Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:46 PM

INPUT INSTRUCTIONS

  TITLE:	Monte Carlo for a two-level path
  	analysis model with continuous dependent variables
  	and random slopes

  montecarlo:
  	names are y1 y2 x1 x2 w;
  	nobservations = 500;
  	ncsizes = 3;
  	csizes = 10 (5) 50 (3) 30 (10);
  	seed = 58459;
  	nreps = 1;
  	within = x1 x2;
  	between = w;
  	save = ex9.5.dat;

  ANALYSIS:
  	TYPE = TWOLEVEL RANDOM;
  	algorithm = integration;

  model population:

  	%WITHIN%

  	x1-x2@1;

  	s2 | y2 on y1;
  	y2 on x2*.5;
  	s1 | y1 on x2;
  	y1 on x1*.25;
  	y1-y2*1;

  	%BETWEEN%
  	w@1;
  	y1 on w*1;
  	y2 on w*1;
  	y1-y2*.5;
  	s1 on w*.3;
  	s2 on w*.6;
  	s1*.5; s2*.75;
  	[s2*.75 s1*.5];

  model:

  	%WITHIN%


  	s2 | y2 on y1;
  	y2 on x2*.5;
  	s1 | y1 on x2;
  	y1 on x1*.25;
  	y1-y2*1;

  	%BETWEEN%

  	y1 on w*1;
  	y2 on w*1;
  	y1-y2*.5;
  	s1 on w*.3;
  	s2 on w*.6;
  	s1*.5; s2*.75;
  	[s2*.75 s1*.5];

  output:
  	tech8 tech9;



*** WARNING in MODEL command
  In the MODEL command, the predictor variable on the WITHIN level refers to the whole observed
  variable.  To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
  This applies to the following statement(s):
    S2 | Y2 ON Y1
*** WARNING in MODEL POPULATION command
  In the MODEL POPULATION command, the predictor variable on the WITHIN level refers to the whole observed
  variable.  To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
  This applies to the following statement(s):
    S2 | Y2 ON Y1
   2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



Monte Carlo for a two-level path
analysis model with continuous dependent variables
and random slopes

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                58459

Number of dependent variables                                    2
Number of independent variables                                  3
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2

Observed independent variables
   X1          X2          W

Continuous latent variables
   S2          S1

Variables with special functions

  Within variables
   X1          X2

  Between variables
   W


Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
  Maximum number of iterations                                 100
  Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
  Maximum number of iterations                                 500
  Convergence criteria
    Loglikelihood change                                 0.100D-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
  Number of M step iterations                                    1
  M step convergence criterion                           0.100D-02
  Basis for M step termination                           ITERATION
  Maximum value for logit thresholds                            15
  Minimum value for logit thresholds                           -15
  Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            0
  Adaptive quadrature                                           ON
Cholesky                                                       OFF


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

          3            50
          5            10
         10            30


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
               -0.132         0.632        -0.040         0.015        -0.098


           Covariances
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1             4.085
 Y2             4.373        10.377
 X1             0.339         0.101         1.013
 X2             0.411         1.292        -0.043         1.155
 W              1.027         1.429        -0.008        -0.005         0.804


           Correlations
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.672         1.000
 X1             0.166         0.031         1.000
 X2             0.189         0.373        -0.040         1.000
 W              0.567         0.495        -0.008        -0.005         1.000




MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

    H0 Value

        Mean                             -1663.599
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -1663.599      -1663.599
           0.980       0.000        -1663.599      -1663.599
           0.950       0.000        -1663.599      -1663.599
           0.900       0.000        -1663.599      -1663.599
           0.800       0.000        -1663.599      -1663.599
           0.700       0.000        -1663.599      -1663.599
           0.500       0.000        -1663.599      -1663.599
           0.300       0.000        -1663.599      -1663.599
           0.200       0.000        -1663.599      -1663.599
           0.100       0.000        -1663.599      -1663.599
           0.050       0.000        -1663.599      -1663.599
           0.020       0.000        -1663.599      -1663.599
           0.010       0.000        -1663.599      -1663.599

Information Criteria

    Akaike (AIC)

        Mean                              3361.197
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         3361.197       3361.197
           0.980       0.000         3361.197       3361.197
           0.950       0.000         3361.197       3361.197
           0.900       0.000         3361.197       3361.197
           0.800       0.000         3361.197       3361.197
           0.700       0.000         3361.197       3361.197
           0.500       0.000         3361.197       3361.197
           0.300       0.000         3361.197       3361.197
           0.200       0.000         3361.197       3361.197
           0.100       0.000         3361.197       3361.197
           0.050       0.000         3361.197       3361.197
           0.020       0.000         3361.197       3361.197
           0.010       0.000         3361.197       3361.197

    Bayesian (BIC)

        Mean                              3432.846
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         3432.846       3432.846
           0.980       0.000         3432.846       3432.846
           0.950       0.000         3432.846       3432.846
           0.900       0.000         3432.846       3432.846
           0.800       0.000         3432.846       3432.846
           0.700       0.000         3432.846       3432.846
           0.500       0.000         3432.846       3432.846
           0.300       0.000         3432.846       3432.846
           0.200       0.000         3432.846       3432.846
           0.100       0.000         3432.846       3432.846
           0.050       0.000         3432.846       3432.846
           0.020       0.000         3432.846       3432.846
           0.010       0.000         3432.846       3432.846

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

        Mean                              3378.887
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         3378.887       3378.887
           0.980       0.000         3378.887       3378.887
           0.950       0.000         3378.887       3378.887
           0.900       0.000         3378.887       3378.887
           0.800       0.000         3378.887       3378.887
           0.700       0.000         3378.887       3378.887
           0.500       0.000         3378.887       3378.887
           0.300       0.000         3378.887       3378.887
           0.200       0.000         3378.887       3378.887
           0.100       0.000         3378.887       3378.887
           0.050       0.000         3378.887       3378.887
           0.020       0.000         3378.887       3378.887
           0.010       0.000         3378.887       3378.887



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Within Level

 Y2         ON
  X2                  0.500     0.5314     0.0000     0.0487     0.0010 1.000 1.000

 Y1         ON
  X1                  0.250     0.3001     0.0000     0.0619     0.0025 1.000 1.000

 Residual Variances
  Y1                  1.000     1.0795     0.0000     0.0637     0.0063 1.000 1.000
  Y2                  1.000     0.9575     0.0000     0.0760     0.0018 1.000 1.000

Between Level

 S1         ON
  W                   0.300     0.2772     0.0000     0.1065     0.0005 1.000 1.000

 S2         ON
  W                   0.600     0.6304     0.0000     0.1116     0.0009 1.000 1.000

 Y1         ON
  W                   1.000     1.2065     0.0000     0.1099     0.0426 1.000 1.000

 Y2         ON
  W                   1.000     0.8252     0.0000     0.0977     0.0306 1.000 1.000

 Y2       WITH
  Y1                  0.000    -0.0480     0.0000     0.0898     0.0023 1.000 0.000

 Intercepts
  Y1                  0.000    -0.0108     0.0000     0.1022     0.0001 1.000 0.000
  Y2                  0.000    -0.0623     0.0000     0.0813     0.0039 1.000 0.000
  S2                  0.750     0.8191     0.0000     0.1052     0.0048 1.000 1.000
  S1                  0.500     0.4284     0.0000     0.0969     0.0051 1.000 1.000

 Residual Variances
  Y1                  0.500     0.6003     0.0000     0.1105     0.0101 1.000 1.000
  Y2                  0.500     0.2134     0.0000     0.0836     0.0821 0.000 1.000
  S2                  0.750     0.7351     0.0000     0.1903     0.0002 1.000 1.000
  S1                  0.500     0.4983     0.0000     0.1061     0.0000 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.447E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 X1                 0             0             0             0
 X2                 0             0             0             0


           THETA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X1                 0             0             0
 X2                 0             0             0             0


           ALPHA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1                 0             0             1             0
 Y2                 0             0             0             2
 X1                 0             0             0             0
 X2                 0             0             0             0


           PSI
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1                 3
 Y2                 0             4
 X1                 0             0             0
 X2                 0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y1            Y2            W
              ________      ________      ________
                    0             0             0


           LAMBDA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              Y1            Y2            W
              ________      ________      ________
 Y1                 0
 Y2                 0             0
 W                  0             0             0


           ALPHA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
                    5             6             7             8             0


           BETA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2                 0             0             0             0             9
 S1                 0             0             0             0            10
 Y1                 0             0             0             0            11
 Y2                 0             0             0             0            12
 W                  0             0             0             0             0


           PSI
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2                13
 S1                 0            14
 Y1                 0             0            15
 Y2                 0             0            16            17
 W                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             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
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           ALPHA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             0.000         0.000         0.250         0.000
 Y2             0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.000         1.000
 X1             0.000         0.000         0.500
 X2             0.000         0.000         0.000         0.500


     STARTING VALUES FOR BETWEEN


           NU
              Y1            Y2            W
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            W
              ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
                0.750         0.500         0.000         0.000         0.000


           BETA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2             0.000         0.000         0.000         0.000         0.600
 S1             0.000         0.000         0.000         0.000         0.300
 Y1             0.000         0.000         0.000         0.000         1.000
 Y2             0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2             0.750
 S1             0.000         0.500
 Y1             0.000         0.000         0.500
 Y2             0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           NU
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             1.000         0.000         0.000         0.000
 Y2             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
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           ALPHA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             0.000         0.000         0.250         0.000
 Y2             0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000


           PSI
              Y1            Y2            X1            X2
              ________      ________      ________      ________
 Y1             1.000
 Y2             0.000         1.000
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000


     POPULATION VALUES FOR BETWEEN


           NU
              Y1            Y2            W
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              Y1            Y2            W
              ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 W              0.000         0.000         0.000


           ALPHA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
                0.750         0.500         0.000         0.000         0.000


           BETA
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2             0.000         0.000         0.000         0.000         0.600
 S1             0.000         0.000         0.000         0.000         0.300
 Y1             0.000         0.000         0.000         0.000         1.000
 Y2             0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              S2            S1            Y1            Y2            W
              ________      ________      ________      ________      ________
 S2             0.750
 S1             0.000         0.500
 Y1             0.000         0.000         0.500
 Y2             0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         1.000


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.16729298D+04    0.0000000    0.0000000  EM
              2 -0.16662590D+04    6.6707345    0.0039875  EM
              3 -0.16649011D+04    1.3579695    0.0008150  EM
              4 -0.16643778D+04    0.5232411    0.0003143  EM
              5 -0.16641022D+04    0.2756552    0.0001656  EM
              6 -0.16639370D+04    0.1651424    0.0000992  EM
              7 -0.16638317D+04    0.1053198    0.0000633  EM
              8 -0.16637619D+04    0.0697774    0.0000419  EM
              9 -0.16637145D+04    0.0474756    0.0000285  EM
             10 -0.16636815D+04    0.0329517    0.0000198  EM
             11 -0.16636583D+04    0.0232286    0.0000140  EM
             12 -0.16636417D+04    0.0165822    0.0000100  EM
             13 -0.16636297D+04    0.0119578    0.0000072  EM
             14 -0.16636210D+04    0.0086966    0.0000052  EM
             15 -0.16636147D+04    0.0063693    0.0000038  EM
             16 -0.16636100D+04    0.0046927    0.0000028  EM
             17 -0.16636065D+04    0.0034750    0.0000021  EM
             18 -0.16636039D+04    0.0025843    0.0000016  EM
             19 -0.16636020D+04    0.0019291    0.0000012  EM
             20 -0.16636005D+04    0.0014444    0.0000009  EM
             21 -0.16635995D+04    0.0010845    0.0000007  EM
             22 -0.16635986D+04    0.0008162    0.0000005  EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    X1
    X2
    W
    CLUSTER

  Save file
    ex9.5.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:46:41
        Ending Time:  22:46:42
       Elapsed Time:  00:00:01



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