Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a Monte Carlo
simulation study for a non-linear CFA
MONTECARLO:
NAMES = y1-y5;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
save = ex5.7.dat;
ANALYSIS:
TYPE = RANDOM;
algorithm = integration;
MODEL MONTECARLO:
f BY y1@1 y2-y5*1;
f*1;
fxf | f XWITH f;
y1-y5 ON fxf*-.25;
y1-y5*1;
MODEL:
f BY y1@1 y2-y5*1;
f*1;
fxf | f XWITH f;
y1-y5 ON fxf*-.25;
y1-y5*1;
OUTPUT:
TECH8 TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a Monte Carlo
simulation study for a non-linear CFA
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 5
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5
Continuous latent variables
F FXF
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 1
Adaptive quadrature ON
Cholesky OFF
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.344 -0.302 -0.342 -0.398 -0.367
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.221
Y2 1.329 2.291
Y3 1.337 1.367 2.401
Y4 1.217 1.245 1.272 2.324
Y5 1.291 1.366 1.444 1.315 2.412
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.589 1.000
Y3 0.579 0.583 1.000
Y4 0.536 0.539 0.538 1.000
Y5 0.558 0.581 0.600 0.555 1.000
MODEL FIT INFORMATION
Number of Free Parameters 20
Loglikelihood
H0 Value
Mean -4027.499
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -4027.499 -4027.499
0.980 0.000 -4027.499 -4027.499
0.950 0.000 -4027.499 -4027.499
0.900 0.000 -4027.499 -4027.499
0.800 0.000 -4027.499 -4027.499
0.700 0.000 -4027.499 -4027.499
0.500 0.000 -4027.499 -4027.499
0.300 0.000 -4027.499 -4027.499
0.200 0.000 -4027.499 -4027.499
0.100 0.000 -4027.499 -4027.499
0.050 0.000 -4027.499 -4027.499
0.020 0.000 -4027.499 -4027.499
0.010 0.000 -4027.499 -4027.499
Information Criteria
Akaike (AIC)
Mean 8094.999
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8094.999 8094.999
0.980 0.000 8094.999 8094.999
0.950 0.000 8094.999 8094.999
0.900 0.000 8094.999 8094.999
0.800 0.000 8094.999 8094.999
0.700 0.000 8094.999 8094.999
0.500 0.000 8094.999 8094.999
0.300 0.000 8094.999 8094.999
0.200 0.000 8094.999 8094.999
0.100 0.000 8094.999 8094.999
0.050 0.000 8094.999 8094.999
0.020 0.000 8094.999 8094.999
0.010 0.000 8094.999 8094.999
Bayesian (BIC)
Mean 8179.291
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8179.291 8179.291
0.980 0.000 8179.291 8179.291
0.950 0.000 8179.291 8179.291
0.900 0.000 8179.291 8179.291
0.800 0.000 8179.291 8179.291
0.700 0.000 8179.291 8179.291
0.500 0.000 8179.291 8179.291
0.300 0.000 8179.291 8179.291
0.200 0.000 8179.291 8179.291
0.100 0.000 8179.291 8179.291
0.050 0.000 8179.291 8179.291
0.020 0.000 8179.291 8179.291
0.010 0.000 8179.291 8179.291
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 8115.810
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8115.810 8115.810
0.980 0.000 8115.810 8115.810
0.950 0.000 8115.810 8115.810
0.900 0.000 8115.810 8115.810
0.800 0.000 8115.810 8115.810
0.700 0.000 8115.810 8115.810
0.500 0.000 8115.810 8115.810
0.300 0.000 8115.810 8115.810
0.200 0.000 8115.810 8115.810
0.100 0.000 8115.810 8115.810
0.050 0.000 8115.810 8115.810
0.020 0.000 8115.810 8115.810
0.010 0.000 8115.810 8115.810
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0397 0.0000 0.0664 0.0016 1.000 1.000
Y3 1.000 1.1054 0.0000 0.0878 0.0111 1.000 1.000
Y4 1.000 0.9760 0.0000 0.0664 0.0006 1.000 1.000
Y5 1.000 1.0812 0.0000 0.0772 0.0066 1.000 1.000
Y1 ON
FXF -0.250 -0.2438 0.0000 0.0696 0.0000 1.000 1.000
Y2 ON
FXF -0.250 -0.2438 0.0000 0.0575 0.0000 1.000 1.000
Y3 ON
FXF -0.250 -0.1828 0.0000 0.0407 0.0045 1.000 1.000
Y4 ON
FXF -0.250 -0.1970 0.0000 0.0574 0.0028 1.000 1.000
Y5 ON
FXF -0.250 -0.2051 0.0000 0.0504 0.0020 1.000 1.000
Intercepts
Y1 0.000 -0.0629 0.0000 0.0925 0.0040 1.000 0.000
Y2 0.000 -0.0210 0.0000 0.0905 0.0004 1.000 0.000
Y3 0.000 -0.1307 0.0000 0.0858 0.0171 1.000 0.000
Y4 0.000 -0.1704 0.0000 0.0881 0.0290 1.000 0.000
Y5 0.000 -0.1300 0.0000 0.0897 0.0169 1.000 0.000
Variances
F 1.000 1.1427 0.0000 0.1417 0.0203 1.000 1.000
Residual Variances
Y1 1.000 0.9709 0.0000 0.0789 0.0008 1.000 1.000
Y2 1.000 0.9444 0.0000 0.0792 0.0031 1.000 1.000
Y3 1.000 0.9489 0.0000 0.0949 0.0026 1.000 1.000
Y4 1.000 1.1654 0.0000 0.0869 0.0274 1.000 1.000
Y5 1.000 1.0025 0.0000 0.0728 0.0000 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.140E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
Y5 0 0 0 0 0
LAMBDA
Y4 Y5
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
Y5 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
Y5 0 0 0 0 0
ALPHA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
0 0 1 2 3
ALPHA
Y4 Y5
________ ________
4 5
BETA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 0 0 0 0 0
FXF 0 0 0 0 0
Y1 0 6 0 0 0
Y2 7 8 0 0 0
Y3 9 10 0 0 0
Y4 11 12 0 0 0
Y5 13 14 0 0 0
BETA
Y4 Y5
________ ________
F 0 0
FXF 0 0
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
Y5 0 0
PSI
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 15
FXF 0 0
Y1 0 0 16
Y2 0 0 0 17
Y3 0 0 0 0 18
Y4 0 0 0 0 0
Y5 0 0 0 0 0
PSI
Y4 Y5
________ ________
Y4 19
Y5 0 20
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 1.000 0.000
Y3 0.000 0.000 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y4 Y5
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 1.000 0.000
Y5 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y4 Y5
________ ________
0.000 0.000
BETA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 0.000 0.000 0.000 0.000 0.000
FXF 0.000 0.000 0.000 0.000 0.000
Y1 1.000 -0.250 0.000 0.000 0.000
Y2 1.000 -0.250 0.000 0.000 0.000
Y3 1.000 -0.250 0.000 0.000 0.000
Y4 1.000 -0.250 0.000 0.000 0.000
Y5 1.000 -0.250 0.000 0.000 0.000
BETA
Y4 Y5
________ ________
F 0.000 0.000
FXF 0.000 0.000
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
Y5 0.000 0.000
PSI
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 1.000
FXF 0.000 0.000
Y1 0.000 0.000 1.000
Y2 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
PSI
Y4 Y5
________ ________
Y4 1.000
Y5 0.000 1.000
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 1.000 0.000
Y3 0.000 0.000 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y4 Y5
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 1.000 0.000
Y5 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y4 Y5
________ ________
0.000 0.000
BETA
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 0.000 0.000 0.000 0.000 0.000
FXF 0.000 0.000 0.000 0.000 0.000
Y1 1.000 -0.250 0.000 0.000 0.000
Y2 1.000 -0.250 0.000 0.000 0.000
Y3 1.000 -0.250 0.000 0.000 0.000
Y4 1.000 -0.250 0.000 0.000 0.000
Y5 1.000 -0.250 0.000 0.000 0.000
BETA
Y4 Y5
________ ________
F 0.000 0.000
FXF 0.000 0.000
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
Y5 0.000 0.000
PSI
F FXF Y1 Y2 Y3
________ ________ ________ ________ ________
F 1.000
FXF 0.000 0.000
Y1 0.000 0.000 1.000
Y2 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 1.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
PSI
Y4 Y5
________ ________
Y4 1.000
Y5 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.40411678D+04 0.0000000 0.0000000 EM
2 -0.40297013D+04 11.4665063 0.0028374 EM
3 -0.40286035D+04 1.0977814 0.0002724 EM
4 -0.40282034D+04 0.4000590 0.0000993 EM
5 -0.40279777D+04 0.2257431 0.0000560 EM
6 -0.40278336D+04 0.1440498 0.0000358 EM
7 -0.40277376D+04 0.0960118 0.0000238 EM
8 -0.40276719D+04 0.0657393 0.0000163 EM
9 -0.40276259D+04 0.0459766 0.0000114 EM
10 -0.40275932D+04 0.0327251 0.0000081 EM
11 -0.40275695D+04 0.0236427 0.0000059 EM
12 -0.40275522D+04 0.0173052 0.0000043 EM
13 -0.40275394D+04 0.0128173 0.0000032 EM
14 -0.40275298D+04 0.0095994 0.0000024 EM
15 -0.40275226D+04 0.0072668 0.0000018 EM
16 -0.40275170D+04 0.0055592 0.0000014 EM
17 -0.40275127D+04 0.0042973 0.0000011 EM
18 -0.40275093D+04 0.0033560 0.0000008 EM
19 -0.40275067D+04 0.0026472 0.0000007 EM
20 -0.40275046D+04 0.0021086 0.0000005 EM
21 -0.40275029D+04 0.0016952 0.0000004 EM
22 -0.40275015D+04 0.0013748 0.0000003 EM
23 -0.40275004D+04 0.0011240 0.0000003 EM
24 -0.40274995D+04 0.0009257 0.0000002 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Save file
ex5.7.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:11
Ending Time: 22:24:13
Elapsed Time: 00:00:02
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