Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a path analysis
with categorical dependent variables
using the theta parameterization
MONTECARLO:
NAMES = u1-u3 x1-x3;
NOBSERVATIONS = 1000;
NREPS = 1;
SEED = 53487;
GENERATE = u1(2) u2(1) u3(3);
CATEGORICAL = u1-u3;
SAVE = ex3.13.dat;
MODEL POPULATION:
[x1-x3@0];
x1-x3@1;
u1 ON x1*3 x2*2 x3*1;
u2 ON x1*1 x2*2 x3*3;
u3 ON u1*1 u2*-1 x2*2;
[u1$1*-1 u1$2*1];
[u2$1*0];
[u3$1*-.5 u3$2*.5 u3$3*1.5];
u1-u3*1;
ANALYSIS:
PARAMETERIZATION = THETA;
MODEL:
u1 ON x1*3 x2*2 x3*1;
u2 ON x1*1 x2*2 x3*3;
u3 ON u1*1 u2*-1 x2*2;
[u1$1*-1 u1$2*1];
[u2$1*0];
[u3$1*-.5 u3$2*.5 u3$3*1.5];
OUTPUT: TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a path analysis
with categorical dependent variables
using the theta parameterization
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
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
Binary and ordered categorical (ordinal)
U1 U2 U3
Observed independent variables
X1 X2 X3
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Parameterization THETA
Link PROBIT
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means/Intercepts/Thresholds
U1$1 U1$2 U2$1 U3$1 U3$2
________ ________ ________ ________ ________
-0.957 1.109 0.064 -0.360 0.288
Means/Intercepts/Thresholds
U3$3
________
0.879
Slopes
X1 X2 X3
________ ________ ________
U1 2.965 1.926 1.050
U2 1.027 2.084 3.025
U3 1.179 1.205 -1.215
Covariances/Correlations/Residual Correlations
U1 U2 U3
________ ________ ________
U1
U2 0.062
U3 0.655 -0.347
MODEL FIT INFORMATION
Number of Free Parameters 15
Chi-Square Test of Model Fit
Degrees of freedom 3
Mean 6.871
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 0.115 6.871
0.980 1.000 0.185 6.871
0.950 1.000 0.352 6.871
0.900 1.000 0.584 6.871
0.800 1.000 1.005 6.871
0.700 1.000 1.424 6.871
0.500 1.000 2.366 6.871
0.300 1.000 3.665 6.871
0.200 1.000 4.642 6.871
0.100 1.000 6.251 6.871
0.050 0.000 7.815 6.871
0.020 0.000 9.837 6.871
0.010 0.000 11.345 6.871
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.036
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 0.000
0.010 0.000
CFI/TLI
CFI
Mean 0.998
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 0.991
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 0.019
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
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
U1 ON
X1 3.000 2.9176 0.0000 0.1524 0.0068 1.000 1.000
X2 2.000 1.9258 0.0000 0.1032 0.0055 1.000 1.000
X3 1.000 1.0300 0.0000 0.0765 0.0009 1.000 1.000
U2 ON
X1 1.000 1.0456 0.0000 0.1053 0.0021 1.000 1.000
X2 2.000 2.0840 0.0000 0.1750 0.0071 1.000 1.000
X3 3.000 3.2132 0.0000 0.2298 0.0455 1.000 1.000
U3 ON
U1 1.000 1.1088 0.0000 0.1839 0.0118 1.000 1.000
U2 -1.000 -1.0263 0.0000 0.1954 0.0007 1.000 1.000
X2 2.000 2.1869 0.0000 0.3233 0.0349 1.000 1.000
Thresholds
U1$1 -1.000 -0.9571 0.0000 0.0812 0.0018 1.000 1.000
U1$2 1.000 1.1093 0.0000 0.0869 0.0119 1.000 1.000
U2$1 0.000 0.0642 0.0000 0.0798 0.0041 1.000 0.000
U3$1 -0.500 -0.6529 0.0000 0.1271 0.0234 1.000 1.000
U3$2 0.500 0.5223 0.0000 0.1238 0.0005 1.000 1.000
U3$3 1.500 1.5925 0.0000 0.2250 0.0086 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.172E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U1$2 U2$1 U3$1 U3$2
________ ________ ________ ________ ________
1 2 3 4 5
TAU
U3$3
________
6
NU
U1 U2 U3
________ ________ ________
0 0 0
LAMBDA
U1 U2 U3
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 0 0 0
THETA
U1 U2 U3
________ ________ ________
U1 0
U2 0 0
U3 0 0 0
ALPHA
U1 U2 U3
________ ________ ________
0 0 0
BETA
U1 U2 U3
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 7 8 0
GAMMA
X1 X2 X3
________ ________ ________
U1 9 10 11
U2 12 13 14
U3 0 15 0
PSI
U1 U2 U3
________ ________ ________
U1 0
U2 0 0
U3 0 0 0
STARTING VALUES
TAU
U1$1 U1$2 U2$1 U3$1 U3$2
________ ________ ________ ________ ________
-1.000 1.000 0.000 -0.500 0.500
TAU
U3$3
________
1.500
NU
U1 U2 U3
________ ________ ________
0.000 0.000 0.000
LAMBDA
U1 U2 U3
________ ________ ________
U1 1.000 0.000 0.000
U2 0.000 1.000 0.000
U3 0.000 0.000 1.000
THETA
U1 U2 U3
________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
ALPHA
U1 U2 U3
________ ________ ________
0.000 0.000 0.000
BETA
U1 U2 U3
________ ________ ________
U1 0.000 0.000 0.000
U2 0.000 0.000 0.000
U3 1.000 -1.000 0.000
GAMMA
X1 X2 X3
________ ________ ________
U1 3.000 2.000 1.000
U2 1.000 2.000 3.000
U3 0.000 2.000 0.000
PSI
U1 U2 U3
________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
POPULATION VALUES
TAU
U1$1 U1$2 U2$1 U3$1 U3$2
________ ________ ________ ________ ________
-1.000 1.000 0.000 -0.500 0.500
TAU
U3$3
________
1.500
NU
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
X3
________
0.000
LAMBDA
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
U1 1.000 0.000 0.000 0.000 0.000
U2 0.000 1.000 0.000 0.000 0.000
U3 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
________
U1 0.000
U2 0.000
U3 0.000
X1 0.000
X2 0.000
X3 1.000
THETA
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 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
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
X3
________
0.000
BETA
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
U1 0.000 0.000 0.000 3.000 2.000
U2 0.000 0.000 0.000 1.000 2.000
U3 1.000 -1.000 0.000 0.000 2.000
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
________
U1 1.000
U2 3.000
U3 0.000
X1 0.000
X2 0.000
X3 0.000
PSI
U1 U2 U3 X1 X2
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
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
U1
U2
U3
X1
X2
X3
Save file
ex3.13.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:33
Ending Time: 22:22:33
Elapsed Time: 00:00:00
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