```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:53 AM

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;

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
(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:  04:53:56
Ending Time:  04:53:58
Elapsed Time:  00:00:02

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