```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:31 AM

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;

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:  03:31:44
Ending Time:  03:31:46
Elapsed Time:  00:00:02

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
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Copyright (c) 1998-2017 Muthen & Muthen
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