Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:26 PM
INPUT INSTRUCTIONS
TITLE: this an example of a Monte Carlo simulation
for a three-level path analysis model
with a continuous and a categorical dependent variable
montecarlo:
names are y u x w y2 z y3;
nobservations = 7500;
nreps = 1;
CSIZES = 50[30(5)];
ncsize = 1[1];
generate = u(1);
categorical = u;
within = x;
between = y2 (level2) w (level3) z y3;
save = ex9.21.dat;
ANALYSIS: TYPE = threelevel;
estimator = bayes;
processors = 2;
biter = (1000);
model population:
%WITHIN%
x@1;
u ON y*.75 x*.5;
y ON x*.25;
y*1;
%Between level2%
w@1;
u ON w*1 y*.5 y2*.7;
y ON w*.5;
y2 ON w*.7;
y with y2*.25;
y*.5; y2*.5; u*.4;
%Between level3%
z@1; y3@1;
u ON y*.6 y2*.8;
y ON z*.6;
y2 ON z*.8;
y3 ON y*.4 y2*.3;
y with y2*.3;
y*.4; y2*.5; u*.5 y3*.6;
u with y3*.2;
model:
%WITHIN%
u ON y*.75 x*.5;
y ON x*.25;
y*1;
%Between level2%
u ON w*1 y*.5 y2*.7;
y ON w*.5;
y2 ON w*.7;
y with y2*.25;
y*.5; y2*.5; u*.4;
%Between level3%
u ON y*.6 y2*.8;
y ON z*.6;
y2 ON z*.8;
y3 ON y*.4 y2*.3;
y with y2*.3;
y*.4; y2*.5; u*.5 y3*.6;
u with y3*.2;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this an example of a Monte Carlo simulation
for a three-level path analysis model
with a continuous and a categorical dependent variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 7500
Number of replications
Requested 1
Completed 1
Value of seed 0
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y2 Y Y3
Binary and ordered categorical (ordinal)
U
Observed independent variables
X W Z
Variables with special functions
Within variables
X
Level 2 between variables
W
Level 3 between variables
Z Y3
Level 2 and level 3 between variables
Y2
Estimator BAYES
Specifications for Bayesian Estimation
Point estimate MEDIAN
Number of Markov chain Monte Carlo (MCMC) chains 2
Random seed for the first chain 0
Starting value information UNPERTURBED
Algorithm used for Markov chain Monte Carlo GIBBS(PX1)
Convergence criterion 0.500D-01
Maximum number of iterations 50000
K-th iteration used for thinning 1
Link PROBIT
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Number of level 3 clusters 50
Size (s) Number of level 2 clusters of Size s
5 30
MODEL FIT INFORMATION
Number of Free Parameters 29
Bayesian Posterior Predictive Checking using Chi-Square
Posterior Predictive P-Value
Mean 0.618
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 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
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
U ON
Y 0.750 0.7531 0.0000 0.0298 0.0000 1.000 1.000
X 0.500 0.4827 0.0000 0.0290 0.0003 1.000 1.000
Y ON
X 0.250 0.2487 0.0000 0.0123 0.0000 1.000 1.000
Residual Variances
Y 1.000 1.0100 0.0000 0.0187 0.0001 1.000 1.000
Between LEVEL2 Level
U ON
W 1.000 1.0791 0.0000 0.0515 0.0063 1.000 1.000
Y 0.500 0.5165 0.0000 0.0648 0.0003 1.000 1.000
Y2 0.700 0.5960 0.0000 0.0587 0.0108 1.000 1.000
Y ON
W 0.500 0.4903 0.0000 0.0219 0.0001 1.000 1.000
Y2 ON
W 0.700 0.6824 0.0000 0.0183 0.0003 1.000 1.000
Y WITH
Y2 0.250 0.2549 0.0000 0.0175 0.0000 1.000 1.000
Residual Variances
U 0.400 0.3712 0.0000 0.0410 0.0008 1.000 1.000
Y2 0.500 0.4777 0.0000 0.0174 0.0005 1.000 1.000
Y 0.500 0.4956 0.0000 0.0255 0.0000 1.000 1.000
Between LEVEL3 Level
U ON
Y 0.600 0.5968 0.0000 0.2155 0.0000 1.000 1.000
Y2 0.800 0.8491 0.0000 0.1859 0.0024 1.000 1.000
Y ON
Z 0.600 0.6371 0.0000 0.1187 0.0014 1.000 1.000
Y2 ON
Z 0.800 0.7762 0.0000 0.1303 0.0006 1.000 1.000
Y3 ON
Y 0.400 0.3129 0.0000 0.2146 0.0076 1.000 0.000
Y2 0.300 0.2900 0.0000 0.1853 0.0001 1.000 0.000
Y WITH
Y2 0.300 0.3607 0.0000 0.1005 0.0037 1.000 1.000
U WITH
Y3 0.200 0.2286 0.0000 0.0919 0.0008 1.000 1.000
Intercepts
Y2 0.000 0.0325 0.0000 0.1140 0.0011 1.000 0.000
Y 0.000 0.0455 0.0000 0.1087 0.0021 1.000 0.000
Y3 0.000 -0.1197 0.0000 0.1028 0.0143 1.000 0.000
Thresholds
U$1 0.000 0.1200 0.0000 0.1072 0.0144 1.000 0.000
Residual Variances
U 0.500 0.5130 0.0000 0.1243 0.0002 1.000 1.000
Y2 0.500 0.5934 0.0000 0.1268 0.0087 1.000 1.000
Y 0.400 0.5104 0.0000 0.1149 0.0122 1.000 1.000
Y3 0.600 0.5257 0.0000 0.1201 0.0055 1.000 1.000
CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES
CORRELATIONS MEAN SQUARE ERROR
Average Std. Dev. Average Std. Dev.
B2_U 0.957 0.000 0.580 0.000
B2_Y 0.900 0.000 0.381 0.000
B3_U 0.989 0.000 0.224 0.000
B3_Y2 0.992 0.000 0.129 0.000
B3_Y 0.990 0.000 0.129 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U$1
________
0
NU
U Y X
________ ________ ________
0 0 0
LAMBDA
U Y X
________ ________ ________
U 0 0 0
Y 0 0 0
X 0 0 0
THETA
U Y X
________ ________ ________
U 0
Y 0 0
X 0 0 0
ALPHA
U Y X
________ ________ ________
0 0 0
BETA
U Y X
________ ________ ________
U 0 1 2
Y 0 0 3
X 0 0 0
PSI
U Y X
________ ________ ________
U 0
Y 0 4
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2
TAU
U$1
________
0
NU
U Y2 Y W
________ ________ ________ ________
0 0 0 0
LAMBDA
U Y2 Y W
________ ________ ________ ________
U 0 0 0 0
Y2 0 0 0 0
Y 0 0 0 0
W 0 0 0 0
THETA
U Y2 Y W
________ ________ ________ ________
U 0
Y2 0 0
Y 0 0 0
W 0 0 0 0
ALPHA
U Y2 Y W
________ ________ ________ ________
0 0 0 0
BETA
U Y2 Y W
________ ________ ________ ________
U 0 5 6 7
Y2 0 0 0 8
Y 0 0 0 9
W 0 0 0 0
PSI
U Y2 Y W
________ ________ ________ ________
U 10
Y2 0 11
Y 0 12 13
W 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL3
TAU
U$1
________
29
NU
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0 0 0 0 0
Y2 0 0 0 0 0
Y 0 0 0 0 0
Y3 0 0 0 0 0
Z 0 0 0 0 0
THETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0
Y2 0 0
Y 0 0 0
Y3 0 0 0 0
Z 0 0 0 0 0
ALPHA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0 14 15 16 0
BETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0 17 18 0 0
Y2 0 0 0 0 19
Y 0 0 0 0 20
Y3 0 21 22 0 0
Z 0 0 0 0 0
PSI
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 23
Y2 0 24
Y 0 25 26
Y3 27 0 0 28
Z 0 0 0 0 0
STARTING VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U Y X
________ ________ ________
0.000 0.000 0.000
LAMBDA
U Y X
________ ________ ________
U 1.000 0.000 0.000
Y 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
U Y X
________ ________ ________
0.000 0.000 0.000
BETA
U Y X
________ ________ ________
U 0.000 0.750 0.500
Y 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 1.000
Y 0.000 1.000
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2
TAU
U$1
________
0.000
NU
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y W
________ ________ ________ ________
U 1.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
U Y2 Y W
________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U Y2 Y W
________ ________ ________ ________
U 0.000 0.700 0.500 1.000
Y2 0.000 0.000 0.000 0.700
Y 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000
PSI
U Y2 Y W
________ ________ ________ ________
U 0.400
Y2 0.000 0.500
Y 0.000 0.250 0.500
W 0.000 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL3
TAU
U$1
________
0.000
NU
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 1.000 0.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y 0.000 0.000 1.000 0.000 0.000
Y3 0.000 0.000 0.000 1.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000 0.800 0.600 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.800
Y 0.000 0.000 0.000 0.000 0.600
Y3 0.000 0.300 0.400 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
PSI
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.500
Y2 0.000 0.500
Y 0.000 0.300 0.400
Y3 0.200 0.000 0.000 0.600
Z 0.000 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
TAU
U$1
________
0.000
NU
U Y X
________ ________ ________
0.000 0.000 0.000
LAMBDA
U Y X
________ ________ ________
U 1.000 0.000 0.000
Y 0.000 1.000 0.000
X 0.000 0.000 1.000
THETA
U Y X
________ ________ ________
U 0.000
Y 0.000 0.000
X 0.000 0.000 0.000
ALPHA
U Y X
________ ________ ________
0.000 0.000 0.000
BETA
U Y X
________ ________ ________
U 0.000 0.750 0.500
Y 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
U Y X
________ ________ ________
U 0.000
Y 0.000 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2
TAU
U$1
________
0.000
NU
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y W
________ ________ ________ ________
U 1.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000
Y 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
U Y2 Y W
________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y W
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U Y2 Y W
________ ________ ________ ________
U 0.000 0.700 0.500 1.000
Y2 0.000 0.000 0.000 0.700
Y 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000
PSI
U Y2 Y W
________ ________ ________ ________
U 0.400
Y2 0.000 0.500
Y 0.000 0.250 0.500
W 0.000 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL3
TAU
U$1
________
0.000
NU
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 1.000 0.000 0.000 0.000 0.000
Y2 0.000 1.000 0.000 0.000 0.000
Y 0.000 0.000 1.000 0.000 0.000
Y3 0.000 0.000 0.000 1.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000
Y2 0.000 0.000
Y 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
ALPHA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.000 0.800 0.600 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.800
Y 0.000 0.000 0.000 0.000 0.600
Y3 0.000 0.300 0.400 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
PSI
U Y2 Y Y3 Z
________ ________ ________ ________ ________
U 0.500
Y2 0.000 0.500
Y 0.000 0.300 0.400
Y3 0.200 0.000 0.000 0.600
Z 0.000 0.000 0.000 0.000 1.000
PRIORS FOR ALL PARAMETERS PRIOR MEAN PRIOR VARIANCE PRIOR STD. DEV.
Parameter 1~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 2~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 3~N(0.000,infinity) 0.0000 infinity infinity
Parameter 4~IG(-1.000,0.000) infinity infinity infinity
Parameter 5~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 6~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 7~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 8~N(0.000,infinity) 0.0000 infinity infinity
Parameter 9~N(0.000,infinity) 0.0000 infinity infinity
Parameter 10~IG(-1.000,0.000) infinity infinity infinity
Parameter 11~IW(1.000,3) infinity infinity infinity
Parameter 12~IW(0.000,3) infinity infinity infinity
Parameter 13~IW(1.000,3) infinity infinity infinity
Parameter 14~N(0.000,infinity) 0.0000 infinity infinity
Parameter 15~N(0.000,infinity) 0.0000 infinity infinity
Parameter 16~N(0.000,infinity) 0.0000 infinity infinity
Parameter 17~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 18~N(0.000,5.000) 0.0000 5.0000 2.2361
Parameter 19~N(0.000,infinity) 0.0000 infinity infinity
Parameter 20~N(0.000,infinity) 0.0000 infinity infinity
Parameter 21~N(0.000,infinity) 0.0000 infinity infinity
Parameter 22~N(0.000,infinity) 0.0000 infinity infinity
Parameter 23~IW(1.000,3) infinity infinity infinity
Parameter 24~IW(1.000,3) infinity infinity infinity
Parameter 25~IW(0.000,3) infinity infinity infinity
Parameter 26~IW(1.000,3) infinity infinity infinity
Parameter 27~IW(0.000,3) infinity infinity infinity
Parameter 28~IW(1.000,3) infinity infinity infinity
Parameter 29~N(0.000,5.000) 0.0000 5.0000 2.2361
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION
CHAIN BSEED
1 0
2 285380
REPLICATION 1:
POTENTIAL PARAMETER WITH
ITERATION SCALE REDUCTION HIGHEST PSR
100 1.470 10
200 1.094 7
300 1.297 10
400 1.095 7
500 1.028 2
600 1.119 7
700 1.104 7
800 1.145 7
900 1.088 7
1000 1.030 2
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U
Y2
Y
Y3
X
W
Z
LEVEL2
LEVEL3
Save file
ex9.21.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:26:57
Ending Time: 22:27:04
Elapsed Time: 00:00:07
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