Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:39 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a random coefficient
            regression
  DATA:	FILE IS ex3.9.dat;
  VARIABLE:	NAMES ARE y x1 x2;
  DEFINE:	CENTER x1 x2 (GRANDMEAN);
  ANALYSIS:	TYPE = RANDOM;
  MODEL:	s | y ON x1;
  	s WITH y;
  	y s ON x2;



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 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

Variables with special functions

  Centering (GRANDMEAN)
   X1          X2


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

Input data file(s)
  ex3.9.dat
Input data format  FREE



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                     0.582       0.779      -4.162    0.20%      -0.935      0.041      0.351
             500.000       3.455       1.861       9.755    0.20%       0.749      1.946
     X1                    0.000       0.029      -2.638    0.20%      -0.827     -0.234      0.005
             500.000       0.940      -0.246       2.961    0.20%       0.276      0.822
     X2                    0.000       0.048      -3.020    0.20%      -0.896     -0.348     -0.015
             500.000       1.117       0.136       3.194    0.20%       0.285      0.850


THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

          H0 Value                        -786.119
          H0 Scaling Correction Factor      0.9938
            for MLR

Information Criteria

          Akaike (AIC)                    1586.238
          Bayesian (BIC)                  1615.740
          Sample-Size Adjusted BIC        1593.522
            (n* = (n + 2) / 24)



MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

 S          ON
    X2                 0.251      0.069      3.622      0.000

 Y          ON
    X2                 0.594      0.046     12.897      0.000

 S        WITH
    Y                  0.650      0.083      7.828      0.000

 Intercepts
    Y                  0.516      0.053      9.741      0.000
    S                  0.986      0.074     13.334      0.000

 Residual Variances
    Y                  0.847      0.078     10.889      0.000
    S                  1.160      0.155      7.462      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.391E-01
       (ratio of smallest to largest eigenvalue)


     Beginning Time:  04:39:40
        Ending Time:  04:39:40
       Elapsed Time:  00:00:00



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