Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a random coefficient
regression
MONTECARLO:
NAMES = y x1 x2;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
SAVE = ex3.9.dat;
ANALYSIS:
TYPE = RANDOM;
MODEL POPULATION:
x1-x2@1; x1 with x2*.25;
s | y ON x1;
[y*.5]; y*.8;
[s*1]; s*.9;
s with y*.5;
y ON x2*.6;
s ON x2*.3;
MODEL:
s | y ON x1;
[y*.5]; y*.8;
[s*1]; s*.9;
s with y*.5;
y ON x2*.6;
s ON x2*.3;
OUTPUT:
TECH8 TECH9;
INPUT READING TERMINATED NORMALLY
this is an example of a random coefficient
regression
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 1
Number of independent variables 2
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X1 X2
Continuous latent variables
S
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Optimization algorithm EMA
SAMPLE STATISTICS FOR THE FIRST REPLICATION
ESTIMATED SAMPLE STATISTICS
Means
Y X1 X2
________ ________ ________
0.582 0.026 0.005
Covariances
Y X1 X2
________ ________ ________
Y 3.455
X1 1.062 0.940
X2 0.897 0.295 1.117
Correlations
Y X1 X2
________ ________ ________
Y 1.000
X1 0.589 1.000
X2 0.457 0.288 1.000
MODEL FIT INFORMATION
Number of Free Parameters 7
Loglikelihood
H0 Value
Mean -786.119
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -786.119 -786.119
0.980 0.000 -786.119 -786.119
0.950 0.000 -786.119 -786.119
0.900 0.000 -786.119 -786.119
0.800 0.000 -786.119 -786.119
0.700 0.000 -786.119 -786.119
0.500 0.000 -786.119 -786.119
0.300 0.000 -786.119 -786.119
0.200 0.000 -786.119 -786.119
0.100 0.000 -786.119 -786.119
0.050 0.000 -786.119 -786.119
0.020 0.000 -786.119 -786.119
0.010 0.000 -786.119 -786.119
Information Criteria
Akaike (AIC)
Mean 1586.238
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1586.238 1586.238
0.980 0.000 1586.238 1586.238
0.950 0.000 1586.238 1586.238
0.900 0.000 1586.238 1586.238
0.800 0.000 1586.238 1586.238
0.700 0.000 1586.238 1586.238
0.500 0.000 1586.238 1586.238
0.300 0.000 1586.238 1586.238
0.200 0.000 1586.238 1586.238
0.100 0.000 1586.238 1586.238
0.050 0.000 1586.238 1586.238
0.020 0.000 1586.238 1586.238
0.010 0.000 1586.238 1586.238
Bayesian (BIC)
Mean 1615.740
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1615.740 1615.740
0.980 0.000 1615.740 1615.740
0.950 0.000 1615.740 1615.740
0.900 0.000 1615.740 1615.740
0.800 0.000 1615.740 1615.740
0.700 0.000 1615.740 1615.740
0.500 0.000 1615.740 1615.740
0.300 0.000 1615.740 1615.740
0.200 0.000 1615.740 1615.740
0.100 0.000 1615.740 1615.740
0.050 0.000 1615.740 1615.740
0.020 0.000 1615.740 1615.740
0.010 0.000 1615.740 1615.740
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1593.522
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 1593.522 1593.522
0.980 0.000 1593.522 1593.522
0.950 0.000 1593.522 1593.522
0.900 0.000 1593.522 1593.522
0.800 0.000 1593.522 1593.522
0.700 0.000 1593.522 1593.522
0.500 0.000 1593.522 1593.522
0.300 0.000 1593.522 1593.522
0.200 0.000 1593.522 1593.522
0.100 0.000 1593.522 1593.522
0.050 0.000 1593.522 1593.522
0.020 0.000 1593.522 1593.522
0.010 0.000 1593.522 1593.522
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
S ON
X2 0.300 0.2514 0.0000 0.0694 0.0024 1.000 1.000
Y ON
X2 0.600 0.5871 0.0000 0.0455 0.0002 1.000 1.000
S WITH
Y 0.500 0.6195 0.0000 0.0803 0.0143 1.000 1.000
Intercepts
Y 0.500 0.4876 0.0000 0.0523 0.0002 1.000 1.000
S 1.000 0.9846 0.0000 0.0739 0.0002 1.000 1.000
Residual Variances
Y 0.800 0.8136 0.0000 0.0760 0.0002 1.000 1.000
S 0.900 1.1600 0.0000 0.1555 0.0676 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.417E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y X1 X2
________ ________ ________
0 0 0
LAMBDA
S Y X1 X2
________ ________ ________ ________
Y 0 0 0 0
X1 0 0 0 0
X2 0 0 0 0
THETA
Y X1 X2
________ ________ ________
Y 0
X1 0 0
X2 0 0 0
ALPHA
S Y X1 X2
________ ________ ________ ________
1 2 0 0
BETA
S Y X1 X2
________ ________ ________ ________
S 0 0 0 3
Y 0 0 0 4
X1 0 0 0 0
X2 0 0 0 0
PSI
S Y X1 X2
________ ________ ________ ________
S 5
Y 6 7
X1 0 0 0
X2 0 0 0 0
STARTING VALUES
NU
Y X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
S Y X1 X2
________ ________ ________ ________
Y 0.000 1.000 0.000 0.000
X1 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 1.000
THETA
Y X1 X2
________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
S Y X1 X2
________ ________ ________ ________
1.000 0.500 0.000 0.000
BETA
S Y X1 X2
________ ________ ________ ________
S 0.000 0.000 0.000 0.300
Y 0.000 0.000 0.000 0.600
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
S Y X1 X2
________ ________ ________ ________
S 0.900
Y 0.500 0.800
X1 0.000 0.000 0.500
X2 0.000 0.000 0.000 0.500
POPULATION VALUES
NU
Y X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
S Y X1 X2
________ ________ ________ ________
Y 0.000 1.000 0.000 0.000
X1 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 1.000
THETA
Y X1 X2
________ ________ ________
Y 0.000
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
S Y X1 X2
________ ________ ________ ________
1.000 0.500 0.000 0.000
BETA
S Y X1 X2
________ ________ ________ ________
S 0.000 0.000 0.000 0.300
Y 0.000 0.000 0.000 0.600
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
S Y X1 X2
________ ________ ________ ________
S 0.900
Y 0.500 0.800
X1 0.000 0.000 1.000
X2 0.000 0.000 0.250 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.78851275D+03 0.0000000 0.0000000 EM
2 -0.78726569D+03 1.2470592 0.0015815 EM
3 -0.78690213D+03 0.3635630 0.0004618 EM
4 -0.78671018D+03 0.1919523 0.0002439 EM
5 -0.78657880D+03 0.1313786 0.0001670 EM
6 -0.78648228D+03 0.0965149 0.0001227 EM
7 -0.78641009D+03 0.0721913 0.0000918 EM
8 -0.78635581D+03 0.0542784 0.0000690 EM
9 -0.78631493D+03 0.0408803 0.0000520 EM
10 -0.78628413D+03 0.0308056 0.0000392 EM
11 -0.78626091D+03 0.0232177 0.0000295 EM
12 -0.78624341D+03 0.0174977 0.0000223 EM
13 -0.78623023D+03 0.0131849 0.0000168 EM
14 -0.78622029D+03 0.0099330 0.0000126 EM
15 -0.78621281D+03 0.0074816 0.0000095 EM
16 -0.78620718D+03 0.0056343 0.0000072 EM
17 -0.78620293D+03 0.0042428 0.0000054 EM
18 -0.78619974D+03 0.0031949 0.0000041 EM
19 -0.78619733D+03 0.0024061 0.0000031 EM
20 -0.78619552D+03 0.0018123 0.0000023 EM
21 -0.78619416D+03 0.0013655 0.0000017 EM
22 -0.78619313D+03 0.0010295 0.0000013 EM
23 -0.78619235D+03 0.0007767 0.0000010 EM
24 -0.78619176D+03 0.0005867 0.0000007 EM
25 -0.78619132D+03 0.0004438 0.0000006 EM
26 -0.78619098D+03 0.0003364 0.0000004 EM
27 -0.78619073D+03 0.0002556 0.0000003 EM
28 -0.78619053D+03 0.0001950 0.0000002 EM
29 -0.78619038D+03 0.0001494 0.0000002 EM
30 -0.78619027D+03 0.0001151 0.0000001 EM
31 -0.78619018D+03 0.0000894 0.0000001 EM
32 -0.78619011D+03 0.0000701 0.0000001 EM
33 -0.78619005D+03 0.0000556 0.0000001 EM
34 -0.78619001D+03 0.0000446 0.0000001 EM
35 -0.78612285D+03 0.0671609 0.0000854 FS
36 -0.78611916D+03 0.0036867 0.0000047 FS
37 -0.78611890D+03 0.0002622 0.0000003 FS
38 -0.78611888D+03 0.0000204 0.0000000 FS
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y
X1
X2
Save file
ex3.9.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:22:37
Ending Time: 22:22:38
Elapsed Time: 00:00:01
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