Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  11:19 PM

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



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             W             Z
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 W                  0             0             0
 Z                  0             0             0             0


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              X             W             Z
              ________      ________      ________
 1                  0             0             0


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              0             0             0             0             0
 S1%B3              0             0             0             0             0
 S2                 0             0             0             0             0
 S12                0             0             0             0             0
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2              0             0             0
 S1%B3              0             0             0
 S2                 0             0             0
 S12                0             0             0
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              0
 S1%B3              0             0
 S2                 0             0             0
 S12                0             0             0             0
 Y                  0             0             0             0             1
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              X             W             Z
              ________      ________      ________
 X                  0
 W                  0             0
 Z                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2


           NU
              Y             X             W             Z
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 W                  0             0             0
 Z                  0             0             0             0


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              X             W             Z
              ________      ________      ________
 1                  0             0             0


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              0             0             0             0             0
 S1%B3              0             0             0             0             0
 S2                 0             0             0             0             0
 S12                0             0             0             0             0
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2              0             0             0
 S1%B3              0             0             0
 S2                 0             0             0
 S12                0             0             0
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              2
 S1%B3              0             0
 S2                 0             0             0
 S12                0             0             0             0
 Y                  3             0             0             0             4
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              X             W             Z
              ________      ________      ________
 X                  0
 W                  0             0
 Z                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL3


           NU
              Y             X             W             Z
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y                  0             0             0
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 W                  0             0             0
 Z                  0             0             0             0


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1                  0             5             6             7             8


           ALPHA
              X             W             Z
              ________      ________      ________
 1                  0             0             0


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              0             0             0             0             0
 S1%B3              0             0             0             0             0
 S2                 0             0             0             0             0
 S12                0             0             0             0             0
 Y                  0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2              0             0             0
 S1%B3              0             0             9
 S2                 0             0            10
 S12                0             0            11
 Y                  0             0            12
 X                  0             0             0
 W                  0             0             0
 Z                  0             0             0


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2              0
 S1%B3              0            13
 S2                 0            14            15
 S12                0            16            17            18
 Y                  0            19            20            21            22
 X                  0             0             0             0             0
 W                  0             0             0             0             0
 Z                  0             0             0             0             0


           PSI
              X             W             Z
              ________      ________      ________
 X                  0
 W                  0             0
 Z                  0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y             X             W             Z
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y              0.000         0.000         0.000
 X              1.000         0.000         0.000
 W              0.000         1.000         0.000
 Z              0.000         0.000         1.000


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              X             W             Z
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          0.000         0.000         0.000         0.000         0.000
 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
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2          0.000         0.000         0.000
 S1%B3          0.000         0.000         0.000
 S2             0.000         0.000         0.000
 S12            0.000         0.000         0.000
 Y              0.000         0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          0.000
 S1%B3          0.000         0.000
 S2             0.000         0.000         0.000
 S12            0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         2.090
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              X             W             Z
              ________      ________      ________
 X              0.499
 W              0.000         0.000
 Z              0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL2


           NU
              Y             X             W             Z
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y              0.000         0.000         0.000
 X              1.000         0.000         0.000
 W              0.000         1.000         0.000
 Z              0.000         0.000         1.000


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              X             W             Z
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          0.000         0.000         0.000         0.000         0.000
 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
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2          0.000         0.000         0.000
 S1%B3          0.000         0.000         0.000
 S2             0.000         0.000         0.000
 S12            0.000         0.000         0.000
 Y              0.000         0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          1.000
 S1%B3          0.000         0.000
 S2             0.000         0.000         0.000
 S12            0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         2.090
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              X             W             Z
              ________      ________      ________
 X              0.000
 W              0.000         0.125
 Z              0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN LEVEL3


           NU
              Y             X             W             Z
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X             W             Z
              ________      ________      ________
 Y              0.000         0.000         0.000
 X              1.000         0.000         0.000
 W              0.000         1.000         0.000
 Z              0.000         0.000         1.000


           THETA
              Y             X             W             Z
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000


           ALPHA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.900


           ALPHA
              X             W             Z
              ________      ________      ________
 1              0.000         0.000         0.000


           BETA
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          0.000         0.000         0.000         0.000         0.000
 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
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           BETA
              X             W             Z
              ________      ________      ________
 S1%B2          0.000         0.000         0.000
 S1%B3          0.000         0.000         0.000
 S2             0.000         0.000         0.000
 S12            0.000         0.000         0.000
 Y              0.000         0.000         0.000
 X              0.000         0.000         0.000
 W              0.000         0.000         0.000
 Z              0.000         0.000         0.000


           PSI
              S1%B2         S1%B3         S2            S12           Y
              ________      ________      ________      ________      ________
 S1%B2          0.000
 S1%B3          0.000         1.000
 S2             0.000         0.000         1.000
 S12            0.000         0.000         0.000         1.000
 Y              0.000         0.000         0.000         0.000         2.090
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              X             W             Z
              ________      ________      ________
 X              0.000
 W              0.000         0.000
 Z              0.000         0.000         0.496


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.13687480D+05    0.0000000    0.0000000  EM
              2 -0.12799660D+05  887.8204842    0.0648637  EM
              3 -0.12599997D+05  199.6622997    0.0155990  EM
              4 -0.12551839D+05   48.1586552    0.0038221  EM
              5 -0.12534343D+05   17.4955441    0.0013939  EM
              6 -0.12525736D+05    8.6074434    0.0006867  EM
              7 -0.12520885D+05    4.8503759    0.0003872  EM
              8 -0.12517957D+05    2.9288000    0.0002339  EM
              9 -0.12516108D+05    1.8491270    0.0001477  EM
             10 -0.12514902D+05    1.2060083    0.0000964  EM
             11 -0.12514095D+05    0.8062991    0.0000644  EM
             12 -0.12513546D+05    0.5496893    0.0000439  EM
             13 -0.12513165D+05    0.3805932    0.0000304  EM
             14 -0.12512898D+05    0.2668782    0.0000213  EM
             15 -0.12512709D+05    0.1890616    0.0000151  EM
             16 -0.12512574D+05    0.1350909    0.0000108  EM
             17 -0.12512477D+05    0.0972188    0.0000078  EM
             18 -0.12512406D+05    0.0703768    0.0000056  EM
             19 -0.12512355D+05    0.0512004    0.0000041  EM
             20 -0.12512318D+05    0.0374076    0.0000030  EM
             21 -0.12512290D+05    0.0274285    0.0000022  EM
             22 -0.12512270D+05    0.0201767    0.0000016  EM
             23 -0.12512255D+05    0.0148793    0.0000012  EM
             24 -0.12512244D+05    0.0109938    0.0000009  EM
             25 -0.12512236D+05    0.0081386    0.0000007  EM
             26 -0.12512230D+05    0.0060389    0.0000005  EM
             27 -0.12512226D+05    0.0044821    0.0000004  EM
             28 -0.12512222D+05    0.0033332    0.0000003  EM
             29 -0.12512220D+05    0.0024817    0.0000002  EM
             30 -0.12512218D+05    0.0018485    0.0000001  EM
             31 -0.12512217D+05    0.0013779    0.0000001  EM
             32 -0.12512215D+05    0.0010280    0.0000001  EM
             33 -0.12512215D+05    0.0007675    0.0000001  EM
             34 -0.12512214D+05    0.0005732    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    0.0001002    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:  23:19:27
        Ending Time:  23:19:30
       Elapsed Time:  00:00:03



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