Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a SEM with
continuous factor indicators and an
interaction between two latent variables
montecarlo:
names = y1-y12;
nobs = 500;
nreps = 1;
save = ex5.13.dat;
analysis:
type = random;
algorithm = integration;
model montecarlo:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
f3 by y7@1 y8-y9*.9;
f4 by y10@1 y11-y12*.7;
y1-y12*1;
f1-f2*1;
f3-f4*.5;
f3 on f1*.5 f2*.7;
f4 on f3*.6;
f1xf2 | f1 XWITH f2;
f3 ON f1xf2*.3;
model:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
f3 by y7@1 y8-y9*.9;
f4 by y10@1 y11-y12*.7;
y1-y12*1;
f1-f2*1;
f3-f4*.5;
f3 on f1*.5 f2*.7;
f4 on f3*.6;
f1xf2 | f1 XWITH f2;
f3 ON f1xf2*.3;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a SEM with
continuous factor indicators and an
interaction between two latent variables
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 12
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
Continuous latent variables
F1 F2 F3 F4 F1XF2
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 2
Adaptive quadrature ON
Cholesky OFF
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.011 -0.010 -0.022 -0.118 -0.083
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
-0.104 -0.060 -0.077 -0.100 0.042
Means
Y11 Y12
________ ________
-0.014 -0.006
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.157
Y2 1.141 2.189
Y3 1.182 1.225 2.170
Y4 0.015 0.083 0.041 1.983
Y5 0.016 0.053 0.006 0.873 1.592
Y6 0.135 0.038 0.081 0.718 0.614
Y7 0.587 0.602 0.607 0.803 0.676
Y8 0.548 0.598 0.627 0.639 0.551
Y9 0.527 0.426 0.463 0.738 0.654
Y10 0.362 0.331 0.326 0.432 0.256
Y11 0.216 0.200 0.228 0.380 0.298
Y12 0.231 0.133 0.232 0.325 0.228
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.617
Y7 0.700 2.658
Y8 0.556 1.428 2.226
Y9 0.659 1.426 1.283 2.294
Y10 0.321 0.872 0.890 0.873 2.200
Y11 0.278 0.631 0.602 0.481 0.862
Y12 0.249 0.482 0.449 0.447 0.704
Covariances
Y11 Y12
________ ________
Y11 1.596
Y12 0.469 1.429
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.525 1.000
Y3 0.547 0.562 1.000
Y4 0.007 0.040 0.020 1.000
Y5 0.009 0.028 0.003 0.491 1.000
Y6 0.072 0.020 0.043 0.401 0.383
Y7 0.245 0.250 0.253 0.350 0.329
Y8 0.250 0.271 0.285 0.304 0.293
Y9 0.237 0.190 0.207 0.346 0.342
Y10 0.166 0.151 0.149 0.207 0.137
Y11 0.117 0.107 0.123 0.213 0.187
Y12 0.131 0.075 0.132 0.193 0.151
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.338 1.000
Y8 0.293 0.587 1.000
Y9 0.342 0.577 0.568 1.000
Y10 0.170 0.361 0.402 0.388 1.000
Y11 0.173 0.306 0.319 0.251 0.460
Y12 0.164 0.248 0.252 0.247 0.397
Correlations
Y11 Y12
________ ________
Y11 1.000
Y12 0.310 1.000
MODEL FIT INFORMATION
Number of Free Parameters 41
Loglikelihood
H0 Value
Mean -9672.069
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -9672.069 -9672.069
0.980 0.000 -9672.069 -9672.069
0.950 0.000 -9672.069 -9672.069
0.900 0.000 -9672.069 -9672.069
0.800 0.000 -9672.069 -9672.069
0.700 0.000 -9672.069 -9672.069
0.500 0.000 -9672.069 -9672.069
0.300 0.000 -9672.069 -9672.069
0.200 0.000 -9672.069 -9672.069
0.100 0.000 -9672.069 -9672.069
0.050 0.000 -9672.069 -9672.069
0.020 0.000 -9672.069 -9672.069
0.010 0.000 -9672.069 -9672.069
Information Criteria
Akaike (AIC)
Mean 19426.138
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19426.138 19426.138
0.980 0.000 19426.138 19426.138
0.950 0.000 19426.138 19426.138
0.900 0.000 19426.138 19426.138
0.800 0.000 19426.138 19426.138
0.700 0.000 19426.138 19426.138
0.500 0.000 19426.138 19426.138
0.300 0.000 19426.138 19426.138
0.200 0.000 19426.138 19426.138
0.100 0.000 19426.138 19426.138
0.050 0.000 19426.138 19426.138
0.020 0.000 19426.138 19426.138
0.010 0.000 19426.138 19426.138
Bayesian (BIC)
Mean 19598.936
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19598.936 19598.936
0.980 0.000 19598.936 19598.936
0.950 0.000 19598.936 19598.936
0.900 0.000 19598.936 19598.936
0.800 0.000 19598.936 19598.936
0.700 0.000 19598.936 19598.936
0.500 0.000 19598.936 19598.936
0.300 0.000 19598.936 19598.936
0.200 0.000 19598.936 19598.936
0.100 0.000 19598.936 19598.936
0.050 0.000 19598.936 19598.936
0.020 0.000 19598.936 19598.936
0.010 0.000 19598.936 19598.936
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 19468.800
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 19468.800 19468.800
0.980 0.000 19468.800 19468.800
0.950 0.000 19468.800 19468.800
0.900 0.000 19468.800 19468.800
0.800 0.000 19468.800 19468.800
0.700 0.000 19468.800 19468.800
0.500 0.000 19468.800 19468.800
0.300 0.000 19468.800 19468.800
0.200 0.000 19468.800 19468.800
0.100 0.000 19468.800 19468.800
0.050 0.000 19468.800 19468.800
0.020 0.000 19468.800 19468.800
0.010 0.000 19468.800 19468.800
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 1.0291 0.0000 0.0751 0.0008 1.000 1.000
Y3 1.000 1.0686 0.0000 0.0807 0.0047 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.800 0.8500 0.0000 0.0717 0.0025 1.000 1.000
Y6 0.800 0.7566 0.0000 0.0794 0.0019 1.000 1.000
F3 BY
Y7 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y8 0.900 0.9102 0.0000 0.0494 0.0001 1.000 1.000
Y9 0.900 0.9181 0.0000 0.0580 0.0003 1.000 1.000
F4 BY
Y10 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y11 0.700 0.6709 0.0000 0.0698 0.0008 1.000 1.000
Y12 0.700 0.5421 0.0000 0.0586 0.0249 0.000 1.000
F3 ON
F1 0.500 0.4382 0.0000 0.0655 0.0038 1.000 1.000
F2 0.700 0.8067 0.0000 0.0838 0.0114 1.000 1.000
F1XF2 0.300 0.3926 0.0000 0.0613 0.0086 1.000 1.000
F4 ON
F3 0.600 0.5853 0.0000 0.0501 0.0002 1.000 1.000
F2 WITH
F1 0.000 0.0545 0.0000 0.0697 0.0030 1.000 0.000
Intercepts
Y1 0.000 -0.0106 0.0000 0.0657 0.0001 1.000 0.000
Y2 0.000 -0.0102 0.0000 0.0662 0.0001 1.000 0.000
Y3 0.000 -0.0213 0.0000 0.0659 0.0005 1.000 0.000
Y4 0.000 -0.1175 0.0000 0.0630 0.0138 1.000 0.000
Y5 0.000 -0.0828 0.0000 0.0564 0.0069 1.000 0.000
Y6 0.000 -0.1039 0.0000 0.0569 0.0108 1.000 0.000
Y7 0.000 -0.0812 0.0000 0.0727 0.0066 1.000 0.000
Y8 0.000 -0.0956 0.0000 0.0661 0.0091 1.000 0.000
Y9 0.000 -0.1186 0.0000 0.0664 0.0141 1.000 0.000
Y10 0.000 0.0299 0.0000 0.0660 0.0009 1.000 0.000
Y11 0.000 -0.0221 0.0000 0.0562 0.0005 1.000 0.000
Y12 0.000 -0.0123 0.0000 0.0542 0.0002 1.000 0.000
Variances
F1 1.000 1.1159 0.0000 0.1381 0.0134 1.000 1.000
F2 1.000 0.9827 0.0000 0.1332 0.0003 1.000 1.000
Residual Variances
Y1 1.000 1.0425 0.0000 0.0930 0.0018 1.000 1.000
Y2 1.000 1.0073 0.0000 0.0925 0.0001 1.000 1.000
Y3 1.000 0.8954 0.0000 0.0912 0.0109 1.000 1.000
Y4 1.000 1.0055 0.0000 0.0952 0.0000 1.000 1.000
Y5 1.000 0.8823 0.0000 0.0779 0.0139 1.000 1.000
Y6 1.000 1.0541 0.0000 0.0800 0.0029 1.000 1.000
Y7 1.000 1.1006 0.0000 0.0978 0.0101 1.000 1.000
Y8 1.000 0.9361 0.0000 0.0805 0.0041 1.000 1.000
Y9 1.000 0.9818 0.0000 0.0795 0.0003 1.000 1.000
Y10 1.000 0.9104 0.0000 0.1207 0.0080 1.000 1.000
Y11 1.000 1.0153 0.0000 0.0816 0.0002 1.000 1.000
Y12 1.000 1.0495 0.0000 0.0717 0.0025 1.000 1.000
F3 0.500 0.4730 0.0000 0.0891 0.0007 1.000 1.000
F4 0.500 0.7563 0.0000 0.1190 0.0657 0.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.302E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
NU
Y11 Y12
________ ________
11 12
LAMBDA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 13 0 0 0 0
Y3 14 0 0 0 0
Y4 0 0 0 0 0
Y5 0 15 0 0 0
Y6 0 16 0 0 0
Y7 0 0 0 0 0
Y8 0 0 17 0 0
Y9 0 0 18 0 0
Y10 0 0 0 0 0
Y11 0 0 0 19 0
Y12 0 0 0 20 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 21
Y2 0 22
Y3 0 0 23
Y4 0 0 0 24
Y5 0 0 0 0 25
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 26
Y7 0 27
Y8 0 0 28
Y9 0 0 0 29
Y10 0 0 0 0 30
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y11 Y12
________ ________
Y11 31
Y12 0 32
ALPHA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
0 0 0 0 0
BETA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0 0 0 0 0
F2 0 0 0 0 0
F3 33 34 0 0 35
F4 0 0 36 0 0
F1XF2 0 0 0 0 0
PSI
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 37
F2 38 39
F3 0 0 40
F4 0 0 0 41
F1XF2 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 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y11 Y12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
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 0.800 0.000 0.000 0.000
Y6 0.000 0.800 0.000 0.000 0.000
Y7 0.000 0.000 1.000 0.000 0.000
Y8 0.000 0.000 0.900 0.000 0.000
Y9 0.000 0.000 0.900 0.000 0.000
Y10 0.000 0.000 0.000 1.000 0.000
Y11 0.000 0.000 0.000 0.700 0.000
Y12 0.000 0.000 0.000 0.700 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.000 1.000
Y8 0.000 0.000 1.000
Y9 0.000 0.000 0.000 1.000
Y10 0.000 0.000 0.000 0.000 1.000
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y11 Y12
________ ________
Y11 1.000
Y12 0.000 1.000
ALPHA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000 0.000
F3 0.500 0.700 0.000 0.000 0.300
F4 0.000 0.000 0.600 0.000 0.000
F1XF2 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 0.500
F4 0.000 0.000 0.000 0.500
F1XF2 0.000 0.000 0.000 0.000 0.000
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y11 Y12
________ ________
0.000 0.000
LAMBDA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
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 0.800 0.000 0.000 0.000
Y6 0.000 0.800 0.000 0.000 0.000
Y7 0.000 0.000 1.000 0.000 0.000
Y8 0.000 0.000 0.900 0.000 0.000
Y9 0.000 0.000 0.900 0.000 0.000
Y10 0.000 0.000 0.000 1.000 0.000
Y11 0.000 0.000 0.000 0.700 0.000
Y12 0.000 0.000 0.000 0.700 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.000 1.000
Y8 0.000 0.000 1.000
Y9 0.000 0.000 0.000 1.000
Y10 0.000 0.000 0.000 0.000 1.000
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y11 Y12
________ ________
Y11 1.000
Y12 0.000 1.000
ALPHA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000 0.000
F3 0.500 0.700 0.000 0.000 0.300
F4 0.000 0.000 0.600 0.000 0.000
F1XF2 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
F3 0.000 0.000 0.500
F4 0.000 0.000 0.000 0.500
F1XF2 0.000 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 -0.96915969D+04 0.0000000 0.0000000 EM
2 -0.96751287D+04 16.4682579 0.0016992 EM
3 -0.96735722D+04 1.5564594 0.0001609 EM
4 -0.96729244D+04 0.6478272 0.0000670 EM
5 -0.96725977D+04 0.3266746 0.0000338 EM
6 -0.96724117D+04 0.1860205 0.0000192 EM
7 -0.96722979D+04 0.1137677 0.0000118 EM
8 -0.96722253D+04 0.0725651 0.0000075 EM
9 -0.96721777D+04 0.0476027 0.0000049 EM
10 -0.96721458D+04 0.0319313 0.0000033 EM
11 -0.96721240D+04 0.0218515 0.0000023 EM
12 -0.96721087D+04 0.0152395 0.0000016 EM
13 -0.96720979D+04 0.0108242 0.0000011 EM
14 -0.96720901D+04 0.0078236 0.0000008 EM
15 -0.96720843D+04 0.0057484 0.0000006 EM
16 -0.96720800D+04 0.0042884 0.0000004 EM
17 -0.96720768D+04 0.0032433 0.0000003 EM
18 -0.96720743D+04 0.0024835 0.0000003 EM
19 -0.96720724D+04 0.0019222 0.0000002 EM
20 -0.96720709D+04 0.0015018 0.0000002 EM
21 -0.96720697D+04 0.0011828 0.0000001 EM
22 -0.96720688D+04 0.0009378 0.0000001 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Y11
Y12
Save file
ex5.13.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:58
Ending Time: 22:23:01
Elapsed Time: 00:00:03
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