Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:03 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a random coefficient
  	regression
  MONTECARLO:			
  	NAMES = y x1 x2;
  	NOBSERVATIONS = 500;
  	NREPS = 1;
  	SEED = 53487;
  	SAVE = ex3.9.dat;
  ANALYSIS:
  	TYPE = RANDOM;
  MODEL POPULATION:
  	x1-x2@1; x1 with x2*.25;
  	s | y ON x1;	
  	[y*.5]; y*.8;
  	[s*1]; s*.9;
  	s with y*.5;
  	y ON x2*.6;
  	s ON x2*.3;	
  MODEL:

  	s | y ON x1;	
  	[y*.5]; y*.8;
  	[s*1]; s*.9;
  	s with y*.5;
  	y ON x2*.6;
  	s ON x2*.3;	
  OUTPUT:
  	TECH8 TECH9;




INPUT READING TERMINATED NORMALLY



this is an example of a random coefficient
regression

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                53487

Number of dependent variables                                    1
Number of independent variables                                  2
Number of continuous latent variables                            1

Observed dependent variables

  Continuous
   Y

Observed independent variables
   X1          X2

Continuous latent variables
   S


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
Optimization algorithm                                         EMA


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     ESTIMATED SAMPLE STATISTICS


           Means
              Y             X1            X2
              ________      ________      ________
 1              0.582         0.026         0.005


           Covariances
              Y             X1            X2
              ________      ________      ________
 Y              3.455
 X1             1.062         0.940
 X2             0.897         0.295         1.117


           Correlations
              Y             X1            X2
              ________      ________      ________
 Y              1.000
 X1             0.589         1.000
 X2             0.457         0.288         1.000




MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

    H0 Value

        Mean                              -786.119
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         -786.119       -786.119
           0.980       0.000         -786.119       -786.119
           0.950       0.000         -786.119       -786.119
           0.900       0.000         -786.119       -786.119
           0.800       0.000         -786.119       -786.119
           0.700       0.000         -786.119       -786.119
           0.500       0.000         -786.119       -786.119
           0.300       0.000         -786.119       -786.119
           0.200       0.000         -786.119       -786.119
           0.100       0.000         -786.119       -786.119
           0.050       0.000         -786.119       -786.119
           0.020       0.000         -786.119       -786.119
           0.010       0.000         -786.119       -786.119

Information Criteria

    Akaike (AIC)

        Mean                              1586.238
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1586.238       1586.238
           0.980       0.000         1586.238       1586.238
           0.950       0.000         1586.238       1586.238
           0.900       0.000         1586.238       1586.238
           0.800       0.000         1586.238       1586.238
           0.700       0.000         1586.238       1586.238
           0.500       0.000         1586.238       1586.238
           0.300       0.000         1586.238       1586.238
           0.200       0.000         1586.238       1586.238
           0.100       0.000         1586.238       1586.238
           0.050       0.000         1586.238       1586.238
           0.020       0.000         1586.238       1586.238
           0.010       0.000         1586.238       1586.238

    Bayesian (BIC)

        Mean                              1615.740
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1615.740       1615.740
           0.980       0.000         1615.740       1615.740
           0.950       0.000         1615.740       1615.740
           0.900       0.000         1615.740       1615.740
           0.800       0.000         1615.740       1615.740
           0.700       0.000         1615.740       1615.740
           0.500       0.000         1615.740       1615.740
           0.300       0.000         1615.740       1615.740
           0.200       0.000         1615.740       1615.740
           0.100       0.000         1615.740       1615.740
           0.050       0.000         1615.740       1615.740
           0.020       0.000         1615.740       1615.740
           0.010       0.000         1615.740       1615.740

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              1593.522
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         1593.522       1593.522
           0.980       0.000         1593.522       1593.522
           0.950       0.000         1593.522       1593.522
           0.900       0.000         1593.522       1593.522
           0.800       0.000         1593.522       1593.522
           0.700       0.000         1593.522       1593.522
           0.500       0.000         1593.522       1593.522
           0.300       0.000         1593.522       1593.522
           0.200       0.000         1593.522       1593.522
           0.100       0.000         1593.522       1593.522
           0.050       0.000         1593.522       1593.522
           0.020       0.000         1593.522       1593.522
           0.010       0.000         1593.522       1593.522



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
 S          ON
  X2                  0.300     0.2514     0.0000     0.0694     0.0024 1.000 1.000

 Y          ON
  X2                  0.600     0.5871     0.0000     0.0454     0.0002 1.000 1.000

 S        WITH
  Y                   0.500     0.6195     0.0000     0.0803     0.0143 1.000 1.000

 Intercepts
  Y                   0.500     0.4876     0.0000     0.0523     0.0002 1.000 1.000
  S                   1.000     0.9846     0.0000     0.0739     0.0002 1.000 1.000

 Residual Variances
  Y                   0.800     0.8136     0.0000     0.0760     0.0002 1.000 1.000
  S                   0.900     1.1600     0.0000     0.1555     0.0676 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.417E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           NU
              Y             X1            X2
              ________      ________      ________
 1                  0             0             0


           LAMBDA
              S             Y             X1            X2
              ________      ________      ________      ________
 Y                  0             0             0             0
 X1                 0             0             0             0
 X2                 0             0             0             0


           THETA
              Y             X1            X2
              ________      ________      ________
 Y                  0
 X1                 0             0
 X2                 0             0             0


           ALPHA
              S             Y             X1            X2
              ________      ________      ________      ________
 1                  1             2             0             0


           BETA
              S             Y             X1            X2
              ________      ________      ________      ________
 S                  0             0             0             3
 Y                  0             0             0             4
 X1                 0             0             0             0
 X2                 0             0             0             0


           PSI
              S             Y             X1            X2
              ________      ________      ________      ________
 S                  5
 Y                  6             7
 X1                 0             0             0
 X2                 0             0             0             0


     STARTING VALUES


           NU
              Y             X1            X2
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              S             Y             X1            X2
              ________      ________      ________      ________
 Y              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
              Y             X1            X2
              ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000


           ALPHA
              S             Y             X1            X2
              ________      ________      ________      ________
 1              1.000         0.500         0.000         0.000


           BETA
              S             Y             X1            X2
              ________      ________      ________      ________
 S              0.000         0.000         0.000         0.300
 Y              0.000         0.000         0.000         0.600
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              S             Y             X1            X2
              ________      ________      ________      ________
 S              0.900
 Y              0.500         0.800
 X1             0.000         0.000         0.500
 X2             0.000         0.000         0.000         0.500


     POPULATION VALUES


           NU
              Y             X1            X2
              ________      ________      ________
 1              0.000         0.000         0.000


           LAMBDA
              S             Y             X1            X2
              ________      ________      ________      ________
 Y              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
              Y             X1            X2
              ________      ________      ________
 Y              0.000
 X1             0.000         0.000
 X2             0.000         0.000         0.000


           ALPHA
              S             Y             X1            X2
              ________      ________      ________      ________
 1              1.000         0.500         0.000         0.000


           BETA
              S             Y             X1            X2
              ________      ________      ________      ________
 S              0.000         0.000         0.000         0.300
 Y              0.000         0.000         0.000         0.600
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              S             Y             X1            X2
              ________      ________      ________      ________
 S              0.900
 Y              0.500         0.800
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.250         1.000


TECHNICAL 8 OUTPUT


   TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.78851275D+03    0.0000000    0.0000000  EM
              2 -0.78726569D+03    1.2470592    0.0015815  EM
              3 -0.78690213D+03    0.3635629    0.0004618  EM
              4 -0.78671018D+03    0.1919516    0.0002439  EM
              5 -0.78657880D+03    0.1313781    0.0001670  EM
              6 -0.78648228D+03    0.0965151    0.0001227  EM
              7 -0.78641009D+03    0.0721914    0.0000918  EM
              8 -0.78635581D+03    0.0542786    0.0000690  EM
              9 -0.78631493D+03    0.0408805    0.0000520  EM
             10 -0.78628412D+03    0.0308072    0.0000392  EM
             11 -0.78626091D+03    0.0232178    0.0000295  EM
             12 -0.78624341D+03    0.0174984    0.0000223  EM
             13 -0.78623022D+03    0.0131849    0.0000168  EM
             14 -0.78622029D+03    0.0099328    0.0000126  EM
             15 -0.78621281D+03    0.0074814    0.0000095  EM
             16 -0.78620718D+03    0.0056341    0.0000072  EM
             17 -0.78620293D+03    0.0042426    0.0000054  EM
             18 -0.78619974D+03    0.0031948    0.0000041  EM
             19 -0.78619733D+03    0.0024058    0.0000031  EM
             20 -0.78619552D+03    0.0018122    0.0000023  EM
             21 -0.78619415D+03    0.0013654    0.0000017  EM
             22 -0.78619313D+03    0.0010293    0.0000013  EM
             23 -0.78619235D+03    0.0007766    0.0000010  EM
             24 -0.78619176D+03    0.0005866    0.0000007  EM
             25 -0.78619132D+03    0.0004437    0.0000006  EM
             26 -0.78619098D+03    0.0003363    0.0000004  EM
             27 -0.78619073D+03    0.0002556    0.0000003  EM
             28 -0.78619053D+03    0.0001949    0.0000002  EM
             29 -0.78619038D+03    0.0001494    0.0000002  EM
             30 -0.78619027D+03    0.0001151    0.0000001  EM
             31 -0.78619018D+03    0.0000894    0.0000001  EM
             32 -0.78619011D+03    0.0000700    0.0000001  EM
             33 -0.78619005D+03    0.0000556    0.0000001  EM
             34 -0.78619001D+03    0.0000447    0.0000001  EM
             35 -0.78612285D+03    0.0671609    0.0000854  FS
             36 -0.78611916D+03    0.0036867    0.0000047  FS
             37 -0.78611890D+03    0.0002622    0.0000003  FS
             38 -0.78611888D+03    0.0000204    0.0000000  FS


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y
    X1
    X2

  Save file
    ex3.9.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  14:03:45
        Ending Time:  14:03:45
       Elapsed Time:  00:00:00



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