 0.000 0.000 0.000
ALPHA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
-20.000 0.500 0.000 0.000 0.000
ALPHA
X1 X2 X3
________ ________ ________
0.000 0.000 0.000
BETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
U2#1 0.000 0.500 0.000 0.000 1.000
U2#2 0.000 0.000 0.000 0.000 -1.000
U1 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
BETA
X1 X2 X3
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 -1.000 0.500 1.000
U2#1 0.000 -1.000 0.000
U2#2 0.000 1.000 0.000
U1 1.000 -0.500 -1.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
X3 0.000 0.000 0.000
PSI
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 1.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
PSI
X1 X2 X3
________ ________ ________
X1 0.500
X2 0.000 0.500
X3 0.000 0.000 0.500
POPULATION VALUES
TAU
U1$1
________
0.000
NU
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X1 X2 X3
________ ________ ________
0.000 0.000 0.000
LAMBDA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 1.000 0.000 0.000 0.000 0.000
Y1 0.000 1.000 0.000 0.000 0.000
U2#1 0.000 0.000 1.000 0.000 0.000
U2#2 0.000 0.000 0.000 1.000 0.000
U1 0.000 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
LAMBDA
X1 X2 X3
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 0.000 0.000 0.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000
U1 0.000 0.000 0.000
X1 1.000 0.000 0.000
X2 0.000 1.000 0.000
X3 0.000 0.000 1.000
THETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 0.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
THETA
X1 X2 X3
________ ________ ________
X1 0.000
X2 0.000 0.000
X3 0.000 0.000 0.000
ALPHA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
-20.000 0.500 0.000 0.000 0.000
ALPHA
X1 X2 X3
________ ________ ________
0.000 0.000 0.000
BETA
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
U2#1 0.000 0.500 0.000 0.000 1.000
U2#2 0.000 0.000 0.000 0.000 -1.000
U1 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
BETA
X1 X2 X3
________ ________ ________
Y1#1 0.000 0.000 0.000
Y1 -1.000 0.500 1.000
U2#1 0.000 -1.000 0.000
U2#2 0.000 1.000 0.000
U1 1.000 -0.500 -1.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000
X3 0.000 0.000 0.000
PSI
Y1#1 Y1 U2#1 U2#2 U1
________ ________ ________ ________ ________
Y1#1 0.000
Y1 0.000 1.000
U2#1 0.000 0.000 0.000
U2#2 0.000 0.000 0.000 0.000
U1 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000 0.000
PSI
X1 X2 X3
________ ________ ________
X1 1.000
X2 0.000 1.000
X3 0.000 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.11978265D+04 0.0000000 0.0000000 EM
2 -0.11818891D+04 15.9373501 0.0133052 EM
3 -0.11813763D+04 0.5128394 0.0004339 EM
4 -0.11813756D+04 0.0007050 0.0000006 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
U2
U1
X1
X2
X3
Save file
ex3.15.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:33
Ending Time: 22:22:34
Elapsed Time: 00:00:01
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