Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:20 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
  DATA:       FILE = ex9.21.dat;
  VARIABLE:   NAMES = u y2 y y3 x w z level2 level3;
              CATEGORICAL  = u;
  		    WITHIN = x;
  		    BETWEEN = y2 (level2) w (level3) z y3;
              CLUSTER = level3 level2;
  ANALYSIS:   TYPE = threelevel;
              ESTIMATOR = BAYES;
              PROCESSORS = 2;
              BITERATIONS = (1000);
  MODEL:      %WITHIN%
  	        u ON y x;
  	        y ON x;
  	        %BETWEEN level2%
              u ON w y y2;
  	        y ON w;
              y2 ON w;
              y WITH y2;
  	        y; y2; u;
              %BETWEEN level3%
              u ON y y2;
              y ON z;
              y2 ON z;
              y3 ON y y2;
              y WITH y2;
  	        y; y2; u; y3;
              u WITH y3;
  OUTPUT: 	TECH1 TECH8;



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 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

  Cluster variables     LEVEL3    LEVEL2

  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

Input data file(s)
  ex9.21.dat
Input data format  FREE


SUMMARY OF DATA

     Number of LEVEL2 clusters                1500
     Number of LEVEL3 clusters                  50


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U
      Category 1    0.495         3715.000
      Category 2    0.505         3785.000



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

     Y2                    0.070      -0.053      -4.350    0.07%      -1.102     -0.286      0.083
            1500.000       1.992      -0.136       5.051    0.07%       0.439      1.309
     Y                     0.080      -0.046      -6.022    0.01%      -1.286     -0.301      0.098
            7500.000       2.617       0.012       6.238    0.01%       0.483      1.443
     Y3                   -0.079      -0.190      -2.194    2.00%      -0.851     -0.315     -0.024
              50.000       0.786      -0.192       1.734    2.00%       0.225      0.509
     X                     0.008       0.008      -4.119    0.01%      -0.842     -0.260      0.001
            7500.000       1.013       0.013       4.022    0.01%       0.268      0.856
     W                     0.030      -0.083      -3.508    0.07%      -0.792     -0.208      0.029
            1500.000       1.007       0.037       2.958    0.07%       0.269      0.851
     Z                     0.017      -0.103      -2.337    2.00%      -0.642     -0.245     -0.036
              50.000       0.823      -0.067       2.055    2.00%       0.254      0.731


THE MODEL ESTIMATION TERMINATED NORMALLY

     USE THE FBITERATIONS OPTION TO INCREASE THE NUMBER OF ITERATIONS BY A FACTOR
     OF AT LEAST TWO TO CHECK CONVERGENCE AND THAT THE PSR VALUE DOES NOT INCREASE.



MODEL FIT INFORMATION

Number of Free Parameters                              29

Bayesian Posterior Predictive Checking using Chi-Square

          95% Confidence Interval for the Difference Between
          the Observed and the Replicated Chi-Square Values

                                -27.924            29.008

          Posterior Predictive P-Value              0.618



MODEL RESULTS

                                Posterior  One-Tailed         95% C.I.
                    Estimate       S.D.      P-Value   Lower 2.5%  Upper 2.5%  Significance

Within Level

 U          ON
    Y                  0.753       0.030      0.000       0.693       0.807      *
    X                  0.483       0.029      0.000       0.430       0.544      *

 Y          ON
    X                  0.249       0.012      0.000       0.225       0.273      *

 Residual Variances
    Y                  1.010       0.019      0.000       0.974       1.048      *

Between LEVEL2 Level

 U          ON
    W                  1.079       0.052      0.000       0.987       1.183      *
    Y                  0.516       0.065      0.000       0.383       0.642      *
    Y2                 0.596       0.059      0.000       0.475       0.700      *

 Y          ON
    W                  0.490       0.022      0.000       0.442       0.532      *

 Y2         ON
    W                  0.682       0.018      0.000       0.644       0.718      *

 Y        WITH
    Y2                 0.255       0.018      0.000       0.222       0.290      *

 Residual Variances
    U                  0.371       0.041      0.000       0.283       0.448      *
    Y2                 0.478       0.017      0.000       0.446       0.513      *
    Y                  0.496       0.026      0.000       0.448       0.547      *

Between LEVEL3 Level

 U          ON
    Y                  0.597       0.215      0.004       0.176       1.044      *
    Y2                 0.849       0.186      0.000       0.479       1.213      *

 Y          ON
    Z                  0.637       0.119      0.000       0.407       0.873      *

 Y2         ON
    Z                  0.776       0.130      0.000       0.521       1.032      *

 Y3         ON
    Y                  0.313       0.215      0.065      -0.116       0.731
    Y2                 0.290       0.185      0.065      -0.079       0.644

 Y        WITH
    Y2                 0.361       0.101      0.000       0.203       0.601      *

 U        WITH
    Y3                 0.229       0.092      0.000       0.091       0.452      *

 Intercepts
    Y2                 0.032       0.114      0.380      -0.194       0.248
    Y                  0.045       0.109      0.342      -0.167       0.249
    Y3                -0.120       0.103      0.122      -0.323       0.081

 Thresholds
    U$1                0.120       0.107      0.129      -0.086       0.331

 Residual Variances
    U                  0.513       0.124      0.000       0.324       0.822      *
    Y2                 0.593       0.127      0.000       0.410       0.887      *
    Y                  0.510       0.115      0.000       0.352       0.807      *
    Y3                 0.526       0.120      0.000       0.354       0.841      *


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         0.000         0.000
 Y              0.000         0.000         0.000
 X              0.000         0.000         0.000


           PSI
              U             Y             X
              ________      ________      ________
 U              1.000
 Y              0.000         1.308
 X              0.000         0.000         0.507


     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         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             W
              ________      ________      ________      ________
 U              1.000
 Y2             0.000         0.996
 Y              0.000         0.000         1.308
 W              0.000         0.000         0.000         0.504


     STARTING VALUES FOR BETWEEN LEVEL3


           TAU
              U$1
              ________
               -0.010


           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         0.070         0.080        -0.079         0.000


           BETA
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              0.000         0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000         0.000
 Z              0.000         0.000         0.000         0.000         0.000


           PSI
              U             Y2            Y             Y3            Z
              ________      ________      ________      ________      ________
 U              1.000
 Y2             0.000         0.996
 Y              0.000         0.000         1.308
 Y3             0.000         0.000         0.000         0.393
 Z              0.000         0.000         0.000         0.000         0.412



     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

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.397               10
     200              1.082               7
     300              1.278               10
     400              1.096               7
     500              1.027               2
     600              1.118               7
     700              1.103               7
     800              1.144               7
     900              1.088               7
     1000             1.030               2


     Beginning Time:  23:20:46
        Ending Time:  23:20:53
       Elapsed Time:  00:00:07



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