Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
TITLE:
this is an example of generating data for a bi-factor
BESEM, with two items loading only on the general factor
(same data generation as ex5.30)
MONTECARLO:
NAMES = y1-y10;
NOBSERVATIONS = 500;
NREPS = 1;
SAVE = ex5.31.dat;
MODEL POPULATION:
fg BY y1-y10*0.7;
f1 BY y1-y4*0.4;
f2 BY y5-y8*0.3;
fg-f2@1;
fg WITH f1-f2@0;
f1 WITH f2*0;
y1-y4*0.35 y5-y8*0.42 y9-y10*0.51;
ANALYSIS:
ROTATION = GEOMIN;
MODEL:
fg BY y1-y10*0.7;
fg@1;
f1 BY y1-y4*0.4 y5-y8*0 (*1);
f2 BY y1-y4*0 y5-y8*0.3 (*1);
fg WITH f1-f2@0;
y1-y4*0.35 y5-y8*0.42 y9-y10*0.51;
*** WARNING in MODEL command
Values given in the MODEL command for EFA factors are used only as
population values in computing coverage. EFA factors cannot be given
starting values.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of generating data for a bi-factor
BESEM, with two items loading only on the general factor
(same data generation as ex5.30)
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 10
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10
Continuous latent variables
FG
EFA factors
*1: F1 F2
Estimator ML
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Optimization Specifications for the Exploratory Factor Analysis
Rotation Algorithm
Number of random starts 30
Maximum number of iterations 10000
Derivative convergence criterion 0.100D-04
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.073 0.049 0.012 -0.042 0.021
Means
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
-0.025 0.022 0.059 -0.018 -0.003
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.990
Y2 0.697 1.033
Y3 0.654 0.683 0.967
Y4 0.669 0.699 0.688 1.059
Y5 0.506 0.589 0.551 0.571 1.047
Y6 0.492 0.493 0.504 0.514 0.633
Y7 0.524 0.554 0.497 0.554 0.596
Y8 0.520 0.523 0.542 0.555 0.679
Y9 0.456 0.513 0.531 0.507 0.524
Y10 0.447 0.443 0.473 0.468 0.442
Covariances
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.976
Y7 0.591 1.028
Y8 0.594 0.623 1.142
Y9 0.495 0.467 0.514 0.989
Y10 0.443 0.397 0.417 0.449 0.959
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.689 1.000
Y3 0.669 0.683 1.000
Y4 0.653 0.669 0.680 1.000
Y5 0.497 0.566 0.547 0.543 1.000
Y6 0.500 0.491 0.519 0.505 0.626
Y7 0.519 0.537 0.498 0.531 0.575
Y8 0.489 0.482 0.516 0.505 0.620
Y9 0.461 0.508 0.543 0.495 0.515
Y10 0.459 0.445 0.492 0.464 0.441
Correlations
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.000
Y7 0.590 1.000
Y8 0.563 0.575 1.000
Y9 0.504 0.463 0.483 1.000
Y10 0.458 0.400 0.398 0.461 1.000
MODEL FIT INFORMATION
Number of Free Parameters 45
Loglikelihood
H0 Value
Mean -5741.460
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -5741.460 -5741.460
0.980 0.000 -5741.460 -5741.460
0.950 0.000 -5741.460 -5741.460
0.900 0.000 -5741.460 -5741.460
0.800 0.000 -5741.460 -5741.460
0.700 0.000 -5741.460 -5741.460
0.500 0.000 -5741.460 -5741.460
0.300 0.000 -5741.460 -5741.460
0.200 0.000 -5741.460 -5741.460
0.100 0.000 -5741.460 -5741.460
0.050 0.000 -5741.460 -5741.460
0.020 0.000 -5741.460 -5741.460
0.010 0.000 -5741.460 -5741.460
H1 Value
Mean -5729.692
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -5729.692 -5729.692
0.980 0.000 -5729.692 -5729.692
0.950 0.000 -5729.692 -5729.692
0.900 0.000 -5729.692 -5729.692
0.800 0.000 -5729.692 -5729.692
0.700 0.000 -5729.692 -5729.692
0.500 0.000 -5729.692 -5729.692
0.300 0.000 -5729.692 -5729.692
0.200 0.000 -5729.692 -5729.692
0.100 0.000 -5729.692 -5729.692
0.050 0.000 -5729.692 -5729.692
0.020 0.000 -5729.692 -5729.692
0.010 0.000 -5729.692 -5729.692
Information Criteria
Akaike (AIC)
Mean 11572.920
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 11572.920 11572.920
0.980 0.000 11572.920 11572.920
0.950 0.000 11572.920 11572.920
0.900 0.000 11572.920 11572.920
0.800 0.000 11572.920 11572.920
0.700 0.000 11572.920 11572.920
0.500 0.000 11572.920 11572.920
0.300 0.000 11572.920 11572.920
0.200 0.000 11572.920 11572.920
0.100 0.000 11572.920 11572.920
0.050 0.000 11572.920 11572.920
0.020 0.000 11572.920 11572.920
0.010 0.000 11572.920 11572.920
Bayesian (BIC)
Mean 11762.577
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 11762.577 11762.577
0.980 0.000 11762.577 11762.577
0.950 0.000 11762.577 11762.577
0.900 0.000 11762.577 11762.577
0.800 0.000 11762.577 11762.577
0.700 0.000 11762.577 11762.577
0.500 0.000 11762.577 11762.577
0.300 0.000 11762.577 11762.577
0.200 0.000 11762.577 11762.577
0.100 0.000 11762.577 11762.577
0.050 0.000 11762.577 11762.577
0.020 0.000 11762.577 11762.577
0.010 0.000 11762.577 11762.577
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 11619.745
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 11619.745 11619.745
0.980 0.000 11619.745 11619.745
0.950 0.000 11619.745 11619.745
0.900 0.000 11619.745 11619.745
0.800 0.000 11619.745 11619.745
0.700 0.000 11619.745 11619.745
0.500 0.000 11619.745 11619.745
0.300 0.000 11619.745 11619.745
0.200 0.000 11619.745 11619.745
0.100 0.000 11619.745 11619.745
0.050 0.000 11619.745 11619.745
0.020 0.000 11619.745 11619.745
0.010 0.000 11619.745 11619.745
Chi-Square Test of Model Fit
Degrees of freedom 20
Mean 23.536
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 8.260 23.536
0.980 1.000 9.237 23.536
0.950 1.000 10.851 23.536
0.900 1.000 12.443 23.536
0.800 1.000 14.578 23.536
0.700 1.000 16.266 23.536
0.500 1.000 19.337 23.536
0.300 1.000 22.775 23.536
0.200 0.000 25.038 23.536
0.100 0.000 28.412 23.536
0.050 0.000 31.410 23.536
0.020 0.000 35.020 23.536
0.010 0.000 37.566 23.536
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.019
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 0.000
CFI/TLI
CFI
Mean 0.999
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 0.997
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 0.011
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 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
FG BY
Y1 0.700 0.6750 0.0000 0.0509 0.0006 1.000 1.000
Y2 0.700 0.7180 0.0000 0.0517 0.0003 1.000 1.000
Y3 0.700 0.7645 0.0000 0.0480 0.0042 1.000 1.000
Y4 0.700 0.7380 0.0000 0.0510 0.0014 1.000 1.000
Y5 0.700 0.7450 0.0000 0.0532 0.0020 1.000 1.000
Y6 0.700 0.7006 0.0000 0.0473 0.0000 1.000 1.000
Y7 0.700 0.6437 0.0000 0.0521 0.0032 1.000 1.000
Y8 0.700 0.7156 0.0000 0.0563 0.0002 1.000 1.000
Y9 0.700 0.7041 0.0000 0.0456 0.0000 1.000 1.000
Y10 0.700 0.6204 0.0000 0.0450 0.0063 1.000 1.000
F1 BY
Y1 0.400 0.4571 0.0000 0.0645 0.0033 1.000 1.000
Y2 0.400 0.4542 0.0000 0.0670 0.0029 1.000 1.000
Y3 0.400 0.3217 0.0000 0.0877 0.0061 1.000 1.000
Y4 0.400 0.3818 0.0000 0.0703 0.0003 1.000 1.000
Y5 0.000 -0.0013 0.0000 0.0307 0.0000 1.000 0.000
Y6 0.000 -0.0495 0.0000 0.0617 0.0025 1.000 0.000
Y7 0.000 0.1223 0.0000 0.0744 0.0149 1.000 0.000
Y8 0.000 0.0024 0.0000 0.0386 0.0000 1.000 0.000
F2 BY
Y1 0.000 0.0014 0.0000 0.0321 0.0000 1.000 0.000
Y2 0.000 0.0047 0.0000 0.0395 0.0000 1.000 0.000
Y3 0.000 -0.1086 0.0000 0.0620 0.0118 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0397 0.0000 1.000 0.000
Y5 0.300 0.3336 0.0000 0.0888 0.0011 1.000 1.000
Y6 0.300 0.3238 0.0000 0.0736 0.0006 1.000 1.000
Y7 0.300 0.4001 0.0000 0.0645 0.0100 1.000 1.000
Y8 0.300 0.3695 0.0000 0.0888 0.0048 1.000 1.000
FG WITH
F1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 WITH
F1 0.000 0.1704 0.0000 0.2437 0.0291 1.000 0.000
Intercepts
Y1 0.000 -0.0730 0.0000 0.0445 0.0053 1.000 0.000
Y2 0.000 0.0487 0.0000 0.0455 0.0024 1.000 0.000
Y3 0.000 0.0116 0.0000 0.0440 0.0001 1.000 0.000
Y4 0.000 -0.0423 0.0000 0.0460 0.0018 1.000 0.000
Y5 0.000 0.0211 0.0000 0.0458 0.0004 1.000 0.000
Y6 0.000 -0.0253 0.0000 0.0442 0.0006 1.000 0.000
Y7 0.000 0.0222 0.0000 0.0454 0.0005 1.000 0.000
Y8 0.000 0.0587 0.0000 0.0478 0.0034 1.000 0.000
Y9 0.000 -0.0178 0.0000 0.0445 0.0003 1.000 0.000
Y10 0.000 -0.0026 0.0000 0.0438 0.0000 1.000 0.000
Variances
FG 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
F2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.350 0.3254 0.0000 0.0325 0.0006 1.000 1.000
Y2 0.350 0.3107 0.0000 0.0311 0.0015 1.000 1.000
Y3 0.350 0.2791 0.0000 0.0312 0.0050 0.000 1.000
Y4 0.350 0.3685 0.0000 0.0292 0.0003 1.000 1.000
Y5 0.420 0.3810 0.0000 0.0337 0.0015 1.000 1.000
Y6 0.420 0.3832 0.0000 0.0341 0.0014 1.000 1.000
Y7 0.420 0.4223 0.0000 0.0482 0.0000 1.000 1.000
Y8 0.420 0.4932 0.0000 0.0413 0.0054 1.000 1.000
Y9 0.510 0.4933 0.0000 0.0465 0.0003 1.000 1.000
Y10 0.510 0.5737 0.0000 0.0455 0.0041 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.886E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
FG F1 F2
________ ________ ________
Y1 11 12 0
Y2 13 14 15
Y3 16 17 18
Y4 19 20 21
Y5 22 23 24
Y6 25 26 27
Y7 28 29 30
Y8 31 32 33
Y9 34 0 0
Y10 35 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 36
Y2 0 37
Y3 0 0 38
Y4 0 0 0 39
Y5 0 0 0 0 40
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
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 41
Y7 0 42
Y8 0 0 43
Y9 0 0 0 44
Y10 0 0 0 0 45
ALPHA
FG F1 F2
________ ________ ________
0 0 0
BETA
FG F1 F2
________ ________ ________
FG 0 0 0
F1 0 0 0
F2 0 0 0
PSI
FG F1 F2
________ ________ ________
FG 0
F1 0 0
F2 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
LAMBDA
FG F1 F2
________ ________ ________
Y1 0.700 0.812 0.000
Y2 0.700 0.848 0.019
Y3 0.700 0.810 0.038
Y4 0.700 0.831 0.059
Y5 0.700 0.654 0.499
Y6 0.700 0.590 0.482
Y7 0.700 0.630 0.419
Y8 0.700 0.630 0.509
Y9 0.700 0.000 0.000
Y10 0.700 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.331
Y2 0.000 0.313
Y3 0.000 0.000 0.310
Y4 0.000 0.000 0.000 0.365
Y5 0.000 0.000 0.000 0.000 0.371
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
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.395
Y7 0.000 0.456
Y8 0.000 0.000 0.485
Y9 0.000 0.000 0.000 0.510
Y10 0.000 0.000 0.000 0.000 0.510
ALPHA
FG F1 F2
________ ________ ________
0.000 0.000 0.000
BETA
FG F1 F2
________ ________ ________
FG 0.000 0.000 0.000
F1 0.000 0.000 0.000
F2 0.000 0.000 0.000
PSI
FG F1 F2
________ ________ ________
FG 1.000
F1 0.000 1.000
F2 0.000 0.000 1.000
TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
FG F1 F2
________ ________ ________
Y1 11 12 13
Y2 14 15 16
Y3 17 18 19
Y4 20 21 22
Y5 23 24 25
Y6 26 27 28
Y7 29 30 31
Y8 32 33 34
Y9 35 0 0
Y10 36 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 37
Y2 0 38
Y3 0 0 39
Y4 0 0 0 40
Y5 0 0 0 0 41
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
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 42
Y7 0 43
Y8 0 0 44
Y9 0 0 0 45
Y10 0 0 0 0 46
ALPHA
FG F1 F2
________ ________ ________
0 0 0
BETA
FG F1 F2
________ ________ ________
FG 0 0 0
F1 0 0 0
F2 0 0 0
PSI
FG F1 F2
________ ________ ________
FG 0
F1 0 0
F2 0 47 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
LAMBDA
FG F1 F2
________ ________ ________
Y1 0.700 0.000 0.000
Y2 0.700 0.000 0.000
Y3 0.700 0.000 0.000
Y4 0.700 0.000 0.000
Y5 0.700 0.000 0.000
Y6 0.700 0.000 0.000
Y7 0.700 0.000 0.000
Y8 0.700 0.000 0.000
Y9 0.700 0.000 0.000
Y10 0.700 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.350
Y2 0.000 0.350
Y3 0.000 0.000 0.350
Y4 0.000 0.000 0.000 0.350
Y5 0.000 0.000 0.000 0.000 0.420
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
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.420
Y7 0.000 0.420
Y8 0.000 0.000 0.420
Y9 0.000 0.000 0.000 0.510
Y10 0.000 0.000 0.000 0.000 0.510
ALPHA
FG F1 F2
________ ________ ________
0.000 0.000 0.000
BETA
FG F1 F2
________ ________ ________
FG 0.000 0.000 0.000
F1 0.000 0.000 0.000
F2 0.000 0.000 0.000
PSI
FG F1 F2
________ ________ ________
FG 1.000
F1 0.000 1.000
F2 0.000 0.000 1.000
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
LAMBDA
FG F1 F2
________ ________ ________
Y1 0.700 0.400 0.000
Y2 0.700 0.400 0.000
Y3 0.700 0.400 0.000
Y4 0.700 0.400 0.000
Y5 0.700 0.000 0.300
Y6 0.700 0.000 0.300
Y7 0.700 0.000 0.300
Y8 0.700 0.000 0.300
Y9 0.700 0.000 0.000
Y10 0.700 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.350
Y2 0.000 0.350
Y3 0.000 0.000 0.350
Y4 0.000 0.000 0.000 0.350
Y5 0.000 0.000 0.000 0.000 0.420
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
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.420
Y7 0.000 0.420
Y8 0.000 0.000 0.420
Y9 0.000 0.000 0.000 0.510
Y10 0.000 0.000 0.000 0.000 0.510
ALPHA
FG F1 F2
________ ________ ________
0.000 0.000 0.000
BETA
FG F1 F2
________ ________ ________
FG 0.000 0.000 0.000
F1 0.000 0.000 0.000
F2 0.000 0.000 0.000
PSI
FG F1 F2
________ ________ ________
FG 1.000
F1 0.000 1.000
F2 0.000 0.000 1.000
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y9
Y10
Save file
ex5.31.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:11
Ending Time: 22:23:11
Elapsed Time: 00:00:00
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