Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a path analysis
with continuous dependent variables
MONTECARLO:
NAMES = y1-y3 x1-x3;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
SAVE = ex3.11.dat;
MODEL POPULATION:
[x1-x3@0];
x1-x3@1;
y1 ON x1*1 x2*2 x3*3;
y2 ON x1*3 x2*2 x3*1;
y3 ON y1*.5 y2*.75 x2*1;
[y1*-1 y2*0 y3*1];
y1*1 y2*1.5 y3*2;
MODEL:
y1 ON x1*1 x2*2 x3*3;
y2 ON x1*3 x2*2 x3*1;
y3 ON y1*.5 y2*.75 x2*1;
[y1*-1 y2*0 y3*1];
y1*1 y2*1.5 y3*2;
OUTPUT: TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a path analysis
with continuous dependent variables
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 3
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2 Y3
Observed independent variables
X1 X2 X3
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 X1 X2
________ ________ ________ ________ ________
-1.108 0.027 0.499 0.046 -0.027
Means
X3
________
-0.012
Covariances
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 17.433
Y2 11.437 17.103
Y3 19.935 20.989 31.757
X1 1.035 3.373 3.059 1.143
X2 2.463 2.335 4.104 0.039 1.066
X3 3.412 1.119 2.673 -0.058 0.096
Covariances
X3
________
X3 1.074
Correlations
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 1.000
Y2 0.662 1.000
Y3 0.847 0.901 1.000
X1 0.232 0.763 0.508 1.000
X2 0.572 0.547 0.705 0.035 1.000
X3 0.789 0.261 0.458 -0.052 0.089
Correlations
X3
________
X3 1.000
MODEL FIT INFORMATION
Number of Free Parameters 15
Loglikelihood
H0 Value
Mean -2364.002
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2364.002 -2364.002
0.980 0.000 -2364.002 -2364.002
0.950 0.000 -2364.002 -2364.002
0.900 0.000 -2364.002 -2364.002
0.800 0.000 -2364.002 -2364.002
0.700 0.000 -2364.002 -2364.002
0.500 0.000 -2364.002 -2364.002
0.300 0.000 -2364.002 -2364.002
0.200 0.000 -2364.002 -2364.002
0.100 0.000 -2364.002 -2364.002
0.050 0.000 -2364.002 -2364.002
0.020 0.000 -2364.002 -2364.002
0.010 0.000 -2364.002 -2364.002
H1 Value
Mean -2363.624
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2363.624 -2363.624
0.980 0.000 -2363.624 -2363.624
0.950 0.000 -2363.624 -2363.624
0.900 0.000 -2363.624 -2363.624
0.800 0.000 -2363.624 -2363.624
0.700 0.000 -2363.624 -2363.624
0.500 0.000 -2363.624 -2363.624
0.300 0.000 -2363.624 -2363.624
0.200 0.000 -2363.624 -2363.624
0.100 0.000 -2363.624 -2363.624
0.050 0.000 -2363.624 -2363.624
0.020 0.000 -2363.624 -2363.624
0.010 0.000 -2363.624 -2363.624
Information Criteria
Akaike (AIC)
Mean 4758.004
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4758.004 4758.004
0.980 0.000 4758.004 4758.004
0.950 0.000 4758.004 4758.004
0.900 0.000 4758.004 4758.004
0.800 0.000 4758.004 4758.004
0.700 0.000 4758.004 4758.004
0.500 0.000 4758.004 4758.004
0.300 0.000 4758.004 4758.004
0.200 0.000 4758.004 4758.004
0.100 0.000 4758.004 4758.004
0.050 0.000 4758.004 4758.004
0.020 0.000 4758.004 4758.004
0.010 0.000 4758.004 4758.004
Bayesian (BIC)
Mean 4821.223
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4821.223 4821.223
0.980 0.000 4821.223 4821.223
0.950 0.000 4821.223 4821.223
0.900 0.000 4821.223 4821.223
0.800 0.000 4821.223 4821.223
0.700 0.000 4821.223 4821.223
0.500 0.000 4821.223 4821.223
0.300 0.000 4821.223 4821.223
0.200 0.000 4821.223 4821.223
0.100 0.000 4821.223 4821.223
0.050 0.000 4821.223 4821.223
0.020 0.000 4821.223 4821.223
0.010 0.000 4821.223 4821.223
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 4773.612
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4773.612 4773.612
0.980 0.000 4773.612 4773.612
0.950 0.000 4773.612 4773.612
0.900 0.000 4773.612 4773.612
0.800 0.000 4773.612 4773.612
0.700 0.000 4773.612 4773.612
0.500 0.000 4773.612 4773.612
0.300 0.000 4773.612 4773.612
0.200 0.000 4773.612 4773.612
0.100 0.000 4773.612 4773.612
0.050 0.000 4773.612 4773.612
0.020 0.000 4773.612 4773.612
0.010 0.000 4773.612 4773.612
Chi-Square Test of Model Fit
Degrees of freedom 3
Mean 0.757
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.115 0.757
0.980 1.000 0.185 0.757
0.950 1.000 0.352 0.757
0.900 1.000 0.584 0.757
0.800 0.000 1.005 0.757
0.700 0.000 1.424 0.757
0.500 0.000 2.366 0.757
0.300 0.000 3.665 0.757
0.200 0.000 4.642 0.757
0.100 0.000 6.251 0.757
0.050 0.000 7.815 0.757
0.020 0.000 9.837 0.757
0.010 0.000 11.345 0.757
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
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 0.001
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
Y1 ON
X1 1.000 0.9924 0.0000 0.0432 0.0001 1.000 1.000
X2 2.000 2.0010 0.0000 0.0448 0.0000 1.000 1.000
X3 3.000 3.0520 0.0000 0.0447 0.0027 1.000 1.000
Y2 ON
X1 3.000 2.9349 0.0000 0.0497 0.0042 1.000 1.000
X2 2.000 1.9915 0.0000 0.0517 0.0001 1.000 1.000
X3 1.000 1.0230 0.0000 0.0515 0.0005 1.000 1.000
Y3 ON
Y1 0.500 0.5066 0.0000 0.0199 0.0000 1.000 1.000
Y2 0.750 0.7456 0.0000 0.0197 0.0000 1.000 1.000
X2 1.000 1.0458 0.0000 0.0719 0.0021 1.000 1.000
Intercepts
Y1 -1.000 -1.0638 0.0000 0.0461 0.0041 1.000 1.000
Y2 0.000 -0.0416 0.0000 0.0531 0.0017 1.000 0.000
Y3 1.000 1.0684 0.0000 0.0625 0.0047 1.000 1.000
Residual Variances
Y1 1.000 1.0614 0.0000 0.0671 0.0038 1.000 1.000
Y2 1.500 1.4080 0.0000 0.0890 0.0085 1.000 1.000
Y3 2.000 1.7170 0.0000 0.1086 0.0801 0.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.979E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
0 0 0 0 0
NU
X3
________
0
LAMBDA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
LAMBDA
X3
________
Y1 0
Y2 0
Y3 0
X1 0
X2 0
X3 0
THETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
X1 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
THETA
X3
________
X3 0
ALPHA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
1 2 3 0 0
ALPHA
X3
________
0
BETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0 0 0 4 5
Y2 0 0 0 7 8
Y3 10 11 0 0 12
X1 0 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
BETA
X3
________
Y1 6
Y2 9
Y3 0
X1 0
X2 0
X3 0
PSI
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 13
Y2 0 14
Y3 0 0 15
X1 0 0 0 0
X2 0 0 0 0 0
X3 0 0 0 0 0
PSI
X3
________
X3 0
STARTING VALUES
NU
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X3
________
0.000
LAMBDA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y3 0.000 0.000 1.000 0.000 0.000
X1 0.000 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 0.000 1.000
X3 0.000 0.000 0.000 0.000 0.000
LAMBDA
X3
________
Y1 0.000
Y2 0.000
Y3 0.000
X1 0.000
X2 0.000
X3 1.000
THETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
X1 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
X3
________
X3 0.000
ALPHA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
-1.000 0.000 1.000 0.046 -0.027
ALPHA
X3
________
-0.012
BETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 2.000
Y2 0.000 0.000 0.000 3.000 2.000
Y3 0.500 0.750 0.000 0.000 1.000
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
BETA
X3
________
Y1 3.000
Y2 1.000
Y3 0.000
X1 0.000
X2 0.000
X3 0.000
PSI
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.500
Y3 0.000 0.000 2.000
X1 0.000 0.000 0.000 1.143
X2 0.000 0.000 0.000 0.039 1.066
X3 0.000 0.000 0.000 -0.058 0.096
PSI
X3
________
X3 1.074
POPULATION VALUES
NU
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X3
________
0.000
LAMBDA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y3 0.000 0.000 1.000 0.000 0.000
X1 0.000 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 0.000 1.000
X3 0.000 0.000 0.000 0.000 0.000
LAMBDA
X3
________
Y1 0.000
Y2 0.000
Y3 0.000
X1 0.000
X2 0.000
X3 1.000
THETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
X1 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
X3
________
X3 0.000
ALPHA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
-1.000 0.000 1.000 0.000 0.000
ALPHA
X3
________
0.000
BETA
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 2.000
Y2 0.000 0.000 0.000 3.000 2.000
Y3 0.500 0.750 0.000 0.000 1.000
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
BETA
X3
________
Y1 3.000
Y2 1.000
Y3 0.000
X1 0.000
X2 0.000
X3 0.000
PSI
Y1 Y2 Y3 X1 X2
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.500
Y3 0.000 0.000 2.000
X1 0.000 0.000 0.000 1.000
X2 0.000 0.000 0.000 0.000 1.000
X3 0.000 0.000 0.000 0.000 0.000
PSI
X3
________
X3 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
X1
X2
X3
Save file
ex3.11.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:32
Ending Time: 22:22:32
Elapsed Time: 00:00:00
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