Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 11:29 PM
INPUT INSTRUCTIONS
title: jasad.inp
montecarlo:
names are y1 y2 x;
nobs = 2000;
nreps = 500;
seed = 578243;
classes = c(3);
genclasses = c(3);
cutpoints = x(0);
analysis:
type = mixture;
model montecarlo:
%overall%
[x@0]; x@1;
i by y1-y2@1;
s by y1@0 y2@1;
[y1-y2@0 i*0 s*1];
i*6.25; ! SD = 2.5
s*1;
!total s variance is 1.25 (1/5 of i variance), SD = 1.12
i with s*.699; !this gives correlation 0.25
y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
! y1 variance = 8.333, SD = 2.89
! y2 variance = 9.135, SD = 3.052
! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01
s on x*1;
!this gives ES = 0.33 in y2 within-group SD terms (for medium class)
!r-squared for s is 20%
[c#1*-1.9459 c#2*-1.2528];
%c#1% !low class (10%)
[i*0.0 s*.75];
!low class grows at 1/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
s on x*0.25;
%c#2% ! high class (20%)
[i*5.0 s*2.25];
!high class grows at 3/4 SD per grade
s on x*.25;
! high class has 1/4 effect of low class, ES = 0.08
%c#3% !medium class (70%)
[i*2.5 s*2.25];
!medium class grows at 3/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
model:
%overall%
i by y1-y2@1;
s by y1@0 y2@1;
[y1-y2@0 i*0 s*1];
i*6.25; ! SD = 2.5
s@0;
!total s variance is 1.25 (1/5 of i variance), SD = 1.12
i with s@0; !this gives correlation 0.25
y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
! y1 variance = 8.333, SD = 2.89
! y2 variance = 9.135, SD = 3.052
! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01
s on x*1;
!this gives ES = 0.33 in y2 within-group SD terms (for medium class)
!r-squared for s is 20%
[c#1*-1.9459 c#2*-1.2528];
%c#1% !low class (10%)
[i*0.0 s*.75];
!low class grows at 1/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
s on x*0.25;
%c#2% ! high class (20%)
[i*5.0 s*2.25];
!high class grows at 3/4 SD per grade
s on x*.25;
! high class has 1/4 effect of low class, ES = 0.08
%c#3% !medium class (70%)
[i*2.5 s*2.25];
!medium class grows at 3/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
output:
tech9;
INPUT READING TERMINATED NORMALLY
jasad.inp
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 2000
Number of replications
Requested 500
Completed 500
Value of seed 578243
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2
Observed independent variables
X
Continuous latent variables
I S
Categorical latent variables
C
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-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
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-05
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-05
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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 X
________ ________ ________
1 2.719 5.249 0.497
Covariances
Y1 Y2 X
________ ________ ________
Y1 10.208
Y2 9.067 11.948
X -0.033 0.152 0.250
Correlations
Y1 Y2 X
________ ________ ________
Y1 1.000
Y2 0.821 1.000
X -0.021 0.088 1.000
TESTS OF MODEL FIT
Number of Free Parameters 14
Loglikelihood
H0 Value
Mean -9292.831
Std Dev 46.972
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.988 -9402.101 -9404.199
0.980 0.982 -9389.296 -9387.473
0.950 0.962 -9370.094 -9366.628
0.900 0.910 -9353.029 -9352.275
0.800 0.804 -9332.362 -9332.160
0.700 0.704 -9317.463 -9316.350
0.500 0.484 -9292.831 -9294.508
0.300 0.290 -9268.199 -9269.957
0.200 0.192 -9253.299 -9255.783
0.100 0.098 -9232.632 -9233.210
0.050 0.064 -9215.567 -9211.921
0.020 0.024 -9196.365 -9194.252
0.010 0.014 -9183.561 -9173.772
Information Criteria
Akaike (AIC)
Mean 18613.661
Std Dev 93.943
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 18395.121 18375.118
0.980 0.976 18420.730 18413.614
0.950 0.936 18459.134 18451.515
0.900 0.902 18493.264 18490.353
0.800 0.808 18534.599 18539.290
0.700 0.710 18564.397 18567.705
0.500 0.516 18613.661 18616.849
0.300 0.296 18662.925 18660.556
0.200 0.196 18692.724 18691.981
0.100 0.090 18734.059 18731.636
0.050 0.038 18768.188 18758.650
0.020 0.018 18806.592 18802.869
0.010 0.012 18832.201 18834.055
Bayesian (BIC)
Mean 18692.074
Std Dev 93.943
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 18473.534 18453.531
0.980 0.976 18499.143 18492.026
0.950 0.936 18537.547 18529.927
0.900 0.902 18571.676 18568.766
0.800 0.808 18613.011 18617.702
0.700 0.710 18642.810 18646.118
0.500 0.516 18692.074 18695.261
0.300 0.296 18741.338 18738.969
0.200 0.196 18771.137 18770.394
0.100 0.090 18812.472 18810.049
0.050 0.038 18846.601 18837.063
0.020 0.018 18885.005 18881.281
0.010 0.012 18910.614 18912.467
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 18647.595
Std Dev 93.943
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.986 18429.055 18409.052
0.980 0.976 18454.664 18447.547
0.950 0.936 18493.068 18485.449
0.900 0.902 18527.197 18524.287
0.800 0.808 18568.533 18573.224
0.700 0.710 18598.331 18601.639
0.500 0.516 18647.595 18650.782
0.300 0.296 18696.859 18694.490
0.200 0.196 18726.658 18725.915
0.100 0.090 18767.993 18765.570
0.050 0.038 18802.122 18792.584
0.020 0.018 18840.526 18836.803
0.010 0.012 18866.135 18867.988
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 217.00849 0.10850
2 507.96889 0.25398
3 1275.02262 0.63751
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 217.00850 0.10850
2 507.96888 0.25398
3 1275.02263 0.63751
CLASSIFICATION QUALITY
Entropy 0.418
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 136 0.06819
2 429 0.21450
3 1435 0.71731
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2 3
1 0.695 0.059 0.246
2 0.028 0.683 0.289
3 0.075 0.155 0.771
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
I BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S BY
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S ON
X 0.250 0.1993 0.8126 0.6804 0.6615 0.938 0.142
I WITH
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 0.000 -0.1966 0.9263 0.9146 0.8950 0.838 0.162
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 0.750 0.7148 0.7568 0.6091 0.5728 0.868 0.342
Variances
I 6.250 6.5269 1.2264 1.0141 1.5776 0.716 0.976
Residual Variances
Y1 2.083 1.3894 0.4718 0.3885 0.7032 0.482 0.830
Y2 0.417 1.9041 0.5350 0.4594 2.4973 0.186 0.914
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class 2
I BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S BY
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S ON
X 0.250 0.0107 1.2626 0.7471 1.6483 0.738 0.364
I WITH
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 5.000 5.3125 1.4696 1.0482 2.2532 0.756 0.962
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 2.250 2.4187 0.9793 0.5840 0.9855 0.706 0.886
Variances
I 6.250 6.5269 1.2264 1.0141 1.5776 0.716 0.976
Residual Variances
Y1 2.083 1.3894 0.4718 0.3885 0.7032 0.482 0.830
Y2 0.417 1.9041 0.5350 0.4594 2.4973 0.186 0.914
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class 3
I BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S BY
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S ON
X 1.000 1.1295 0.7206 0.2898 0.5350 0.874 0.948
I WITH
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 2.500 2.3560 0.6458 0.4512 0.4369 0.722 0.920
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S 2.250 2.2269 0.4516 0.2631 0.2041 0.824 0.964
Variances
I 6.250 6.5269 1.2264 1.0141 1.5776 0.716 0.976
Residual Variances
Y1 2.083 1.3894 0.4718 0.3885 0.7032 0.482 0.830
Y2 0.417 1.9041 0.5350 0.4594 2.4973 0.186 0.914
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Categorical Latent Variables
Means
C#1 -1.946 -1.8513 0.7893 0.6991 0.6306 0.878 0.826
C#2 -1.253 -1.2545 1.4755 0.9933 2.1726 0.714 0.418
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.125E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 1
Y2 0 2
X 0 0 0
ALPHA
I S X
________ ________ ________
1 3 4 0
BETA
I S X
________ ________ ________
I 0 0 0
S 0 0 5
X 0 0 0
PSI
I S X
________ ________ ________
I 6
S 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 1
Y2 0 2
X 0 0 0
ALPHA
I S X
________ ________ ________
1 7 8 0
BETA
I S X
________ ________ ________
I 0 0 0
S 0 0 9
X 0 0 0
PSI
I S X
________ ________ ________
I 6
S 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 3
NU
Y1 Y2 X
________ ________ ________
1 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 1
Y2 0 2
X 0 0 0
ALPHA
I S X
________ ________ ________
1 10 11 0
BETA
I S X
________ ________ ________
I 0 0 0
S 0 0 12
X 0 0 0
PSI
I S X
________ ________ ________
I 6
S 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 13 14 0
GAMMA(C)
X
________
C#1 0
C#2 0
C#3 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 0.000 0.750 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 5.000 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 3
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 2.500 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 1.000
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 -1.946 -1.253 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
C#3 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 0.000 0.750 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.699 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 5.000 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.699 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 3
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 2.500 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 1.000
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.699 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 -1.946 -1.253 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
C#3 0.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
REPLICATION 45:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 1 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 45:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 2 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 45:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 3 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 313:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 1 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 313:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 2 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 313:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 3 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
Beginning Time: 23:29:34
Ending Time: 23:31:31
Elapsed Time: 00:01:57
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