Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:14 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level time series analysis
      with a first-order autoregressive AR(1) IRT model for binary factor indicators
      with random thresholds, a random AR(1) slope, and a random residual variance
  DATA:	FILE = ex9.35part2.dat;
  VARIABLE:	NAMES = u1-u4 subject;
  	CATEGORICAL = u1-u4;
  	CLUSTER = subject;
  ANALYSIS:	TYPE = TWOLEVEL RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (3000);
  MODEL:	%WITHIN%
  	f BY u1-u4*(&1 1-4);
  	s | f ON f&1;
  	logvf | f;
  	%BETWEEN%
  	fb BY u1-u4* (1-4);
  	[logvf@0];
  	fb s logvf WITH fb s logvf;
  OUTPUT:	TECH1 TECH8;	



INPUT READING TERMINATED NORMALLY



this is an example of a two-level time series analysis
with a first-order autoregressive AR(1) IRT model for binary factor indicators
with random thresholds, a random AR(1) slope, and a random residual variance

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of dependent variables                                    4
Number of independent variables                                  0
Number of continuous latent variables                            5

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Continuous latent variables
   F           F&1         FB          S           LOGVF

Variables with special functions

  Cluster variable      SUBJECT

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
  Treatment of categorical mediator                         LATENT
  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)
  ex9.35part2.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                        200

       Size (s)    Cluster ID with Size s

        100        1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
                   22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
                   40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
                   58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
                   76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
                   94 95 96 97 98 99 100 101 102 103 104 105 106 107 108
                   109 110 111 112 113 114 115 116 117 118 119 120 121
                   122 123 124 125 126 127 128 129 130 131 132 133 134
                   135 136 137 138 139 140 141 142 143 144 145 146 147
                   148 149 150 151 152 153 154 155 156 157 158 159 160
                   161 162 163 164 165 166 167 168 169 170 171 172 173
                   174 175 176 177 178 179 180 181 182 183 184 185 186
                   187 188 189 190 191 192 193 194 195 196 197 198 199
                   200



UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.484         9688.000
      Category 2    0.516        10312.000
    U2
      Category 1    0.489         9775.000
      Category 2    0.511        10225.000
    U3
      Category 1    0.497         9938.000
      Category 2    0.503        10062.000
    U4
      Category 1    0.511        10222.000
      Category 2    0.489         9778.000



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                              19



MODEL RESULTS

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

Within Level

 F        BY
    U1                 0.964       0.027      0.000       0.913       1.020      *
    U2                 0.990       0.029      0.000       0.934       1.048      *
    U3                 1.009       0.027      0.000       0.958       1.064      *
    U4                 0.979       0.026      0.000       0.932       1.032      *

Between Level

 FB       BY
    U1                 0.964       0.027      0.000       0.913       1.020      *
    U2                 0.990       0.029      0.000       0.934       1.048      *
    U3                 1.009       0.027      0.000       0.958       1.064      *
    U4                 0.979       0.026      0.000       0.932       1.032      *

 FB       WITH
    S                 -0.003       0.008      0.356      -0.019       0.013
    LOGVF              0.002       0.017      0.464      -0.034       0.033

 S        WITH
    LOGVF             -0.005       0.007      0.215      -0.019       0.007

 Means
    S                  0.293       0.016      0.000       0.260       0.324      *
    LOGVF              0.000       0.000      1.000       0.000       0.000

 Thresholds
    U1$1              -0.067       0.048      0.082      -0.162       0.024
    U2$1              -0.040       0.052      0.210      -0.145       0.054
    U3$1              -0.014       0.053      0.399      -0.124       0.087
    U4$1               0.038       0.050      0.221      -0.058       0.135

 Variances
    FB                 0.165       0.028      0.000       0.116       0.224      *
    S                  0.030       0.004      0.000       0.023       0.039      *
    LOGVF              0.111       0.022      0.000       0.076       0.161      *

 Residual Variances
    U1                 0.280       0.040      0.000       0.212       0.368      *
    U2                 0.320       0.043      0.000       0.245       0.413      *
    U3                 0.340       0.046      0.000       0.262       0.441      *
    U4                 0.289       0.041      0.000       0.219       0.382      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    0             0             0             0


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              F             F&1
              ________      ________
 U1                 1             0
 U2                 2             0
 U3                 3             0
 U4                 4             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0             0
 F&1                0             0


           PSI
              F             F&1
              ________      ________
 F                  0
 F&1                0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                   16            17            18            19


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              FB            S             LOGVF
              ________      ________      ________
 U1                 1             0             0
 U2                 2             0             0
 U3                 3             0             0
 U4                 4             0             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 5
 U2                 0             6
 U3                 0             0             7
 U4                 0             0             0             8


           ALPHA
              FB            S             LOGVF
              ________      ________      ________
                    0             9             0


           BETA
              FB            S             LOGVF
              ________      ________      ________
 FB                 0             0             0
 S                  0             0             0
 LOGVF              0             0             0


           PSI
              FB            S             LOGVF
              ________      ________      ________
 FB                10
 S                 11            12
 LOGVF             13            14            15


     STARTING VALUES FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 U1             1.000         0.000
 U2             1.000         0.000
 U3             1.000         0.000
 U4             1.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000


           ALPHA
              F             F&1
              ________      ________
                0.000         0.000


           BETA
              F             F&1
              ________      ________
 F              0.000         0.000
 F&1            0.000         0.000


           PSI
              F             F&1
              ________      ________
 F              0.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
               -0.035        -0.025        -0.007         0.025


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              FB            S             LOGVF
              ________      ________      ________
 U1             1.000         0.000         0.000
 U2             1.000         0.000         0.000
 U3             1.000         0.000         0.000
 U4             1.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000


           ALPHA
              FB            S             LOGVF
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              FB            S             LOGVF
              ________      ________      ________
 FB             0.000         0.000         0.000
 S              0.000         0.000         0.000
 LOGVF          0.000         0.000         0.000


           PSI
              FB            S             LOGVF
              ________      ________      ________
 FB             1.000
 S              0.000         1.000
 LOGVF          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(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 4~N(0.000,5.000)              0.0000              5.0000              2.2361
     Parameter 5~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 6~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 7~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 8~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~IW(1.000,4)              infinity            infinity            infinity
     Parameter 11~IW(0.000,4)              infinity            infinity            infinity
     Parameter 12~IW(1.000,4)              infinity            infinity            infinity
     Parameter 13~IW(0.000,4)              infinity            infinity            infinity
     Parameter 14~IW(0.000,4)              infinity            infinity            infinity
     Parameter 15~IW(1.000,4)              infinity            infinity            infinity
     Parameter 16~N(0.000,5.000)             0.0000              5.0000              2.2361
     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(0.000,5.000)             0.0000              5.0000              2.2361


TECHNICAL 8 OUTPUT



     Kolmogorov-Smirnov comparing posterior distributions across chains 1 and 2 using 100 draws.





     Parameter   KS Statistic P-value
     Parameter 6    0.1100    0.5560
     Parameter 2    0.1000    0.6766
     Parameter 17    0.0900    0.7942
     Parameter 18    0.0900    0.7942
     Parameter 8    0.0800    0.8938
     Parameter 3    0.0700    0.9610
     Parameter 19    0.0600    0.9921
     Parameter 16    0.0500    0.9995
     Parameter 5    0.0500    0.9995
     Parameter 4    0.0400    1.0000
     Parameter 7    0.0300    1.0000
     Parameter 9    0.0200    1.0000
     Parameter 10    0.0200    1.0000
     Parameter 15    0.0100    1.0000
     Parameter 1    0.0100    1.0000
     Parameter 14    0.0000    1.0000
     Parameter 11    0.0000    1.0000
     Parameter 13    0.0000    1.0000
     Parameter 12    0.0000    1.0000



     Simulated prior distributions

     Parameter       Prior Mean  Prior Variance  Prior Std. Dev.


     Parameter 1         0.0050          4.9231          2.2188
     Parameter 2         0.0037          4.9991          2.2359
     Parameter 3        -0.0395          5.2395          2.2890
     Parameter 4         0.1095          5.4076          2.3254
     Parameter 5 Improper Prior
     Parameter 6 Improper Prior
     Parameter 7 Improper Prior
     Parameter 8 Improper Prior
     Parameter 9 Improper Prior
     Parameter 10         3.7844        729.5422         27.0100
     Parameter 11         0.4237        226.3395         15.0446
     Parameter 12         3.6823        860.9938         29.3427
     Parameter 13        -1.2939       1961.9041         44.2934
     Parameter 14         0.2845        105.6557         10.2789
     Parameter 15         7.0643       7497.0317         86.5854
     Parameter 16         0.0316          4.9704          2.2294
     Parameter 17        -0.1059          4.9900          2.2338
     Parameter 18         0.0194          5.0519          2.2476
     Parameter 19        -0.0873          4.7525          2.1800


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              2.908               2
     200              1.779               15
     300              1.919               15
     400              1.541               15
     500              1.339               2
     600              1.086               10
     700              1.063               10
     800              1.094               4
     900              1.070               2
     1000             1.232               2
     1100             1.144               2
     1200             1.250               4
     1300             1.225               4
     1400             1.287               4
     1500             1.287               4
     1600             1.238               3
     1700             1.282               3
     1800             1.316               3
     1900             1.190               3
     2000             1.220               3
     2100             1.228               3
     2200             1.172               3
     2300             1.134               3
     2400             1.098               3
     2500             1.131               3
     2600             1.110               3
     2700             1.067               2
     2800             1.053               2
     2900             1.047               2
     3000             1.034               2


     Beginning Time:  05:14:11
        Ending Time:  05:16:08
       Elapsed Time:  00:01:57



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