Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:13 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level time series analysis
      with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
      for continuous factor indicators with random intercepts, a random AR(1) slope,
      and a random residual variance
  DATA:	FILE = ex9.34.dat;
  VARIABLE:	NAMES = y1-y4 subject;
  	CLUSTER = subject;
  ANALYSIS:	TYPE = TWOLEVEL RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (2000);
  MODEL:	%WITHIN%
  	f BY y1-y4(&1);
  	s | f ON f&1;
  	logv | f;
  	%BETWEEN%
  	fb BY y1-y4*;
  	fb@1;
  	fb s logv WITH fb s logv;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;	



INPUT READING TERMINATED NORMALLY



this is an example of a two-level time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts, 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

  Continuous
   Y1          Y2          Y3          Y4

Continuous latent variables
   F           F&1         FB          S           LOGV

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

Input data file(s)
  ex9.34.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 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

     Y1                    0.074       0.031      -6.095    0.01%      -1.194     -0.312      0.060
           20000.000       2.272      -0.023       5.966    0.01%       0.438      1.343
     Y2                    0.029      -0.030      -6.340    0.01%      -1.261     -0.353      0.041
           20000.000       2.346      -0.017       6.551    0.01%       0.430      1.335
     Y3                    0.014       0.009      -6.011    0.01%      -1.266     -0.373      0.019
           20000.000       2.345      -0.037       6.411    0.01%       0.408      1.298
     Y4                   -0.049       0.016      -6.845    0.01%      -1.321     -0.441     -0.054
           20000.000       2.296       0.018       6.087    0.01%       0.329      1.228


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                              26

Information Criteria

          Deviance (DIC)                       189996.355
          Estimated Number of Parameters (pD)   18216.929



MODEL RESULTS

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

Within Level

 F        BY
    Y1                 1.000       0.000      0.000       1.000       1.000
    Y2                 1.001       0.007      0.000       0.987       1.015      *
    Y3                 0.999       0.007      0.000       0.985       1.012      *
    Y4                 0.994       0.007      0.000       0.980       1.009      *

 Residual Variances
    Y1                 0.495       0.007      0.000       0.482       0.508      *
    Y2                 0.500       0.007      0.000       0.487       0.514      *
    Y3                 0.499       0.007      0.000       0.486       0.512      *
    Y4                 0.511       0.007      0.000       0.496       0.524      *

Between Level

 FB       BY
    Y1                 0.600       0.055      0.000       0.490       0.709      *
    Y2                 0.661       0.058      0.000       0.556       0.778      *
    Y3                 0.653       0.057      0.000       0.549       0.774      *
    Y4                 0.606       0.058      0.000       0.498       0.729      *

 FB       WITH
    S                  0.012       0.015      0.193      -0.016       0.042
    LOGV              -0.014       0.015      0.162      -0.044       0.013

 S        WITH
    LOGV              -0.004       0.002      0.026      -0.009       0.000

 Means
    S                  0.300       0.012      0.000       0.277       0.322      *
    LOGV               0.003       0.016      0.424      -0.027       0.035

 Intercepts
    Y1                 0.074       0.060      0.095      -0.037       0.200
    Y2                 0.030       0.062      0.309      -0.091       0.152
    Y3                 0.013       0.063      0.416      -0.105       0.139
    Y4                -0.046       0.060      0.218      -0.166       0.071

 Variances
    FB                 1.000       0.000      0.000       1.000       1.000
    S                  0.019       0.003      0.000       0.014       0.026      *
    LOGV               0.012       0.003      0.000       0.006       0.019      *

 Residual Variances
    Y1                 0.300       0.041      0.000       0.230       0.385      *
    Y2                 0.290       0.042      0.000       0.217       0.378      *
    Y3                 0.305       0.043      0.000       0.228       0.397      *
    Y4                 0.319       0.042      0.000       0.247       0.413      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              F             F&1
              ________      ________
 Y1                 0             0
 Y2                 1             0
 Y3                 2             0
 Y4                 3             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                 4
 Y2                 0             5
 Y3                 0             0             6
 Y4                 0             0             0             7


           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


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                    8             9            10            11


           LAMBDA
              FB            S             LOGV
              ________      ________      ________
 Y1                12             0             0
 Y2                13             0             0
 Y3                14             0             0
 Y4                15             0             0


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1                16
 Y2                 0            17
 Y3                 0             0            18
 Y4                 0             0             0            19


           ALPHA
              FB            S             LOGV
              ________      ________      ________
                    0            20            21


           BETA
              FB            S             LOGV
              ________      ________      ________
 FB                 0             0             0
 S                  0             0             0
 LOGV               0             0             0


           PSI
              FB            S             LOGV
              ________      ________      ________
 FB                 0
 S                 22            23
 LOGV              24            25            26


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              F             F&1
              ________      ________
 Y1             1.000         0.000
 Y2             1.000         0.000
 Y3             1.000         0.000
 Y4             1.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.136
 Y2             0.000         1.173
 Y3             0.000         0.000         1.172
 Y4             0.000         0.000         0.000         1.148


           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


           NU
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
                0.074         0.029         0.014        -0.049


           LAMBDA
              FB            S             LOGV
              ________      ________      ________
 Y1             1.000         0.000         0.000
 Y2             1.000         0.000         0.000
 Y3             1.000         0.000         0.000
 Y4             1.000         0.000         0.000


           THETA
              Y1            Y2            Y3            Y4
              ________      ________      ________      ________
 Y1             1.136
 Y2             0.000         1.173
 Y3             0.000         0.000         1.172
 Y4             0.000         0.000         0.000         1.148


           ALPHA
              FB            S             LOGV
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              FB            S             LOGV
              ________      ________      ________
 FB             0.000         0.000         0.000
 S              0.000         0.000         0.000
 LOGV           0.000         0.000         0.000


           PSI
              FB            S             LOGV
              ________      ________      ________
 FB             1.000
 S              0.000         1.000
 LOGV           0.000         0.000         1.000



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

     Parameter 1~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 2~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~IG(-1.000,0.000)          infinity            infinity            infinity
     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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 10~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 11~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 12~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 13~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 14~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 15~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 16~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 17~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 18~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 19~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 20~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 21~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 22~IW(0.000,-4)
     Parameter 23~IW(0.000,-4)
     Parameter 24~IW(0.000,-4)
     Parameter 25~IW(0.000,-4)
     Parameter 26~IW(0.000,-4)


TECHNICAL 8 OUTPUT



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





     Parameter   KS Statistic P-value
     Parameter 18    0.0800    0.8938
     Parameter 15    0.0800    0.8938
     Parameter 9    0.0700    0.9610
     Parameter 13    0.0600    0.9921
     Parameter 19    0.0400    1.0000
     Parameter 10    0.0400    1.0000
     Parameter 12    0.0400    1.0000
     Parameter 14    0.0400    1.0000
     Parameter 8    0.0300    1.0000
     Parameter 16    0.0300    1.0000
     Parameter 17    0.0300    1.0000
     Parameter 21    0.0200    1.0000
     Parameter 11    0.0200    1.0000
     Parameter 22    0.0100    1.0000
     Parameter 20    0.0100    1.0000
     Parameter 5    0.0100    1.0000
     Parameter 2    0.0000    1.0000
     Parameter 25    0.0000    1.0000
     Parameter 1    0.0000    1.0000
     Parameter 4    0.0000    1.0000
     Parameter 23    0.0000    1.0000
     Parameter 24    0.0000    1.0000
     Parameter 3    0.0000    1.0000
     Parameter 7    0.0000    1.0000
     Parameter 26    0.0000    1.0000
     Parameter 6    0.0000    1.0000



     Simulated prior distributions

     Parameter       Prior Mean  Prior Variance  Prior Std. Dev.


     Parameter 1 Improper Prior
     Parameter 2 Improper Prior
     Parameter 3 Improper Prior
     Parameter 4 Improper Prior
     Parameter 5 Improper Prior
     Parameter 6 Improper Prior
     Parameter 7 Improper Prior
     Parameter 8 Improper Prior
     Parameter 9 Improper Prior
     Parameter 10 Improper Prior
     Parameter 11 Improper Prior
     Parameter 12 Improper Prior
     Parameter 13 Improper Prior
     Parameter 14 Improper Prior
     Parameter 15 Improper Prior
     Parameter 16 Improper Prior
     Parameter 17 Improper Prior
     Parameter 18 Improper Prior
     Parameter 19 Improper Prior
     Parameter 20 Improper Prior
     Parameter 21 Improper Prior
     Parameter 22 Improper Prior
     Parameter 23 Improper Prior
     Parameter 24 Improper Prior
     Parameter 25 Improper Prior
     Parameter 26 Improper Prior


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.229               9
     200              1.711               21
     300              1.117               21
     400              1.253               21
     500              1.077               21
     600              1.026               26
     700              1.034               26
     800              1.051               26
     900              1.137               21
     1000             1.091               21
     1100             1.042               21
     1200             1.011               13
     1300             1.032               22
     1400             1.031               22
     1500             1.037               22
     1600             1.041               22
     1700             1.041               24
     1800             1.032               24
     1900             1.024               24
     2000             1.040               21


PLOT INFORMATION

The following plots are available:

  Histograms (sample values)
  Scatterplots (sample values)
  Between-level histograms (sample values, sample means/variances)
  Between-level scatterplots (sample values, sample means/variances)
  Time series plots (sample values, ACF, PACF)
  Bayesian posterior parameter distributions
  Bayesian posterior parameter trace plots
  Bayesian autocorrelation plots

     Beginning Time:  05:13:20
        Ending Time:  05:14:11
       Elapsed Time:  00:00:51



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