Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:20 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a three-level MIMIC with
continuous factor indicators, two covariates on within,
one covariate on between 2, one covariate on between 3,
and random slopes on both within and between 2
DATA: FILE = ex9.22.dat;
VARIABLE: NAMES = y1-y6 x1 x2 w z level2 level3;
CLUSTER = level3 level2;
WITHIN = x1 x2;
BETWEEN = (level2) w (level3) z;
ANALYSIS: TYPE = THREELEVEL RANDOM;
MODEL: %WITHIN%
fw1 BY y1-y3;
fw2 BY y4-y6;
fw1 ON x1;
s | fw2 ON x2;
%BETWEEN level2%
fb2 BY y1-y6;
sf2 | fb2 ON w;
ss | s ON w;
fb2 WITH s;
%BETWEEN level3%
fb3 BY y1-y6;
fb3 ON z;
s ON z;
sf2 ON z;
ss ON z;
fb3 WITH s sf2 ss;
s WITH sf2 ss;
sf2 WITH ss;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a three-level MIMIC with
continuous factor indicators, two covariates on within,
one covariate on between 2, one covariate on between 3,
and random slopes on both within and between 2
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 7500
Number of dependent variables 6
Number of independent variables 4
Number of continuous latent variables 7
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Observed independent variables
X1 X2 W Z
Continuous latent variables
FW1 FW2 FB2 S FB3 SF2
SS
Variables with special functions
Cluster variables LEVEL3 LEVEL2
Within variables
X1 X2
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)
ex9.22.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
Y1 0.591 0.045 -8.980 0.01% -1.484 -0.015 0.621
7500.000 6.257 0.208 10.821 0.01% 1.230 2.625
Y2 0.579 0.033 -9.214 0.01% -1.473 -0.036 0.542
7500.000 6.175 0.302 9.718 0.01% 1.145 2.600
Y3 0.620 0.074 -10.111 0.01% -1.429 -0.034 0.567
7500.000 6.152 0.192 10.593 0.01% 1.217 2.680
Y4 0.648 0.323 -11.342 0.01% -1.494 -0.045 0.596
7500.000 7.537 1.651 17.621 0.01% 1.228 2.734
Y5 0.528 0.339 -12.802 0.01% -1.656 -0.154 0.449
7500.000 7.378 1.585 18.984 0.01% 1.092 2.683
Y6 0.591 0.250 -11.746 0.01% -1.557 -0.049 0.604
7500.000 7.348 1.541 18.501 0.01% 1.191 2.681
X1 -0.012 -0.003 -4.200 0.01% -0.865 -0.256 -0.002
7500.000 0.998 0.008 3.861 0.01% 0.243 0.834
X2 0.008 0.045 -4.119 0.01% -0.827 -0.250 -0.001
7500.000 0.993 0.011 3.954 0.01% 0.245 0.849
W 0.016 -0.012 -3.947 0.07% -0.787 -0.237 0.012
1500.000 0.996 0.245 3.412 0.07% 0.242 0.835
Z 0.205 0.342 -1.505 2.00% -0.721 -0.071 0.185
50.000 0.840 -0.360 2.528 2.00% 0.481 0.943
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS -0.799D-17. PROBLEM INVOLVING THE FOLLOWING PARAMETER:
Parameter 51, %BETWEEN LEVEL3%: SF2 ON Z
THE NONIDENTIFICATION IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE
NUMBER OF LEVEL 3 CLUSTERS. REDUCE THE NUMBER OF PARAMETERS.
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 62
Loglikelihood
H0 Value -80911.886
H0 Scaling Correction Factor 0.9890
for MLR
Information Criteria
Akaike (AIC) 161947.772
Bayesian (BIC) 162376.977
Sample-Size Adjusted BIC 162179.954
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
FW1 BY
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.016 63.019 0.000
Y3 0.985 0.016 60.476 0.000
FW2 BY
Y4 1.000 0.000 999.000 999.000
Y5 1.003 0.012 80.546 0.000
Y6 1.013 0.013 78.798 0.000
FW1 ON
X1 0.789 0.015 51.328 0.000
FW2 WITH
FW1 -0.017 0.019 -0.880 0.379
Residual Variances
Y1 1.018 0.026 38.878 0.000
Y2 0.944 0.025 37.679 0.000
Y3 1.045 0.022 46.695 0.000
Y4 1.033 0.031 32.829 0.000
Y5 0.990 0.026 38.169 0.000
Y6 0.994 0.025 40.459 0.000
FW1 0.996 0.028 35.262 0.000
FW2 1.005 0.031 32.168 0.000
Between LEVEL2 Level
FB2 BY
Y1 1.000 0.000 999.000 999.000
Y2 1.019 0.022 46.857 0.000
Y3 0.991 0.024 42.156 0.000
Y4 1.039 0.028 36.568 0.000
Y5 1.037 0.023 44.692 0.000
Y6 1.000 0.026 38.127 0.000
FB2 WITH
S 0.017 0.019 0.913 0.361
Residual Variances
Y1 0.492 0.031 15.685 0.000
Y2 0.444 0.035 12.840 0.000
Y3 0.476 0.027 17.356 0.000
Y4 0.491 0.034 14.307 0.000
Y5 0.542 0.031 17.253 0.000
Y6 0.554 0.039 14.222 0.000
FB2 0.455 0.028 16.511 0.000
S 0.610 0.037 16.405 0.000
Between LEVEL3 Level
FB3 BY
Y1 1.000 0.000 999.000 999.000
Y2 0.961 0.152 6.327 0.000
Y3 0.971 0.144 6.745 0.000
Y4 1.008 0.105 9.603 0.000
Y5 0.889 0.125 7.104 0.000
Y6 0.903 0.120 7.509 0.000
FB3 ON
Z 0.757 0.116 6.533 0.000
S ON
Z 0.310 0.079 3.905 0.000
SF2 ON
Z 0.130 0.086 1.513 0.130
SS ON
Z 0.343 0.081 4.218 0.000
FB3 WITH
S 0.025 0.047 0.532 0.595
SF2 0.065 0.049 1.336 0.182
SS -0.036 0.033 -1.088 0.277
S WITH
SF2 0.044 0.050 0.887 0.375
SS 0.047 0.040 1.185 0.236
SF2 WITH
SS 0.018 0.048 0.372 0.710
Intercepts
Y1 0.423 0.104 4.055 0.000
Y2 0.416 0.109 3.823 0.000
Y3 0.457 0.104 4.406 0.000
Y4 0.467 0.098 4.776 0.000
Y5 0.365 0.089 4.121 0.000
Y6 0.427 0.078 5.454 0.000
S 0.222 0.083 2.687 0.007
SF2 1.103 0.093 11.915 0.000
SS 0.446 0.077 5.810 0.000
Residual Variances
Y1 0.300 0.096 3.140 0.002
Y2 0.216 0.066 3.265 0.001
Y3 0.238 0.057 4.163 0.000
Y4 0.135 0.035 3.876 0.000
Y5 0.125 0.033 3.767 0.000
Y6 0.156 0.045 3.494 0.000
FB3 0.242 0.085 2.852 0.004
S 0.318 0.072 4.441 0.000
SF2 0.362 0.066 5.460 0.000
SS 0.221 0.044 5.063 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix -0.799E-17
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y6 X1 X2
________ ________ ________
0 0 0
LAMBDA
FW1 FW2 X1 X2
________ ________ ________ ________
Y1 0 0 0 0
Y2 1 0 0 0
Y3 2 0 0 0
Y4 0 0 0 0
Y5 0 3 0 0
Y6 0 4 0 0
X1 0 0 0 0
X2 0 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 5
Y2 0 6
Y3 0 0 7
Y4 0 0 0 8
Y5 0 0 0 0 9
Y6 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
Y6 X1 X2
________ ________ ________
Y6 10
X1 0 0
X2 0 0 0
ALPHA
FW1 FW2 X1 X2
________ ________ ________ ________
0 0 0 0
BETA
FW1 FW2 X1 X2
________ ________ ________ ________
FW1 0 0 11 0
FW2 0 0 0 0
X1 0 0 0 0
X2 0 0 0 0
PSI
FW1 FW2 X1 X2
________ ________ ________ ________
FW1 12
FW2 13 14
X1 0 0 0
X2 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y6 W
________ ________
0 0
LAMBDA
FB2 S%B2 W
________ ________ ________
Y1 0 0 0
Y2 15 0 0
Y3 16 0 0
Y4 17 0 0
Y5 18 0 0
Y6 19 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 20
Y2 0 21
Y3 0 0 22
Y4 0 0 0 23
Y5 0 0 0 0 24
Y6 0 0 0 0 0
W 0 0 0 0 0
THETA
Y6 W
________ ________
Y6 25
W 0 0
ALPHA
FB2 S%B2 W
________ ________ ________
0 0 0
BETA
FB2 S%B2 W
________ ________ ________
FB2 0 0 0
S%B2 0 0 0
W 0 0 0
PSI
FB2 S%B2 W
________ ________ ________
FB2 26
S%B2 27 28
W 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
29 30 31 32 33
NU
Y6 Z
________ ________
34 0
LAMBDA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 35 0 0 0 0
Y3 36 0 0 0 0
Y4 37 0 0 0 0
Y5 38 0 0 0 0
Y6 39 0 0 0 0
Z 0 0 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 40
Y2 0 41
Y3 0 0 42
Y4 0 0 0 43
Y5 0 0 0 0 44
Y6 0 0 0 0 0
Z 0 0 0 0 0
THETA
Y6 Z
________ ________
Y6 45
Z 0 0
ALPHA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
0 46 47 48 0
BETA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0 0 0 0 49
S%B3 0 0 0 0 50
SF2 0 0 0 0 51
SS 0 0 0 0 52
Z 0 0 0 0 0
PSI
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 53
S%B3 54 55
SF2 56 57 58
SS 59 60 61 62
Z 0 0 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 X1 X2
________ ________ ________
0.000 0.000 0.000
LAMBDA
FW1 FW2 X1 X2
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000
Y5 0.000 1.000 0.000 0.000
Y6 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
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 3.129
Y2 0.000 3.088
Y3 0.000 0.000 3.076
Y4 0.000 0.000 0.000 3.769
Y5 0.000 0.000 0.000 0.000 3.689
Y6 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
Y6 X1 X2
________ ________ ________
Y6 3.674
X1 0.000 0.000
X2 0.000 0.000 0.000
ALPHA
FW1 FW2 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
FW1 FW2 X1 X2
________ ________ ________ ________
FW1 0.000 0.000 0.000 0.000
FW2 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
FW1 FW2 X1 X2
________ ________ ________ ________
FW1 0.050
FW2 0.000 0.050
X1 0.000 0.000 0.499
X2 0.000 0.000 0.000 0.497
STARTING VALUES FOR BETWEEN LEVEL2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6 W
________ ________
0.000 0.000
LAMBDA
FB2 S%B2 W
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 1.000 0.000 0.000
Y5 1.000 0.000 0.000
Y6 1.000 0.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 3.129
Y2 0.000 3.088
Y3 0.000 0.000 3.076
Y4 0.000 0.000 0.000 3.769
Y5 0.000 0.000 0.000 0.000 3.689
Y6 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
THETA
Y6 W
________ ________
Y6 3.674
W 0.000 0.000
ALPHA
FB2 S%B2 W
________ ________ ________
0.000 0.000 0.000
BETA
FB2 S%B2 W
________ ________ ________
FB2 0.000 0.000 0.000
S%B2 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
FB2 S%B2 W
________ ________ ________
FB2 0.050
S%B2 0.000 1.000
W 0.000 0.000 0.498
STARTING VALUES FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.591 0.579 0.620 0.648 0.528
NU
Y6 Z
________ ________
0.591 0.000
LAMBDA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000 0.000
Y5 1.000 0.000 0.000 0.000 0.000
Y6 1.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 3.129
Y2 0.000 3.088
Y3 0.000 0.000 3.076
Y4 0.000 0.000 0.000 3.769
Y5 0.000 0.000 0.000 0.000 3.689
Y6 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Z
________ ________
Y6 3.674
Z 0.000 0.000
ALPHA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.000 0.000 0.000 0.000 0.000
S%B3 0.000 0.000 0.000 0.000 0.000
SF2 0.000 0.000 0.000 0.000 0.000
SS 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
PSI
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.050
S%B3 0.000 1.000
SF2 0.000 0.000 1.000
SS 0.000 0.000 0.000 1.000
Z 0.000 0.000 0.000 0.000 0.420
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.92332101D+05 0.0000000 0.0000000 EM
2 -0.82319921D+05 ************ 0.1084366 EM
3 -0.81093001D+05 1226.9206591 0.0149043 EM
4 -0.80954553D+05 138.4478685 0.0017073 EM
5 -0.80925422D+05 29.1303221 0.0003598 EM
6 -0.80916610D+05 8.8123365 0.0001089 EM
7 -0.80913612D+05 2.9980612 0.0000371 EM
8 -0.80912536D+05 1.0757368 0.0000133 EM
9 -0.80912137D+05 0.3993450 0.0000049 EM
10 -0.80911985D+05 0.1521575 0.0000019 EM
11 -0.80911926D+05 0.0592601 0.0000007 EM
12 -0.80911902D+05 0.0235604 0.0000003 EM
13 -0.80911892D+05 0.0095357 0.0000001 EM
14 -0.80911889D+05 0.0039312 0.0000000 EM
15 -0.80911887D+05 0.0016486 0.0000000 EM
16 -0.80911886D+05 0.0007044 0.0000000 EM
Beginning Time: 23:20:54
Ending Time: 23:20:57
Elapsed Time: 00:00:03
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen