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;



INPUT READING TERMINATED NORMALLY



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



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