Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 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
montecarlo:
names are y1-y6 x1 x2 w z;
nobservations = 7500;
nreps = 1;
CSIZES = 50[30(5)];
ncsize = 1[1];
save = ex9.22.dat;
WITHIN = x1 x2;
BETWEEN = (level2) w (level3) z;
ANALYSIS: TYPE = THREELEVEL RANDOM;
MODEL POPULATION:
%WITHIN%
x1-x2@1;
fw1 BY y1@1 y2-y3*1;
fw2 BY y4@1 y5-y6*1;
fw1 on x1*.8;
s | fw2 ON x2;
fw1-fw2*1;
fw1 with fw2*0;
y1-y6*1;
%BETWEEN Level2%
w@1;
fb2 BY y1@1 y2-y6*1;
y1-y6*.5;
fb2*.5;
sf2 | fb2 on w;
ss | s on w;
s*.6;
fb2 with s*0;
%Between Level3%
z@1;
fb3 BY y1@1 y2-y6*1;
fb3 ON z*.5;
fb3*.3;
s ON z*.3;
s*.3;
sf2 ON z*.2;
sf2*.3;
ss ON z*.3;
ss*.3;
fb3 with s*0;
fb3 with sf2*0;
fb3 with ss*0;
s with sf2*0;
s with ss*0;
sf2 with ss*0;
[s*.2];
[sf2*1];
[ss*.5];
y1-y6*.2;
[y1-y6*.5];
MODEL:
%WITHIN%
! x1-x2@1;
fw1 BY y1@1 y2-y3*1;
fw2 BY y4@1 y5-y6*1;
fw1 on x1*.8;
s | fw2 ON x2;
fw1-fw2*1;
fw1 with fw2*0;
y1-y6*1;
%BETWEEN Level2%
! w@1;
fb2 BY y1@1 y2-y6*1;
y1-y6*.5;
fb2*.5;
sf2 | fb2 on w;
ss | s on w;
s*.6;
fb2 with s*0;
%Between Level3%
! z@1;
fb3 BY y1@1 y2-y6*1;
fb3 ON z*.5;
fb3*.3;
s ON z*.3;
s*.3;
sf2 ON z*.2;
sf2*.3;
ss ON z*.3;
ss*.3;
fb3 with s*0;
fb3 with sf2*0;
fb3 with ss*0;
s with sf2*0;
s with ss*0;
sf2 with ss*0;
[s*.2];
[sf2*1];
[ss*.5];
y1-y6*.2;
[y1-y6*.5];
output:
tech8 tech9;
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 replications
Requested 1
Completed 1
Value of seed 0
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
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
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 Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y1 0.414 Y2 0.431 Y3 0.417
Y4 0.367 Y5 0.384 Y6 0.365
Average cluster size for LEVEL3 level 150.000
Estimated Intraclass Correlations for the Y Variables for LEVEL3 level
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y1 0.164 Y2 0.150 Y3 0.154
Y4 0.121 Y5 0.097 Y6 0.102
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
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
Means
Y6 X1 X2 W Z
________ ________ ________ ________ ________
0.000 -0.012 0.008 0.000 0.000
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.641
Y2 1.620 2.559
Y3 1.603 1.584 2.615
Y4 -0.027 -0.022 -0.019 3.842
Y5 -0.036 -0.022 -0.046 2.811 3.806
Y6 -0.030 -0.053 -0.027 2.851 2.846
X1 0.779 0.792 0.776 -0.006 -0.010
X2 -0.003 -0.007 -0.001 0.319 0.293
W 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
Covariances
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 3.875
X1 -0.025 0.998
X2 0.296 -0.009 0.993
W 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.623 1.000
Y3 0.610 0.612 1.000
Y4 -0.009 -0.007 -0.006 1.000
Y5 -0.011 -0.007 -0.015 0.735 1.000
Y6 -0.009 -0.017 -0.008 0.739 0.741
X1 0.480 0.496 0.480 -0.003 -0.005
X2 -0.002 -0.005 -0.001 0.163 0.151
W 0.000 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
Correlations
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 1.000
X1 -0.013 1.000
X2 0.151 -0.009 1.000
W 0.000 0.000 0.000 0.000
Z 0.000 0.000 0.000 0.000 0.000
ESTIMATED SAMPLE STATISTICS FOR BETWEEN LEVEL2
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
Means
Y6 X1 X2 W Z
________ ________ ________ ________ ________
0.000 0.000 0.000 0.016 0.000
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.588
Y2 2.143 2.640
Y3 2.062 2.149 2.545
Y4 2.219 2.190 2.186 2.751
Y5 2.202 2.207 2.205 2.268 2.815
Y6 2.117 2.157 2.117 2.168 2.177
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 1.138 1.159 1.095 1.168 1.171
Z 0.000 0.000 0.000 0.000 0.000
Covariances
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 2.648
X1 0.000 0.000
X2 0.000 0.000 0.000
W 1.143 0.000 0.000 0.996
Z 0.000 0.000 0.000 0.000 0.000
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.820 1.000
Y3 0.803 0.829 1.000
Y4 0.832 0.812 0.826 1.000
Y5 0.816 0.810 0.824 0.815 1.000
Y6 0.809 0.816 0.815 0.803 0.797
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.708 0.715 0.687 0.705 0.699
Z 0.000 0.000 0.000 0.000 0.000
Correlations
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 1.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.704 0.000 0.000 1.000
Z 0.000 0.000 0.000 0.000 0.000
ESTIMATED SAMPLE STATISTICS FOR BETWEEN LEVEL3
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.591 0.579 0.620 0.648 0.528
Means
Y6 X1 X2 W Z
________ ________ ________ ________ ________
0.591 0.000 0.000 0.000 0.205
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.023
Y2 0.686 0.921
Y3 0.698 0.765 0.937
Y4 0.812 0.691 0.676 0.909
Y5 0.651 0.699 0.618 0.685 0.714
Y6 0.629 0.613 0.627 0.684 0.572
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
Z 0.652 0.584 0.652 0.638 0.519
Covariances
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 0.737
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
Z 0.659 0.000 0.000 0.000 0.840
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.707 1.000
Y3 0.714 0.824 1.000
Y4 0.842 0.755 0.732 1.000
Y5 0.762 0.862 0.756 0.850 1.000
Y6 0.724 0.744 0.754 0.836 0.789
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
Z 0.703 0.664 0.735 0.730 0.670
Correlations
Y6 X1 X2 W Z
________ ________ ________ ________ ________
Y6 1.000
X1 0.000 0.000
X2 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
Z 0.837 0.000 0.000 0.000 1.000
MODEL FIT INFORMATION
Number of Free Parameters 62
Loglikelihood
H0 Value
Mean -80911.886
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -80911.886 -80911.886
0.980 0.000 -80911.886 -80911.886
0.950 0.000 -80911.886 -80911.886
0.900 0.000 -80911.886 -80911.886
0.800 0.000 -80911.886 -80911.886
0.700 0.000 -80911.886 -80911.886
0.500 0.000 -80911.886 -80911.886
0.300 0.000 -80911.886 -80911.886
0.200 0.000 -80911.886 -80911.886
0.100 0.000 -80911.886 -80911.886
0.050 0.000 -80911.886 -80911.886
0.020 0.000 -80911.886 -80911.886
0.010 0.000 -80911.886 -80911.886
Information Criteria
Akaike (AIC)
Mean 161947.773
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 161947.773 161947.773
0.980 0.000 161947.773 161947.773
0.950 0.000 161947.773 161947.773
0.900 0.000 161947.773 161947.773
0.800 0.000 161947.773 161947.773
0.700 0.000 161947.773 161947.773
0.500 0.000 161947.773 161947.773
0.300 0.000 161947.773 161947.773
0.200 0.000 161947.773 161947.773
0.100 0.000 161947.773 161947.773
0.050 0.000 161947.773 161947.773
0.020 0.000 161947.773 161947.773
0.010 0.000 161947.773 161947.773
Bayesian (BIC)
Mean 162376.977
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 162376.977 162376.977
0.980 0.000 162376.977 162376.977
0.950 0.000 162376.977 162376.977
0.900 0.000 162376.977 162376.977
0.800 0.000 162376.977 162376.977
0.700 0.000 162376.977 162376.977
0.500 0.000 162376.977 162376.977
0.300 0.000 162376.977 162376.977
0.200 0.000 162376.977 162376.977
0.100 0.000 162376.977 162376.977
0.050 0.000 162376.977 162376.977
0.020 0.000 162376.977 162376.977
0.010 0.000 162376.977 162376.977
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 162179.955
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 162179.955 162179.955
0.980 0.000 162179.955 162179.955
0.950 0.000 162179.955 162179.955
0.900 0.000 162179.955 162179.955
0.800 0.000 162179.955 162179.955
0.700 0.000 162179.955 162179.955
0.500 0.000 162179.955 162179.955
0.300 0.000 162179.955 162179.955
0.200 0.000 162179.955 162179.955
0.100 0.000 162179.955 162179.955
0.050 0.000 162179.955 162179.955
0.020 0.000 162179.955 162179.955
0.010 0.000 162179.955 162179.955
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
FW1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0004 0.0000 0.0159 0.0000 1.000 1.000
Y3 1.000 0.9850 0.0000 0.0163 0.0002 1.000 1.000
FW2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 1.000 1.0026 0.0000 0.0124 0.0000 1.000 1.000
Y6 1.000 1.0127 0.0000 0.0129 0.0002 1.000 1.000
FW1 ON
X1 0.800 0.7886 0.0000 0.0154 0.0001 1.000 1.000
FW1 WITH
FW2 0.000 -0.0168 0.0000 0.0191 0.0003 1.000 0.000
Residual Variances
Y1 1.000 1.0182 0.0000 0.0262 0.0003 1.000 1.000
Y2 1.000 0.9443 0.0000 0.0251 0.0031 0.000 1.000
Y3 1.000 1.0455 0.0000 0.0224 0.0021 0.000 1.000
Y4 1.000 1.0329 0.0000 0.0315 0.0011 1.000 1.000
Y5 1.000 0.9903 0.0000 0.0259 0.0001 1.000 1.000
Y6 1.000 0.9940 0.0000 0.0246 0.0000 1.000 1.000
FW1 1.000 0.9964 0.0000 0.0283 0.0000 1.000 1.000
FW2 1.000 1.0050 0.0000 0.0313 0.0000 1.000 1.000
Between LEVEL2 Level
FB2 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0184 0.0000 0.0217 0.0003 1.000 1.000
Y3 1.000 0.9907 0.0000 0.0235 0.0001 1.000 1.000
Y4 1.000 1.0382 0.0000 0.0284 0.0015 1.000 1.000
Y5 1.000 1.0360 0.0000 0.0232 0.0013 1.000 1.000
Y6 1.000 0.9996 0.0000 0.0262 0.0000 1.000 1.000
FB2 WITH
S 0.000 0.0175 0.0000 0.0191 0.0003 1.000 0.000
Residual Variances
Y1 0.500 0.4921 0.0000 0.0314 0.0001 1.000 1.000
Y2 0.500 0.4434 0.0000 0.0345 0.0032 1.000 1.000
Y3 0.500 0.4757 0.0000 0.0274 0.0006 1.000 1.000
Y4 0.500 0.4909 0.0000 0.0343 0.0001 1.000 1.000
Y5 0.500 0.5415 0.0000 0.0314 0.0017 1.000 1.000
Y6 0.500 0.5535 0.0000 0.0389 0.0029 1.000 1.000
FB2 0.500 0.4551 0.0000 0.0275 0.0020 1.000 1.000
S 0.600 0.6090 0.0000 0.0371 0.0001 1.000 1.000
Between LEVEL3 Level
FB3 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 0.9612 0.0000 0.1519 0.0015 1.000 1.000
Y3 1.000 0.9706 0.0000 0.1439 0.0009 1.000 1.000
Y4 1.000 1.0076 0.0000 0.1049 0.0001 1.000 1.000
Y5 1.000 0.8890 0.0000 0.1251 0.0123 1.000 1.000
Y6 1.000 0.9028 0.0000 0.1202 0.0094 1.000 1.000
FB3 ON
Z 0.500 0.7568 0.0000 0.1159 0.0659 0.000 1.000
S ON
Z 0.300 0.3103 0.0000 0.0795 0.0001 1.000 1.000
SF2 ON
Z 0.200 0.1300 0.0000 0.0859 0.0049 1.000 0.000
SS ON
Z 0.300 0.3434 0.0000 0.0814 0.0019 1.000 1.000
FB3 WITH
S 0.000 0.0249 0.0000 0.0468 0.0006 1.000 0.000
SF2 0.000 0.0654 0.0000 0.0490 0.0043 1.000 0.000
SS 0.000 -0.0362 0.0000 0.0332 0.0013 1.000 0.000
S WITH
SF2 0.000 0.0445 0.0000 0.0502 0.0020 1.000 0.000
SS 0.000 0.0473 0.0000 0.0400 0.0022 1.000 0.000
SF2 WITH
SS 0.000 0.0177 0.0000 0.0476 0.0003 1.000 0.000
Intercepts
Y1 0.500 0.4232 0.0000 0.1044 0.0059 1.000 1.000
Y2 0.500 0.4161 0.0000 0.1088 0.0070 1.000 1.000
Y3 0.500 0.4569 0.0000 0.1037 0.0019 1.000 1.000
Y4 0.500 0.4668 0.0000 0.0978 0.0011 1.000 1.000
Y5 0.500 0.3649 0.0000 0.0885 0.0183 1.000 1.000
Y6 0.500 0.4271 0.0000 0.0783 0.0053 1.000 1.000
S 0.200 0.2218 0.0000 0.0825 0.0005 1.000 1.000
SF2 1.000 1.1035 0.0000 0.0925 0.0107 1.000 1.000
SS 0.500 0.4459 0.0000 0.0768 0.0029 1.000 1.000
Residual Variances
Y1 0.200 0.3005 0.0000 0.0957 0.0101 1.000 1.000
Y2 0.200 0.2161 0.0000 0.0662 0.0003 1.000 1.000
Y3 0.200 0.2380 0.0000 0.0572 0.0014 1.000 1.000
Y4 0.200 0.1350 0.0000 0.0348 0.0042 1.000 1.000
Y5 0.200 0.1254 0.0000 0.0333 0.0056 0.000 1.000
Y6 0.200 0.1556 0.0000 0.0445 0.0020 1.000 1.000
FB3 0.300 0.2424 0.0000 0.0850 0.0033 1.000 1.000
S 0.300 0.3184 0.0000 0.0717 0.0003 1.000 1.000
SF2 0.300 0.3619 0.0000 0.0663 0.0038 1.000 1.000
SS 0.300 0.2209 0.0000 0.0436 0.0063 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix -0.245E-16
(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 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
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 1.000
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 0.800 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 1.000
FW2 0.000 1.000
X1 0.000 0.000 0.500
X2 0.000 0.000 0.000 0.500
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 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
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 0.500
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 0.500
S%B2 0.000 0.600
W 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
NU
Y6 Z
________ ________
0.500 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 0.200
Y2 0.000 0.200
Y3 0.000 0.000 0.200
Y4 0.000 0.000 0.000 0.200
Y5 0.000 0.000 0.000 0.000 0.200
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 0.200
Z 0.000 0.000
ALPHA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
0.000 0.200 1.000 0.500 0.000
BETA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.000 0.000 0.000 0.000 0.500
S%B3 0.000 0.000 0.000 0.000 0.300
SF2 0.000 0.000 0.000 0.000 0.200
SS 0.000 0.000 0.000 0.000 0.300
Z 0.000 0.000 0.000 0.000 0.000
PSI
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.300
S%B3 0.000 0.300
SF2 0.000 0.000 0.300
SS 0.000 0.000 0.000 0.300
Z 0.000 0.000 0.000 0.000 0.500
POPULATION 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 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 1.000
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 1.000
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 0.800 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 1.000
FW2 0.000 1.000
X1 0.000 0.000 1.000
X2 0.000 0.000 0.000 1.000
POPULATION 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 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.500
Y5 0.000 0.000 0.000 0.000 0.500
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 0.500
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 0.500
S%B2 0.000 0.600
W 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN LEVEL3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.500 0.500 0.500 0.500 0.500
NU
Y6 Z
________ ________
0.500 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 0.200
Y2 0.000 0.200
Y3 0.000 0.000 0.200
Y4 0.000 0.000 0.000 0.200
Y5 0.000 0.000 0.000 0.000 0.200
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 0.200
Z 0.000 0.000
ALPHA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
0.000 0.200 1.000 0.500 0.000
BETA
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.000 0.000 0.000 0.000 0.500
S%B3 0.000 0.000 0.000 0.000 0.300
SF2 0.000 0.000 0.000 0.000 0.200
SS 0.000 0.000 0.000 0.000 0.300
Z 0.000 0.000 0.000 0.000 0.000
PSI
FB3 S%B3 SF2 SS Z
________ ________ ________ ________ ________
FB3 0.300
S%B3 0.000 0.300
SF2 0.000 0.000 0.300
SS 0.000 0.000 0.000 0.300
Z 0.000 0.000 0.000 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.80942857D+05 0.0000000 0.0000000 EM
2 -0.80914719D+05 28.1373777 0.0003476 EM
3 -0.80912619D+05 2.1001257 0.0000260 EM
4 -0.80912153D+05 0.4659906 0.0000058 EM
5 -0.80911996D+05 0.1568697 0.0000019 EM
6 -0.80911935D+05 0.0617190 0.0000008 EM
7 -0.80911908D+05 0.0263382 0.0000003 EM
8 -0.80911897D+05 0.0118726 0.0000001 EM
9 -0.80911891D+05 0.0055632 0.0000001 EM
10 -0.80911888D+05 0.0026834 0.0000000 EM
11 -0.80911887D+05 0.0013241 0.0000000 EM
12 -0.80911886D+05 0.0006611 0.0000000 EM
TECHNICAL 8 OUTPUT FOR THE H1 MODEL FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.86223729D+05 0.0000000 0.0000000 EM
2 -0.83090063D+05 3133.6659335 0.0363434 EM
3 -0.83033853D+05 56.2100228 0.0006765 EM
4 -0.83030450D+05 3.4036723 0.0000410 EM
5 -0.83029747D+05 0.7024601 0.0000085 EM
6 -0.83029400D+05 0.3470544 0.0000042 EM
7 -0.83029171D+05 0.2289480 0.0000028 EM
8 -0.83029002D+05 0.1685819 0.0000020 EM
9 -0.83028871D+05 0.1310398 0.0000016 EM
10 -0.83028766D+05 0.1051619 0.0000013 EM
11 -0.83028680D+05 0.0862198 0.0000010 EM
12 -0.83028608D+05 0.0717973 0.0000009 EM
13 -0.83028548D+05 0.0604983 0.0000007 EM
14 -0.83028496D+05 0.0514504 0.0000006 EM
15 -0.83028452D+05 0.0440780 0.0000005 EM
16 -0.83028414D+05 0.0379861 0.0000005 EM
17 -0.83028381D+05 0.0328949 0.0000004 EM
18 -0.83028353D+05 0.0286002 0.0000003 EM
19 -0.83028328D+05 0.0249498 0.0000003 EM
20 -0.83028306D+05 0.0218275 0.0000003 EM
21 -0.83028287D+05 0.0191426 0.0000002 EM
22 -0.83028270D+05 0.0168237 0.0000002 EM
23 -0.83028255D+05 0.0148134 0.0000002 EM
24 -0.83028242D+05 0.0130648 0.0000002 EM
25 -0.83028231D+05 0.0115397 0.0000001 EM
26 -0.83028220D+05 0.0102062 0.0000001 EM
27 -0.83028211D+05 0.0090377 0.0000001 EM
28 -0.83028203D+05 0.0080118 0.0000001 EM
29 -0.83028196D+05 0.0071095 0.0000001 EM
30 -0.83028190D+05 0.0063147 0.0000001 EM
31 -0.83028184D+05 0.0056135 0.0000001 EM
32 -0.83028179D+05 0.0049942 0.0000001 EM
33 -0.83028175D+05 0.0044464 0.0000001 EM
34 -0.83028171D+05 0.0039615 0.0000000 EM
35 -0.83028167D+05 0.0035317 0.0000000 EM
36 -0.83028164D+05 0.0031504 0.0000000 EM
37 -0.83028161D+05 0.0028119 0.0000000 EM
38 -0.83028159D+05 0.0025111 0.0000000 EM
39 -0.83028157D+05 0.0022435 0.0000000 EM
40 -0.83028155D+05 0.0020054 0.0000000 EM
41 -0.83028153D+05 0.0017934 0.0000000 EM
42 -0.83028151D+05 0.0016044 0.0000000 EM
43 -0.83028150D+05 0.0014359 0.0000000 EM
44 -0.83028149D+05 0.0012855 0.0000000 EM
45 -0.83028147D+05 0.0011513 0.0000000 EM
46 -0.83028146D+05 0.0010315 0.0000000 EM
47 -0.83028145D+05 0.0009244 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
REPLICATION 1:
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 -0.245D-16. 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.
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
X1
X2
W
Z
LEVEL2
LEVEL3
Save file
ex9.22.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:04
Ending Time: 22:27:09
Elapsed Time: 00:00:05
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