Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:26 PM

INPUT INSTRUCTIONS

  TITLE:	this an example of a Monte Carlo simulation
      for a three-level path analysis model
      with a continuous and a categorical dependent variable

  montecarlo:
  		names are y u x w y2 z y3;
  		nobservations = 7500;
  		nreps = 1;
  		CSIZES = 50[30(5)];
  		ncsize = 1[1];
          generate = u(1);
          categorical = u;
  		within = x;
  		between = y2 (level2) w (level3) z y3;
          save = ex9.21.dat;

  ANALYSIS:  TYPE = threelevel;
          estimator = bayes;
          processors = 2;
          biter = (1000);

  model population:

  	%WITHIN%
  	x@1;
  	u ON y*.75 x*.5;
  	y ON x*.25;
  	y*1;

  	%Between level2%
  	w@1;
  	u ON w*1 y*.5 y2*.7;
  	y ON w*.5;
      y2 ON w*.7;
      y with y2*.25;
  	y*.5; y2*.5; u*.4;

      %Between level3%
  	z@1; y3@1;
      u ON y*.6 y2*.8;
  	y ON z*.6;
      y2 ON z*.8;
      y3 ON y*.4 y2*.3;
      y with y2*.3;
  	y*.4; y2*.5; u*.5 y3*.6;
      u with y3*.2;

  model:
      %WITHIN%
  	u ON y*.75 x*.5;
  	y ON x*.25;
  	y*1;

  	%Between level2%

  	u ON w*1 y*.5 y2*.7;
  	y ON w*.5;
      y2 ON w*.7;
      y with y2*.25;
  	y*.5; y2*.5; u*.4;

      %Between level3%

      u ON y*.6 y2*.8;
  	y ON z*.6;
      y2 ON z*.8;
      y3 ON y*.4 y2*.3;
      y with y2*.3;
  	y*.4; y2*.5; u*.5 y3*.6;
      u with y3*.2;


  output:
  	tech8 tech9;



INPUT READING TERMINATED NORMALLY



this an example of a Monte Carlo simulation
for a three-level path analysis model
with a continuous and a categorical dependent variable

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        7500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    4
Number of independent variables                                  3
Number of continuous latent variables                            0

Observed dependent variables

  Continuous
   Y2          Y           Y3

  Binary and ordered categorical (ordinal)
   U

Observed independent variables
   X           W           Z

Variables with special functions

  Within variables
   X

  Level 2 between variables
   W

  Level 3 between variables
   Z           Y3

  Level 2 and level 3 between variables
   Y2


Estimator                                                    BAYES
Specifications for Bayesian Estimation
  Point estimate                                            MEDIAN
  Number of Markov chain Monte Carlo (MCMC) chains               2
  Random seed for the first chain                                0
  Starting value information                           UNPERTURBED
  Algorithm used for Markov chain Monte Carlo           GIBBS(PX1)
  Convergence criterion                                  0.500D-01
  Maximum number of iterations                               50000
  K-th iteration used for thinning                               1
Link                                                        PROBIT


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

     Number of level 3 clusters            50

       Size (s)    Number of level 2 clusters of Size s

          5            30





MODEL FIT INFORMATION

Number of Free Parameters                       29

Bayesian Posterior Predictive Checking using Chi-Square

    Posterior Predictive P-Value

        Mean                                 0.618
        Std Dev                              0.000
        Number of successful computations        1

        Cumulative Distribution Function
           Value    Function Value
           0.990       1.000
           0.980       1.000
           0.950       1.000
           0.900       1.000
           0.800       1.000
           0.700       1.000
           0.500       0.000
           0.300       0.000
           0.200       0.000
           0.100       0.000
           0.050       0.000
           0.020       0.000
           0.010       0.000



MODEL RESULTS

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

Within Level

 U          ON
  Y                   0.750     0.7531     0.0000     0.0298     0.0000 1.000 1.000
  X                   0.500     0.4827     0.0000     0.0290     0.0003 1.000 1.000

 Y          ON
  X                   0.250     0.2487     0.0000     0.0123     0.0000 1.000 1.000

 Residual Variances
  Y                   1.000     1.0100     0.0000     0.0187     0.0001 1.000 1.000

Between LEVEL2 Level

 U          ON
  W                   1.000     1.0791     0.0000     0.0515     0.0063 1.000 1.000
  Y                   0.500     0.5165     0.0000     0.0648     0.0003 1.000 1.000
  Y2                  0.700     0.5960     0.0000     0.0587     0.0108 1.000 1.000

 Y          ON
  W                   0.500     0.4903     0.0000     0.0219     0.0001 1.000 1.000

 Y2         ON
  W                   0.700     0.6824     0.0000     0.0183     0.0003 1.000 1.000

 Y        WITH
  Y2                  0.250     0.2549     0.0000     0.0175     0.0000 1.000 1.000

 Residual Variances
  U                   0.400     0.3712     0.0000     0.0410     0.0008 1.000 1.000
  Y2                  0.500     0.4777     0.0000     0.0174     0.0005 1.000 1.000
  Y                   0.500     0.4956     0.0000     0.0255     0.0000 1.000 1.000

Between LEVEL3 Level

 U          ON
  Y                   0.600     0.5968     0.0000     0.2155     0.0000 1.000 1.000
  Y2                  0.800     0.8491     0.0000     0.1859     0.0024 1.000 1.000

 Y          ON
  Z                   0.600     0.6371     0.0000     0.1187     0.0014 1.000 1.000

 Y2         ON
  Z                   0.800     0.7762     0.0000     0.1303     0.0006 1.000 1.000

 Y3         ON
  Y                   0.400     0.3129     0.0000     0.2146     0.0076 1.000 0.000
  Y2                  0.300     0.2900     0.0000     0.1853     0.0001 1.000 0.000

 Y        WITH
  Y2                  0.300     0.3607     0.0000     0.1005     0.0037 1.000 1.000

 U        WITH
  Y3                  0.200     0.2286     0.0000     0.0919     0.0008 1.000 1.000

 Intercepts
  Y2                  0.000     0.0325     0.0000     0.1140     0.0011 1.000 0.000
  Y                   0.000     0.0455     0.0000     0.1087     0.0021 1.000 0.000
  Y3                  0.000    -0.1197     0.0000     0.1028     0.0143 1.000 0.000

 Thresholds
  U$1                 0.000     0.1200     0.0000     0.1072     0.0144 1.000 0.000

 Residual Variances
  U                   0.500     0.5130     0.0000     0.1243     0.0002 1.000 1.000
  Y2                  0.500     0.5934     0.0000     0.1268     0.0087 1.000 1.000
  Y                   0.400     0.5104     0.0000     0.1149     0.0122 1.000 1.000
  Y3                  0.600     0.5257     0.0000     0.1201     0.0055 1.000 1.000


CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES

                        CORRELATIONS                MEAN SQUARE ERROR
                    Average    Std. Dev.           Average    Std. Dev.
  B2_U                0.957       0.000              0.580       0.000
  B2_Y                0.900       0.000              0.381       0.000
  B3_U                0.989       0.000              0.224       0.000
  B3_Y2               0.992       0.000              0.129       0.000
  B3_Y                0.990       0.000              0.129       0.000


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U$1
              ________
                    0


           NU
              U             Y             X
              ________      ________      ________
                    0             0             0


           LAMBDA
              U             Y             X
              ________      ________      ________
 U                  0             0             0
 Y                  0             0             0
 X                  0             0             0


           THETA
              U             Y             X
              ________      ________      ________
 U                  0
 Y                  0             0
 X                  0             0             0


           ALPHA
              U             Y             X
              ________      ________      ________
                    0             0             0


           BETA
              U             Y             X
              ________      ________      ________
 U                  0             1             2
 Y                  0             0             3
 X                  0             0             0


           PSI
              U             Y             X
              ________      ________      ________
 U                  0
 Y                  0             4
 X                  0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL2


           TAU
              U$1
              ________
                    0


           NU
              U             Y2            Y             W
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              U             Y2            Y             W
              ________      ________      ________      ________
 U                  0             0             0             0
 Y2                 0             0             0             0
 Y                  0             0             0             0
 W                  0             0             0             0


           THETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U                  0
 Y2                 0             0
 Y                  0             0             0
 W                  0             0             0             0


           ALPHA
              U             Y2            Y             W
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U                  0             5             6             7
 Y2                 0             0             0             8
 Y                  0             0             0             9
 W                  0             0             0             0


           PSI
              U             Y2            Y             W
              ________      ________      ________      ________
 U                 10
 Y2                 0            11
 Y                  0            12            13
 W                  0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN LEVEL3


           TAU
              U$1
              ________
                   29


           NU
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                    0             0             0             0             0


           LAMBDA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U                  0             0             0             0             0
 Y2                 0             0             0             0             0
 Y                  0             0             0             0             0
 Y3                 0             0             0             0             0
 Z                  0             0             0             0             0


           THETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U                  0
 Y2                 0             0
 Y                  0             0             0
 Y3                 0             0             0             0
 Z                  0             0             0             0             0


           ALPHA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                    0            14            15            16             0


           BETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U                  0            17            18             0             0
 Y2                 0             0             0             0            19
 Y                  0             0             0             0            20
 Y3                 0            21            22             0             0
 Z                  0             0             0             0             0


           PSI
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U                 23
 Y2                 0            24
 Y                  0            25            26
 Y3                27             0             0            28
 Z                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U             Y             X
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              U             Y             X
              ________      ________      ________
 U              1.000         0.000         0.000
 Y              0.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              U             Y             X
              ________      ________      ________
 U              0.000
 Y              0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              U             Y             X
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              U             Y             X
              ________      ________      ________
 U              0.000         0.750         0.500
 Y              0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              U             Y             X
              ________      ________      ________
 U              1.000
 Y              0.000         1.000
 X              0.000         0.000         0.500


     STARTING VALUES FOR BETWEEN LEVEL2


           TAU
              U$1
              ________
                0.000


           NU
              U             Y2            Y             W
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              1.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.000
 Y2             0.000         0.000
 Y              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           ALPHA
              U             Y2            Y             W
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.000         0.700         0.500         1.000
 Y2             0.000         0.000         0.000         0.700
 Y              0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.400
 Y2             0.000         0.500
 Y              0.000         0.250         0.500
 W              0.000         0.000         0.000         0.500


     STARTING VALUES FOR BETWEEN LEVEL3


           TAU
              U$1
              ________
                0.000


           NU
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              1.000         0.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000         0.000
 Y3             0.000         0.000         0.000         1.000         0.000
 Z              0.000         0.000         0.000         0.000         1.000


           THETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.000
 Y2             0.000         0.000
 Y              0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.000         0.800         0.600         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.800
 Y              0.000         0.000         0.000         0.000         0.600
 Y3             0.000         0.300         0.400         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.500
 Y2             0.000         0.500
 Y              0.000         0.300         0.400
 Y3             0.200         0.000         0.000         0.600
 Z              0.000         0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           TAU
              U$1
              ________
                0.000


           NU
              U             Y             X
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              U             Y             X
              ________      ________      ________
 U              1.000         0.000         0.000
 Y              0.000         1.000         0.000
 X              0.000         0.000         1.000


           THETA
              U             Y             X
              ________      ________      ________
 U              0.000
 Y              0.000         0.000
 X              0.000         0.000         0.000


           ALPHA
              U             Y             X
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              U             Y             X
              ________      ________      ________
 U              0.000         0.750         0.500
 Y              0.000         0.000         0.250
 X              0.000         0.000         0.000


           PSI
              U             Y             X
              ________      ________      ________
 U              0.000
 Y              0.000         1.000
 X              0.000         0.000         1.000


     POPULATION VALUES FOR BETWEEN LEVEL2


           TAU
              U$1
              ________
                0.000


           NU
              U             Y2            Y             W
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              1.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         1.000


           THETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.000
 Y2             0.000         0.000
 Y              0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           ALPHA
              U             Y2            Y             W
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.000         0.700         0.500         1.000
 Y2             0.000         0.000         0.000         0.700
 Y              0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             W
              ________      ________      ________      ________
 U              0.400
 Y2             0.000         0.500
 Y              0.000         0.250         0.500
 W              0.000         0.000         0.000         1.000


     POPULATION VALUES FOR BETWEEN LEVEL3


           TAU
              U$1
              ________
                0.000


           NU
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              1.000         0.000         0.000         0.000         0.000
 Y2             0.000         1.000         0.000         0.000         0.000
 Y              0.000         0.000         1.000         0.000         0.000
 Y3             0.000         0.000         0.000         1.000         0.000
 Z              0.000         0.000         0.000         0.000         1.000


           THETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.000
 Y2             0.000         0.000
 Y              0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           ALPHA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           BETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.000         0.800         0.600         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.800
 Y              0.000         0.000         0.000         0.000         0.600
 Y3             0.000         0.300         0.400         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.500
 Y2             0.000         0.500
 Y              0.000         0.300         0.400
 Y3             0.200         0.000         0.000         0.600
 Z              0.000         0.000         0.000         0.000         1.000



     PRIORS FOR ALL PARAMETERS            PRIOR MEAN      PRIOR VARIANCE     PRIOR STD. DEV.

     Parameter 1~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 2~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 5~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 6~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 7~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 8~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 11~IW(1.000,3)              infinity            infinity            infinity
     Parameter 12~IW(0.000,3)              infinity            infinity            infinity
     Parameter 13~IW(1.000,3)              infinity            infinity            infinity
     Parameter 14~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 15~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 16~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 17~N(0.000,5.000)             0.0000              5.0000              2.2361
     Parameter 18~N(0.000,5.000)             0.0000              5.0000              2.2361
     Parameter 19~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 20~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 21~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 22~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 23~IW(1.000,3)              infinity            infinity            infinity
     Parameter 24~IW(1.000,3)              infinity            infinity            infinity
     Parameter 25~IW(0.000,3)              infinity            infinity            infinity
     Parameter 26~IW(1.000,3)              infinity            infinity            infinity
     Parameter 27~IW(0.000,3)              infinity            infinity            infinity
     Parameter 28~IW(1.000,3)              infinity            infinity            infinity
     Parameter 29~N(0.000,5.000)             0.0000              5.0000              2.2361


TECHNICAL 8 OUTPUT


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

     REPLICATION 1:


                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.470               10
     200              1.094               7
     300              1.297               10
     400              1.095               7
     500              1.028               2
     600              1.119               7
     700              1.104               7
     800              1.145               7
     900              1.088               7
     1000             1.030               2


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U
    Y2
    Y
    Y3
    X
    W
    Z
    LEVEL2
    LEVEL3

  Save file
    ex9.21.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:26:57
        Ending Time:  22:27:04
       Elapsed Time:  00:00:07



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