Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:17 AM

INPUT INSTRUCTIONS

  TITLE:	two-level time series analysis with a univariate first-order autoregressive AR(1) m
      for a continuous dependent variable with a covariate, linear trend, random slopes,
      and a random residual variance
  DATA:	FILE = ex9.37.dat;
  VARIABLE:	NAMES = y x w xm time subject;
  	WITHIN = x time;
  	BETWEEN = w xm;
  	CLUSTER = subject;
  	LAGGED = y(1);
  DEFINE:	CENTER x (GROUPMEAN);
  ANALYSIS:	TYPE = TWOLEVEL RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (3000);
  MODEL:	%WITHIN%
  	sy | y ON y&1;
  	sx | y ON x;
  	s | y ON time;
  	logv | y;
  	%BETWEEN%
  	sy ON w xm;
  	sx ON w xm;
  	s ON w xm;
  	logv ON w xm;
  	y ON w xm;
  	sy-logv y WITH sy-logv y;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE= PLOT3;



*** WARNING
  Input line exceeded 90 characters. Some input may be truncated.
  TITLE:	two-level time series analysis with a univariate first-order autoregressive AR(1) mo
   1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



two-level time series analysis with a univariate first-order autoregressive AR(1) mo
for a continuous dependent variable with a covariate, linear trend, random slopes,
and a random residual variance

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of dependent variables                                    1
Number of independent variables                                  5
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y

Observed independent variables
   X           W           XM          TIME        Y&1

Continuous latent variables
   SY          SX          S           LOGV

Variables with special functions

  Cluster variable      SUBJECT

  Within variables
   X           TIME        Y&1

  Between variables
   W           XM

  Centering (GROUPMEAN)
   X


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)
  ex9.37.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



COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100

     Number of missing data patterns             2


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              Y             X             TIME          W             XM
              ________      ________      ________      ________      ________
 Y              1.000
 X              1.000         1.000
 TIME           1.000         1.000         1.000
 W              1.000         1.000         1.000         1.000
 XM             1.000         1.000         1.000         1.000         1.000



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

     Y                     1.950       0.271      -4.681    0.01%       0.512      1.469      1.876
           20000.000       2.956       0.425      11.083    0.01%       2.314      3.344
     X                     0.000       0.027      -3.876    0.01%      -0.834     -0.258     -0.002
           20000.000       0.981      -0.015       3.891    0.01%       0.245      0.832
     TIME                 50.500       0.000       1.000    1.00%      20.000     40.000     50.500
           20000.000     833.250      -1.200     100.000    1.00%      60.000     80.000
     W                    -0.067       0.070      -2.681    0.50%      -1.046     -0.386     -0.059
             200.000       1.094      -0.509       2.781    0.50%       0.307      0.862
     XM                   -0.059      -0.029      -3.062    0.50%      -1.004     -0.326      0.019
             200.000       1.132       0.216       3.251    0.50%       0.247      0.723


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                              30

Information Criteria

          Deviance (DIC)                        57879.089
          Estimated Number of Parameters (pD)     773.982



MODEL RESULTS

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

Within Level

Between Level

 SY         ON
    W                  0.078       0.013      0.000       0.052       0.102      *
    XM                 0.031       0.012      0.005       0.007       0.055      *

 SX         ON
    W                  0.234       0.036      0.000       0.168       0.306      *
    XM                 0.273       0.035      0.000       0.200       0.339      *

 S          ON
    W                  0.000       0.000      0.188      -0.001       0.000
    XM                 0.000       0.000      0.298      -0.001       0.001

 LOGV       ON
    W                  0.008       0.011      0.224      -0.013       0.031
    XM                -0.001       0.011      0.464      -0.023       0.021

 Y          ON
    W                  0.358       0.069      0.000       0.221       0.490      *
    XM                 0.399       0.066      0.000       0.271       0.532      *

 SY       WITH
    SX                 0.001       0.006      0.411      -0.010       0.012
    S                  0.000       0.000      0.343       0.000       0.000
    LOGV              -0.001       0.002      0.263      -0.005       0.002
    Y                 -0.015       0.010      0.072      -0.036       0.005

 SX       WITH
    S                  0.000       0.000      0.322       0.000       0.000
    LOGV              -0.003       0.006      0.316      -0.014       0.008
    Y                 -0.003       0.029      0.451      -0.060       0.057

 S        WITH
    LOGV               0.000       0.000      0.496       0.000       0.000
    Y                 -0.001       0.000      0.001      -0.002       0.000      *

 LOGV     WITH
    Y                  0.008       0.010      0.220      -0.012       0.029

 Intercepts
    Y                  1.992       0.060      0.000       1.874       2.110      *
    SY                 0.316       0.011      0.000       0.294       0.339      *
    SX                 0.522       0.033      0.000       0.454       0.582      *
    S                  0.000       0.000      0.443      -0.001       0.001
    LOGV               0.018       0.011      0.058      -0.008       0.037

 Residual Variances
    Y                  0.612       0.077      0.000       0.483       0.778      *
    SY                 0.019       0.003      0.000       0.014       0.024      *
    SX                 0.208       0.023      0.000       0.170       0.259      *
    S                  0.000       0.000      0.000       0.000       0.000      *
    LOGV               0.004       0.002      0.000       0.002       0.008      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y             X             TIME          Y&1
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y                  0             0             0             0
 X                  0             0             0             0
 TIME               0             0             0             0
 Y&1                0             0             0             0


           THETA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 TIME               0             0             0
 Y&1                0             0             0             0


           ALPHA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y                  0             0             0             0
 X                  0             0             0             0
 TIME               0             0             0             0
 Y&1                0             0             0             0


           PSI
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 TIME               0             0             0
 Y&1                0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y             W             XM
              ________      ________      ________
                    0             0             0


           LAMBDA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           LAMBDA
              W             XM
              ________      ________
 Y                  0             0
 W                  0             0
 XM                 0             0


           THETA
              Y             W             XM
              ________      ________      ________
 Y                  0
 W                  0             0
 XM                 0             0             0


           ALPHA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
                    1             2             3             4             5


           ALPHA
              W             XM
              ________      ________
                    0             0


           BETA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 SY                 0             0             0             0             0
 SX                 0             0             0             0             0
 S                  0             0             0             0             0
 LOGV               0             0             0             0             0
 Y                  0             0             0             0             0
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           BETA
              W             XM
              ________      ________
 SY                 6             7
 SX                 8             9
 S                 10            11
 LOGV              12            13
 Y                 14            15
 W                  0             0
 XM                 0             0


           PSI
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 SY                16
 SX                17            18
 S                 19            20            21
 LOGV              22            23            24            25
 Y                 26            27            28            29            30
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           PSI
              W             XM
              ________      ________
 W                  0
 XM                 0             0


     STARTING VALUES FOR WITHIN


           NU
              Y             X             TIME          Y&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           LAMBDA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y              1.000         0.000         0.000         0.000
 X              0.000         1.000         0.000         0.000
 TIME           0.000         0.000         1.000         0.000
 Y&1            0.000         0.000         0.000         1.000


           THETA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 TIME           0.000         0.000         0.000
 Y&1            0.000         0.000         0.000         0.000


           ALPHA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000
 TIME           0.000         0.000         0.000         0.000
 Y&1            0.000         0.000         0.000         0.000


           PSI
              Y             X             TIME          Y&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.490
 TIME           0.000         0.000       416.625
 Y&1            0.000         0.000         0.000         1.479


     STARTING VALUES FOR BETWEEN


           NU
              Y             W             XM
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000
 XM             0.000         0.000         0.000         0.000         0.000


           LAMBDA
              W             XM
              ________      ________
 Y              0.000         0.000
 W              1.000         0.000
 XM             0.000         1.000


           THETA
              Y             W             XM
              ________      ________      ________
 Y              0.000
 W              0.000         0.000
 XM             0.000         0.000         0.000


           ALPHA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         1.950


           ALPHA
              W             XM
              ________      ________
                0.000         0.000


           BETA
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 SY             0.000         0.000         0.000         0.000         0.000
 SX             0.000         0.000         0.000         0.000         0.000
 S              0.000         0.000         0.000         0.000         0.000
 LOGV           0.000         0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000
 XM             0.000         0.000         0.000         0.000         0.000


           BETA
              W             XM
              ________      ________
 SY             0.000         0.000
 SX             0.000         0.000
 S              0.000         0.000
 LOGV           0.000         0.000
 Y              0.000         0.000
 W              0.000         0.000
 XM             0.000         0.000


           PSI
              SY            SX            S             LOGV          Y
              ________      ________      ________      ________      ________
 SY             1.000
 SX             0.000         1.000
 S              0.000         0.000         1.000
 LOGV           0.000         0.000         0.000         1.000
 Y              0.000         0.000         0.000         0.000         1.478
 W              0.000         0.000         0.000         0.000         0.000
 XM             0.000         0.000         0.000         0.000         0.000


           PSI
              W             XM
              ________      ________
 W              0.547
 XM             0.000         0.566



     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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 5~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 6~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 7~N(0.000,infinity)           0.0000            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~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 17~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 18~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 19~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 20~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 21~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 22~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 23~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 24~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 25~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 26~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 27~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 28~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 29~IW(0.000,-6)             infinity            infinity            infinity
     Parameter 30~IW(0.000,-6)             infinity            infinity            infinity


TECHNICAL 8 OUTPUT



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





     Parameter   KS Statistic P-value
     Parameter 9    0.0800    0.8938
     Parameter 30    0.0600    0.9921
     Parameter 2    0.0500    0.9995
     Parameter 14    0.0500    0.9995
     Parameter 15    0.0400    1.0000
     Parameter 8    0.0200    1.0000
     Parameter 5    0.0200    1.0000
     Parameter 12    0.0200    1.0000
     Parameter 1    0.0100    1.0000
     Parameter 4    0.0100    1.0000
     Parameter 18    0.0100    1.0000
     Parameter 26    0.0100    1.0000
     Parameter 27    0.0100    1.0000
     Parameter 13    0.0100    1.0000
     Parameter 17    0.0000    1.0000
     Parameter 16    0.0000    1.0000
     Parameter 7    0.0000    1.0000
     Parameter 3    0.0000    1.0000
     Parameter 24    0.0000    1.0000
     Parameter 6    0.0000    1.0000
     Parameter 11    0.0000    1.0000
     Parameter 10    0.0000    1.0000
     Parameter 23    0.0000    1.0000
     Parameter 29    0.0000    1.0000
     Parameter 28    0.0000    1.0000
     Parameter 19    0.0000    1.0000
     Parameter 21    0.0000    1.0000
     Parameter 22    0.0000    1.0000
     Parameter 25    0.0000    1.0000
     Parameter 20    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
     Parameter 27 Improper Prior
     Parameter 28 Improper Prior
     Parameter 29 Improper Prior
     Parameter 30 Improper Prior


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.210               13
     200              1.313               4
     300              1.198               23
     400              1.099               13
     500              1.258               29
     600              1.271               29
     700              1.241               29
     800              1.301               13
     900              1.265               13
     1000             1.214               13
     1100             1.128               13
     1200             1.154               13
     1300             1.081               13
     1400             1.064               13
     1500             1.057               13
     1600             1.054               4
     1700             1.042               4
     1800             1.066               4
     1900             1.033               4
     2000             1.055               4
     2100             1.048               13
     2200             1.044               13
     2300             1.065               13
     2400             1.047               13
     2500             1.036               13
     2600             1.026               23
     2700             1.019               23
     2800             1.022               23
     2900             1.026               12
     3000             1.018               23


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:  05:17:10
        Ending Time:  05:19:10
       Elapsed Time:  00:02:00



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