Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:26 PM
INPUT INSTRUCTIONS
title: this is an example of 3-level regression
montecarlo:
names are y x w z;
nobservations = 7500;
nreps = 1;
CSIZES = 50[30(5)];
ncsize = 1[1];
within = x;
between =(level2) w (level3) z;
cutpoints = w(0);
save = ex9.20.dat;
ANALYSIS: TYPE = threelevel random;
model population:
%within%
x@1;
s1 | y on x;
y*1;
%between level2%
w@1;
s2 | y on w;
y*.6;
s12 | s1 on w;
s1*.4;
y with s1*.3;
%between level3%
z@1;
y on z*.6;
y*.4;
[y*.5];
s1 on z*.2;
s1*.4;
[s1*.4];
s2 on z*.3;
s2*.4;
[s2*.7];
s12 on z*.2;
s12*.5;
[s12*.4];
y with s1*.2;
y with s2*.1;
y with s12*0;
s1 with s2*.2;
model:
%within%
s1 | y on x;
y*1;
%between level2%
s2 | y on w;
y*.6;
s12 | s1 on w;
s1*.4;
y with s1*.3;
%between level3%
y on z*.6;
y*.4;
[y*.5];
s1 on z*.2;
s1*.4;
[s1*.4];
s2 on z*.3;
s2*.4;
[s2*.7];
s12 on z*.2;
s12*.5;
[s12*.4];
y with s1*.2;
y with s2*.1;
y with s12*0;
s1 with s2*.2;
s1 with s12*0;
s2 with s12*0;
output:
tech9;
*** WARNING in MODEL command
In the MODEL command, the predictor variable refers to the whole observed variable
in the following statement(s):
S2 | Y ON W
*** WARNING in MODEL POPULATION command
In the MODEL POPULATION command, the predictor variable refers to the whole observed variable
in the following statement(s):
S2 | Y ON W
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of 3-level regression
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 1
Number of independent variables 3
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y
Observed independent variables
X W Z
Continuous latent variables
S1 S2 S12
Variables with special functions
Within variables
X
Level 2 between variables
W
Level 3 between variables
Z
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
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-02
Optimization algorithm EMA
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
Average cluster size for LEVEL2 level 5.000
Estimated Intraclass Correlations for the Y Variables for LEVEL2 level
Intraclass
Variable Correlation
Y 0.180
Average cluster size for LEVEL3 level 150.000
Estimated Intraclass Correlations for the Y Variables for LEVEL3 level
Intraclass
Variable Correlation
Y 0.187
SAMPLE STATISTICS FOR THE FIRST REPLICATION
NOTE: The sample statistics for within and between refer to the
maximum-likelihood estimated within and between covariance
matrices, respectively.
ESTIMATED SAMPLE STATISTICS FOR WITHIN
Means
Y X W Z
________ ________ ________ ________
0.000 -0.010 0.000 0.000
Covariances
Y X W Z
________ ________ ________ ________
Y 2.638
X 0.633 0.997
W 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000
Correlations
Y X W Z
________ ________ ________ ________
Y 1.000
X 0.390 1.000
W 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000
ESTIMATED SAMPLE STATISTICS FOR BETWEEN LEVEL2
Means
Y X W Z
________ ________ ________ ________
0.000 0.000 0.468 0.000
Covariances
Y X W Z
________ ________ ________ ________
Y 0.748
X 0.000 0.000
W 0.144 0.000 0.249
Z 0.000 0.000 0.000 0.000
Correlations
Y X W Z
________ ________ ________ ________
Y 1.000
X 0.000 0.000
W 0.334 0.000 1.000
Z 0.000 0.000 0.000 0.000
ESTIMATED SAMPLE STATISTICS FOR BETWEEN LEVEL3
Means
Y X W Z
________ ________ ________ ________
0.900 0.000 0.000 0.079
Covariances
Y X W Z
________ ________ ________ ________
Y 0.780
X 0.000 0.000
W 0.000 0.000 0.000
Z 0.626 0.000 0.000 0.992
Correlations
Y X W Z
________ ________ ________ ________
Y 1.000
X 0.000 0.000
W 0.000 0.000 0.000
Z 0.711 0.000 0.000 1.000
MODEL FIT INFORMATION
Number of Free Parameters 22
Loglikelihood
H0 Value
Mean -12512.213
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -12512.213 -12512.213
0.980 0.000 -12512.213 -12512.213
0.950 0.000 -12512.213 -12512.213
0.900 0.000 -12512.213 -12512.213
0.800 0.000 -12512.213 -12512.213
0.700 0.000 -12512.213 -12512.213
0.500 0.000 -12512.213 -12512.213
0.300 0.000 -12512.213 -12512.213
0.200 0.000 -12512.213 -12512.213
0.100 0.000 -12512.213 -12512.213
0.050 0.000 -12512.213 -12512.213
0.020 0.000 -12512.213 -12512.213
0.010 0.000 -12512.213 -12512.213
Information Criteria
Akaike (AIC)
Mean 25068.425
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 25068.425 25068.425
0.980 0.000 25068.425 25068.425
0.950 0.000 25068.425 25068.425
0.900 0.000 25068.425 25068.425
0.800 0.000 25068.425 25068.425
0.700 0.000 25068.425 25068.425
0.500 0.000 25068.425 25068.425
0.300 0.000 25068.425 25068.425
0.200 0.000 25068.425 25068.425
0.100 0.000 25068.425 25068.425
0.050 0.000 25068.425 25068.425
0.020 0.000 25068.425 25068.425
0.010 0.000 25068.425 25068.425
Bayesian (BIC)
Mean 25220.724
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 25220.724 25220.724
0.980 0.000 25220.724 25220.724
0.950 0.000 25220.724 25220.724
0.900 0.000 25220.724 25220.724
0.800 0.000 25220.724 25220.724
0.700 0.000 25220.724 25220.724
0.500 0.000 25220.724 25220.724
0.300 0.000 25220.724 25220.724
0.200 0.000 25220.724 25220.724
0.100 0.000 25220.724 25220.724
0.050 0.000 25220.724 25220.724
0.020 0.000 25220.724 25220.724
0.010 0.000 25220.724 25220.724
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 25150.812
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 25150.812 25150.812
0.980 0.000 25150.812 25150.812
0.950 0.000 25150.812 25150.812
0.900 0.000 25150.812 25150.812
0.800 0.000 25150.812 25150.812
0.700 0.000 25150.812 25150.812
0.500 0.000 25150.812 25150.812
0.300 0.000 25150.812 25150.812
0.200 0.000 25150.812 25150.812
0.100 0.000 25150.812 25150.812
0.050 0.000 25150.812 25150.812
0.020 0.000 25150.812 25150.812
0.010 0.000 25150.812 25150.812
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Residual Variances
Y 1.000 1.0397 0.0000 0.0173 0.0016 0.000 1.000
Between LEVEL2 Level
Y WITH
S1 0.300 0.3073 0.0000 0.0196 0.0001 1.000 1.000
Residual Variances
Y 0.600 0.5929 0.0000 0.0310 0.0001 1.000 1.000
S1 0.400 0.3732 0.0000 0.0242 0.0007 1.000 1.000
Between LEVEL3 Level
S1 ON
Z 0.200 0.1185 0.0000 0.0877 0.0066 1.000 0.000
S2 ON
Z 0.300 0.2939 0.0000 0.0905 0.0000 1.000 1.000
S12 ON
Z 0.200 0.2194 0.0000 0.1070 0.0004 1.000 1.000
Y ON
Z 0.600 0.5166 0.0000 0.0955 0.0070 1.000 1.000
Y WITH
S1 0.200 0.1497 0.0000 0.0670 0.0025 1.000 1.000
S2 0.100 -0.0633 0.0000 0.0623 0.0267 0.000 0.000
S12 0.000 0.0218 0.0000 0.0848 0.0005 1.000 0.000
S1 WITH
S2 0.200 0.2571 0.0000 0.0538 0.0033 1.000 1.000
S12 0.000 -0.0961 0.0000 0.0936 0.0092 1.000 0.000
S2 WITH
S12 0.000 -0.1924 0.0000 0.0806 0.0370 0.000 1.000
Intercepts
Y 0.500 0.5961 0.0000 0.0928 0.0092 1.000 1.000
S1 0.400 0.4033 0.0000 0.1013 0.0000 1.000 1.000
S2 0.700 0.5531 0.0000 0.0943 0.0216 1.000 1.000
S12 0.400 0.4636 0.0000 0.1257 0.0040 1.000 1.000
Residual Variances
Y 0.400 0.3725 0.0000 0.0634 0.0008 1.000 1.000
S1 0.400 0.4736 0.0000 0.0756 0.0054 1.000 1.000
S2 0.400 0.3121 0.0000 0.0820 0.0077 1.000 1.000
S12 0.500 0.6412 0.0000 0.1454 0.0199 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.161E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y X
________ ________
0 0
LAMBDA
Y X
________ ________
Y 0 0
X 0 0
THETA
Y X
________ ________
Y 0
X 0 0
ALPHA
Y X
________ ________
0 0
BETA
Y X
________ ________
Y 0 0
X 0 0
PSI
Y X
________ ________
Y 1
X 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2
NU
Y W
________ ________
0 0
LAMBDA
S1%B2 Y W
________ ________ ________
Y 0 0 0
W 0 0 0
THETA
Y W
________ ________
Y 0
W 0 0
ALPHA
S1%B2 Y W
________ ________ ________
0 0 0
BETA
S1%B2 Y W
________ ________ ________
S1%B2 0 0 0
Y 0 0 0
W 0 0 0
PSI
S1%B2 Y W
________ ________ ________
S1%B2 2
Y 3 4
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL3
NU
Y Z
________ ________
0 0
LAMBDA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
Y 0 0 0 0 0
Z 0 0 0 0 0
THETA
Y Z
________ ________
Y 0
Z 0 0
ALPHA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
5 6 7 8 0
BETA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0 0 0 0 9
S2 0 0 0 0 10
S12 0 0 0 0 11
Y 0 0 0 0 12
Z 0 0 0 0 0
PSI
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 13
S2 14 15
S12 16 17 18
Y 19 20 21 22
Z 0 0 0 0 0
STARTING VALUES FOR WITHIN
NU
Y X
________ ________
0.000 0.000
LAMBDA
Y X
________ ________
Y 1.000 0.000
X 0.000 1.000
THETA
Y X
________ ________
Y 0.000
X 0.000 0.000
ALPHA
Y X
________ ________
0.000 0.000
BETA
Y X
________ ________
Y 0.000 0.000
X 0.000 0.000
PSI
Y X
________ ________
Y 1.000
X 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL2
NU
Y W
________ ________
0.000 0.000
LAMBDA
S1%B2 Y W
________ ________ ________
Y 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y W
________ ________
Y 0.000
W 0.000 0.000
ALPHA
S1%B2 Y W
________ ________ ________
0.000 0.000 0.000
BETA
S1%B2 Y W
________ ________ ________
S1%B2 0.000 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
S1%B2 Y W
________ ________ ________
S1%B2 0.400
Y 0.300 0.600
W 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL3
NU
Y Z
________ ________
0.000 0.000
LAMBDA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
Y Z
________ ________
Y 0.000
Z 0.000 0.000
ALPHA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
0.400 0.700 0.400 0.500 0.000
BETA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0.000 0.000 0.000 0.000 0.200
S2 0.000 0.000 0.000 0.000 0.300
S12 0.000 0.000 0.000 0.000 0.200
Y 0.000 0.000 0.000 0.000 0.600
Z 0.000 0.000 0.000 0.000 0.000
PSI
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0.400
S2 0.200 0.400
S12 0.000 0.000 0.500
Y 0.200 0.100 0.000 0.400
Z 0.000 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y X
________ ________
0.000 0.000
LAMBDA
Y X
________ ________
Y 1.000 0.000
X 0.000 1.000
THETA
Y X
________ ________
Y 0.000
X 0.000 0.000
ALPHA
Y X
________ ________
0.000 0.000
BETA
Y X
________ ________
Y 0.000 0.000
X 0.000 0.000
PSI
Y X
________ ________
Y 1.000
X 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL2
NU
Y W
________ ________
0.000 0.000
LAMBDA
S1%B2 Y W
________ ________ ________
Y 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y W
________ ________
Y 0.000
W 0.000 0.000
ALPHA
S1%B2 Y W
________ ________ ________
0.000 0.000 0.000
BETA
S1%B2 Y W
________ ________ ________
S1%B2 0.000 0.000 0.000
Y 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
S1%B2 Y W
________ ________ ________
S1%B2 0.400
Y 0.300 0.600
W 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL3
NU
Y Z
________ ________
0.000 0.000
LAMBDA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
Y 0.000 0.000 0.000 1.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
Y Z
________ ________
Y 0.000
Z 0.000 0.000
ALPHA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
0.400 0.700 0.400 0.500 0.000
BETA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0.000 0.000 0.000 0.000 0.200
S2 0.000 0.000 0.000 0.000 0.300
S12 0.000 0.000 0.000 0.000 0.200
Y 0.000 0.000 0.000 0.000 0.600
Z 0.000 0.000 0.000 0.000 0.000
PSI
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0.400
S2 0.200 0.400
S12 0.000 0.000 0.500
Y 0.200 0.100 0.000 0.400
Z 0.000 0.000 0.000 0.000 1.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y
X
W
Z
LEVEL2
LEVEL3
Save file
ex9.20.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:26:55
Ending Time: 22:26:57
Elapsed Time: 00:00:02
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