Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
TITLE: this is an example of BSEM analysis of a MIMIC model
with cross-loadings and direct effects
(same data generation as for ex5.8)
MONTECARLO:
NAMES = y1-y6 x1-x3;
NOBSERVATIONS = 500;
NREPS = 1;
save = ex5.32.dat;
MODEL POPULATION:
[x1@0 x2@1 x3@2]; x1@3 x2@2 x3@1;
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*1;
f1 on x1*.5 x2*.6 x3*.7;
f2 on x1*.7 x2*.6 x3*.5;
f1-f2*.7;
f1 with f2*.25;
y1-y6*.5;
MODEL:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*1;
f1 on x1*.5 x2*.6 x3*.7;
f2 on x1*.7 x2*.6 x3*.5;
f1-f2*.7;
f1 with f2*.25;
y1-y6*.5;
OUTPUT:
TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of BSEM analysis of a MIMIC model
with cross-loadings and direct effects
(same data generation as for ex5.8)
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 6
Number of independent variables 3
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Observed independent variables
X1 X2 X3
Continuous latent variables
F1 F2
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
________ ________ ________ ________ ________
2.066 2.088 2.088 1.663 1.623
Means
Y6 X1 X2 X3
________ ________ ________ ________
1.596 -0.061 1.033 2.090
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 3.227
Y2 2.790 3.388
Y3 2.752 2.847 3.295
Y4 2.385 2.441 2.434 3.595
Y5 2.206 2.305 2.296 2.990 3.290
Y6 2.248 2.344 2.374 2.953 2.905
X1 1.426 1.486 1.500 2.044 1.964
X2 1.367 1.411 1.356 1.380 1.364
X3 0.727 0.722 0.737 0.429 0.404
Covariances
Y6 X1 X2 X3
________ ________ ________ ________
Y6 3.434
X1 1.957 2.921
X2 1.465 0.176 2.082
X3 0.418 -0.151 0.125 1.042
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.844 1.000
Y3 0.844 0.852 1.000
Y4 0.700 0.699 0.707 1.000
Y5 0.677 0.690 0.697 0.869 1.000
Y6 0.675 0.687 0.706 0.841 0.864
X1 0.465 0.472 0.484 0.631 0.634
X2 0.527 0.531 0.518 0.504 0.521
X3 0.396 0.384 0.398 0.222 0.218
Correlations
Y6 X1 X2 X3
________ ________ ________ ________
Y6 1.000
X1 0.618 1.000
X2 0.548 0.071 1.000
X3 0.221 -0.087 0.085 1.000
MODEL FIT INFORMATION
Number of Free Parameters 25
Loglikelihood
H0 Value
Mean -4000.617
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -4000.617 -4000.617
0.980 0.000 -4000.617 -4000.617
0.950 0.000 -4000.617 -4000.617
0.900 0.000 -4000.617 -4000.617
0.800 0.000 -4000.617 -4000.617
0.700 0.000 -4000.617 -4000.617
0.500 0.000 -4000.617 -4000.617
0.300 0.000 -4000.617 -4000.617
0.200 0.000 -4000.617 -4000.617
0.100 0.000 -4000.617 -4000.617
0.050 0.000 -4000.617 -4000.617
0.020 0.000 -4000.617 -4000.617
0.010 0.000 -4000.617 -4000.617
H1 Value
Mean -3990.606
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3990.606 -3990.606
0.980 0.000 -3990.606 -3990.606
0.950 0.000 -3990.606 -3990.606
0.900 0.000 -3990.606 -3990.606
0.800 0.000 -3990.606 -3990.606
0.700 0.000 -3990.606 -3990.606
0.500 0.000 -3990.606 -3990.606
0.300 0.000 -3990.606 -3990.606
0.200 0.000 -3990.606 -3990.606
0.100 0.000 -3990.606 -3990.606
0.050 0.000 -3990.606 -3990.606
0.020 0.000 -3990.606 -3990.606
0.010 0.000 -3990.606 -3990.606
Information Criteria
Akaike (AIC)
Mean 8051.235
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8051.235 8051.235
0.980 0.000 8051.235 8051.235
0.950 0.000 8051.235 8051.235
0.900 0.000 8051.235 8051.235
0.800 0.000 8051.235 8051.235
0.700 0.000 8051.235 8051.235
0.500 0.000 8051.235 8051.235
0.300 0.000 8051.235 8051.235
0.200 0.000 8051.235 8051.235
0.100 0.000 8051.235 8051.235
0.050 0.000 8051.235 8051.235
0.020 0.000 8051.235 8051.235
0.010 0.000 8051.235 8051.235
Bayesian (BIC)
Mean 8156.600
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8156.600 8156.600
0.980 0.000 8156.600 8156.600
0.950 0.000 8156.600 8156.600
0.900 0.000 8156.600 8156.600
0.800 0.000 8156.600 8156.600
0.700 0.000 8156.600 8156.600
0.500 0.000 8156.600 8156.600
0.300 0.000 8156.600 8156.600
0.200 0.000 8156.600 8156.600
0.100 0.000 8156.600 8156.600
0.050 0.000 8156.600 8156.600
0.020 0.000 8156.600 8156.600
0.010 0.000 8156.600 8156.600
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 8077.248
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8077.248 8077.248
0.980 0.000 8077.248 8077.248
0.950 0.000 8077.248 8077.248
0.900 0.000 8077.248 8077.248
0.800 0.000 8077.248 8077.248
0.700 0.000 8077.248 8077.248
0.500 0.000 8077.248 8077.248
0.300 0.000 8077.248 8077.248
0.200 0.000 8077.248 8077.248
0.100 0.000 8077.248 8077.248
0.050 0.000 8077.248 8077.248
0.020 0.000 8077.248 8077.248
0.010 0.000 8077.248 8077.248
Chi-Square Test of Model Fit
Degrees of freedom 20
Mean 20.023
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 8.260 20.023
0.980 1.000 9.237 20.023
0.950 1.000 10.851 20.023
0.900 1.000 12.443 20.023
0.800 1.000 14.578 20.023
0.700 1.000 16.266 20.023
0.500 1.000 19.337 20.023
0.300 0.000 22.775 20.023
0.200 0.000 25.038 20.023
0.100 0.000 28.412 20.023
0.050 0.000 31.410 20.023
0.020 0.000 35.020 20.023
0.010 0.000 37.566 20.023
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.002
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 0.008
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
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0324 0.0000 0.0297 0.0010 1.000 1.000
Y3 1.000 1.0220 0.0000 0.0292 0.0005 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 1.000 0.9730 0.0000 0.0255 0.0007 1.000 1.000
Y6 1.000 0.9765 0.0000 0.0273 0.0006 1.000 1.000
F1 ON
X1 0.500 0.4966 0.0000 0.0262 0.0000 1.000 1.000
X2 0.600 0.5662 0.0000 0.0310 0.0011 1.000 1.000
X3 0.700 0.6905 0.0000 0.0432 0.0001 1.000 1.000
F2 ON
X1 0.700 0.6784 0.0000 0.0262 0.0005 1.000 1.000
X2 0.600 0.6011 0.0000 0.0297 0.0000 1.000 1.000
X3 0.500 0.4323 0.0000 0.0404 0.0046 1.000 1.000
F1 WITH
F2 0.250 0.2282 0.0000 0.0396 0.0005 1.000 1.000
Intercepts
Y1 0.000 0.0684 0.0000 0.1081 0.0047 1.000 0.000
Y2 0.000 0.0250 0.0000 0.1101 0.0006 1.000 0.000
Y3 0.000 0.0457 0.0000 0.1086 0.0021 1.000 0.000
Y4 0.000 0.1795 0.0000 0.1011 0.0322 1.000 0.000
Y5 0.000 0.1803 0.0000 0.0962 0.0325 1.000 0.000
Y6 0.000 0.1474 0.0000 0.0990 0.0217 1.000 0.000
Residual Variances
Y1 0.500 0.5294 0.0000 0.0460 0.0009 1.000 1.000
Y2 0.500 0.5124 0.0000 0.0463 0.0002 1.000 1.000
Y3 0.500 0.4772 0.0000 0.0442 0.0005 1.000 1.000
Y4 0.500 0.5414 0.0000 0.0465 0.0017 1.000 1.000
Y5 0.500 0.3989 0.0000 0.0380 0.0102 0.000 1.000
Y6 0.500 0.5216 0.0000 0.0447 0.0005 1.000 1.000
F1 0.700 0.7202 0.0000 0.0615 0.0004 1.000 1.000
F2 0.700 0.6426 0.0000 0.0560 0.0033 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.364E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 X1 X2 X3
________ ________ ________ ________
6 0 0 0
LAMBDA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 7 0 0 0 0
Y3 8 0 0 0 0
Y4 0 0 0 0 0
Y5 0 9 0 0 0
Y6 0 10 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 11
Y2 0 12
Y3 0 0 13
Y4 0 0 0 14
Y5 0 0 0 0 15
Y6 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
THETA
Y6 X1 X2 X3
________ ________ ________ ________
Y6 16
X1 0 0
X2 0 0 0
X3 0 0 0 0
ALPHA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
0 0 0 0 0
BETA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 0 0 17 18 19
F2 0 0 20 21 22
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
PSI
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 23
F2 24 25
X1 0 0 0
X2 0 0 0 0
X3 0 0 0 0 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 X1 X2 X3
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.035 0.000 0.000 0.000 0.000
Y3 1.021 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
Y5 0.000 0.984 0.000 0.000 0.000
Y6 0.000 0.972 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
X3 0.000 0.000 0.000 0.000 1.000
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
Y6 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
Y6 X1 X2 X3
________ ________ ________ ________
Y6 0.500
X1 0.000 0.000
X2 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000
ALPHA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
0.000 0.000 -0.061 1.033 2.090
BETA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 0.000 0.000 0.500 0.600 0.700
F2 0.000 0.000 0.700 0.600 0.500
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
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 0.700
F2 0.250 0.700
X1 0.000 0.000 2.921
X2 0.000 0.000 0.176 2.082
X3 0.000 0.000 -0.151 0.125 1.042
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 X1 X2 X3
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
Y5 0.000 1.000 0.000 0.000 0.000
Y6 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
X3 0.000 0.000 0.000 0.000 1.000
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
Y6 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
Y6 X1 X2 X3
________ ________ ________ ________
Y6 0.500
X1 0.000 0.000
X2 0.000 0.000 0.000
X3 0.000 0.000 0.000 0.000
ALPHA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
0.000 0.000 0.000 1.000 2.000
BETA
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 0.000 0.000 0.500 0.600 0.700
F2 0.000 0.000 0.700 0.600 0.500
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
F1 F2 X1 X2 X3
________ ________ ________ ________ ________
F1 0.700
F2 0.250 0.700
X1 0.000 0.000 3.000
X2 0.000 0.000 0.000 2.000
X3 0.000 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
X1
X2
X3
Save file
ex5.32.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:11
Ending Time: 22:23:12
Elapsed Time: 00:00:01
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