Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
INPUT INSTRUCTIONS
TITLE: this is an example of 3-level regression
DATA: FILE = ex9.20.dat;
VARIABLE: NAMES = y x w z level2 level3;
CLUSTER = level3 level2;
WITHIN = x;
BETWEEN =(level2) w (level3) z;
ANALYSIS: TYPE = THREELEVEL RANDOM;
MODEL: %WITHIN%
s1 | y ON x;
%BETWEEN level2%
s2 | y ON w;
s12 | s1 ON w;
s1;
y WITH s1;
%BETWEEN level3%
y ON z;
s1 ON z;
s2 ON z;
s12 ON z;
y WITH s1 s2 s12;
s1 WITH s2 s12;
s2 WITH s12;
OUTPUT: TECH1 TECH8;
*** 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
1 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 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
Cluster variables LEVEL3 LEVEL2
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
Input data file(s)
ex9.20.dat
Input data format FREE
SUMMARY OF DATA
Number of LEVEL2 clusters 1500
Number of LEVEL3 clusters 50
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y 0.900 0.370 -12.967 0.01% -0.744 0.356 0.798
7500.000 4.180 1.354 11.884 0.01% 1.272 2.428
X -0.010 -0.024 -4.119 0.01% -0.852 -0.272 -0.001
7500.000 0.997 0.024 3.536 0.01% 0.250 0.831
W 0.468 0.128 0.000 53.20% 0.000 0.000 0.000
1500.000 0.249 -1.984 1.000 46.80% 1.000 1.000
Z 0.079 0.577 -1.916 2.00% -0.747 -0.192 0.135
50.000 0.992 0.584 2.989 2.00% 0.286 0.755
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 22
Loglikelihood
H0 Value -12512.213
H0 Scaling Correction Factor 0.9115
for MLR
Information Criteria
Akaike (AIC) 25068.425
Bayesian (BIC) 25220.724
Sample-Size Adjusted BIC 25150.812
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Residual Variances
Y 1.040 0.017 59.953 0.000
Between LEVEL2 Level
Y WITH
S1 0.307 0.020 15.696 0.000
Residual Variances
Y 0.593 0.031 19.118 0.000
S1 0.373 0.024 15.406 0.000
Between LEVEL3 Level
S1 ON
Z 0.118 0.088 1.351 0.177
S2 ON
Z 0.294 0.091 3.246 0.001
S12 ON
Z 0.219 0.107 2.050 0.040
Y ON
Z 0.517 0.095 5.412 0.000
Y WITH
S1 0.150 0.067 2.234 0.025
S2 -0.063 0.062 -1.015 0.310
S12 0.022 0.085 0.258 0.796
S1 WITH
S2 0.257 0.054 4.782 0.000
S12 -0.096 0.094 -1.026 0.305
S2 WITH
S12 -0.193 0.081 -2.388 0.017
Intercepts
Y 0.596 0.093 6.425 0.000
S1 0.403 0.101 3.983 0.000
S2 0.553 0.094 5.863 0.000
S12 0.464 0.126 3.687 0.000
Residual Variances
Y 0.372 0.063 5.872 0.000
S1 0.474 0.076 6.265 0.000
S2 0.312 0.082 3.809 0.000
S12 0.641 0.145 4.409 0.000
QUALITY OF NUMERICAL RESULTS
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 2.090
X 0.000 0.498
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 1.000
Y 0.000 2.090
W 0.000 0.000 0.124
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
________ ________ ________ ________ ________
0.000 0.000 0.000 0.900 0.000
BETA
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 0.000 0.000 0.000 0.000 0.000
S2 0.000 0.000 0.000 0.000 0.000
S12 0.000 0.000 0.000 0.000 0.000
Y 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
PSI
S1%B3 S2 S12 Y Z
________ ________ ________ ________ ________
S1%B3 1.000
S2 0.000 1.000
S12 0.000 0.000 1.000
Y 0.000 0.000 0.000 2.090
Z 0.000 0.000 0.000 0.000 0.496
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.13687243D+05 0.0000000 0.0000000 EM
2 -0.12799603D+05 887.6398087 0.0648516 EM
3 -0.12599987D+05 199.6152604 0.0155954 EM
4 -0.12551837D+05 48.1509217 0.0038215 EM
5 -0.12534342D+05 17.4941208 0.0013937 EM
6 -0.12525735D+05 8.6070218 0.0006867 EM
7 -0.12520885D+05 4.8501952 0.0003872 EM
8 -0.12517957D+05 2.9287079 0.0002339 EM
9 -0.12516107D+05 1.8490753 0.0001477 EM
10 -0.12514901D+05 1.2059779 0.0000964 EM
11 -0.12514095D+05 0.8062803 0.0000644 EM
12 -0.12513546D+05 0.5496771 0.0000439 EM
13 -0.12513165D+05 0.3805852 0.0000304 EM
14 -0.12512898D+05 0.2668728 0.0000213 EM
15 -0.12512709D+05 0.1890579 0.0000151 EM
16 -0.12512574D+05 0.1350883 0.0000108 EM
17 -0.12512477D+05 0.0972172 0.0000078 EM
18 -0.12512406D+05 0.0703755 0.0000056 EM
19 -0.12512355D+05 0.0511994 0.0000041 EM
20 -0.12512318D+05 0.0374069 0.0000030 EM
21 -0.12512290D+05 0.0274279 0.0000022 EM
22 -0.12512270D+05 0.0201764 0.0000016 EM
23 -0.12512255D+05 0.0148794 0.0000012 EM
24 -0.12512244D+05 0.0109934 0.0000009 EM
25 -0.12512236D+05 0.0081384 0.0000007 EM
26 -0.12512230D+05 0.0060358 0.0000005 EM
27 -0.12512226D+05 0.0044829 0.0000004 EM
28 -0.12512222D+05 0.0033339 0.0000003 EM
29 -0.12512220D+05 0.0024817 0.0000002 EM
30 -0.12512218D+05 0.0018488 0.0000001 EM
31 -0.12512217D+05 0.0013781 0.0000001 EM
32 -0.12512215D+05 0.0010281 0.0000001 EM
33 -0.12512215D+05 0.0007676 0.0000001 EM
34 -0.12512214D+05 0.0005733 0.0000000 EM
35 -0.12512214D+05 0.0004284 0.0000000 EM
36 -0.12512213D+05 0.0003202 0.0000000 EM
37 -0.12512213D+05 0.0002394 0.0000000 EM
38 -0.12512213D+05 0.0001791 0.0000000 EM
39 -0.12512213D+05 0.0001340 0.0000000 EM
40 -0.12512213D+05 0.0001003 0.0000000 EM
41 -0.12512213D+05 0.0000750 0.0000000 EM
42 -0.12512213D+05 0.0000562 0.0000000 EM
43 -0.12512213D+05 0.0000421 0.0000000 EM
44 -0.12512213D+05 0.0000315 0.0000000 EM
45 -0.12512213D+05 0.0000236 0.0000000 EM
Beginning Time: 23:20:44
Ending Time: 23:20:46
Elapsed Time: 00:00:02
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