Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   6:56 AM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a cross-classified time series analysis
      with a univariate first-order autoregressive AR(1) model for a
      continuous dependent variable with a covariate, linear trend, and random slope
  DATA:	FILE = ex9.39.dat;
  VARIABLE:	NAMES = w xm y x time subject;
  	USEVARIABLES = w xm y x timew timet;
  	WITHIN = x timew;
  	BETWEEN = (subject) w xm (time) timet;
  	CLUSTER = subject time;
  	LAGGED = y(1);
  DEFINE:	timew = time;
  	timet = time;
  	CENTER x (GROUPMEAN subject);
  ANALYSIS:	TYPE = CROSSCLASSIFIED RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (5000);
  MODEL:	%WITHIN%
  	y ON y&1;
  	s | y ON timew;
  	sx | y ON x;
  	%BETWEEN subject%
  	y s sx ON w xm;
  	y s sx WITH y s sx;
  	%BETWEEN time%
  	sx ON timet;
  	y WITH sx;
  	s@0;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;




INPUT READING TERMINATED NORMALLY



this is an example of a cross-classified time series analysis
with a univariate first-order autoregressive AR(1) model for a
continuous dependent variable with a covariate, linear trend, and random slope

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of dependent variables                                    1
Number of independent variables                                  6
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y

Observed independent variables
   W           XM          X           TIMEW       TIMET       Y&1

Continuous latent variables
   S           SX

Variables with special functions

  Cluster variables     SUBJECT   TIME

  Within variables
   X           TIMEW       Y&1

  Level 2a between variables
   TIMET

  Level 2b between variables
   W           XM


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)
  ex9.39.dat
Input data format  FREE


SUMMARY OF DATA

     Cluster information for SUBJECT

       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             TIMEW         W             XM
              ________      ________      ________      ________      ________
 Y              1.000
 X              1.000         1.000
 TIMEW          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
 TIMET          1.000         1.000         1.000         1.000         1.000


           Covariance Coverage
              TIMET
              ________
 TIMET          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                     1.999       0.212      -5.895    0.01%       0.404      1.482      1.950
           20000.000       3.664       0.438      12.588    0.01%       2.407      3.567
     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
     TIMEW                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
     TIMET                50.500       0.000       1.000    1.00%      20.000     40.000     50.500
             100.000     833.250      -1.200     100.000    1.00%      60.000     80.000


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                              21

Information Criteria

          Deviance (DIC)                        58984.565
          Estimated Number of Parameters (pD)     653.699



MODEL RESULTS

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

Within Level

 Y          ON
    Y&1                0.363       0.005      0.000       0.353       0.373      *

 Residual Variances
    Y                  1.082       0.011      0.000       1.061       1.103      *

Between TIME Level

 SX         ON
    TIMET             -0.002       0.002      0.054      -0.007       0.000

 Y        WITH
    SX                -0.018       0.037      0.311      -0.094       0.055

 Variances
    Y                  0.534       0.084      0.000       0.401       0.729      *
    S                  0.000       0.000      0.000       0.000       0.000

 Residual Variances
    SX                 0.213       0.039      0.000       0.155       0.306      *

Between SUBJECT Level

 S          ON
    W                  0.000       0.000      0.095      -0.001       0.000
    XM                 0.000       0.000      0.123      -0.001       0.000

 SX         ON
    W                  0.221       0.037      0.000       0.149       0.294      *
    XM                 0.253       0.036      0.000       0.182       0.323      *

 Y          ON
    W                  0.337       0.064      0.000       0.213       0.463      *
    XM                 0.419       0.064      0.000       0.295       0.546      *

 Y        WITH
    S                  0.000       0.000      0.026      -0.001       0.000
    SX                 0.000       0.029      0.498      -0.058       0.057

 S        WITH
    SX                 0.000       0.000      0.097       0.000       0.000

 Intercepts
    Y                  1.989       0.129      0.000       1.723       2.239      *
    S                  0.002       0.001      0.055       0.000       0.004
    SX                 0.727       0.119      0.000       0.550       1.014      *

 Residual Variances
    Y                  0.613       0.073      0.000       0.488       0.772      *
    S                  0.000       0.000      0.000       0.000       0.000      *
    SX                 0.205       0.023      0.000       0.167       0.255      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
                    0             0             0             0


           LAMBDA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y                  0             0             0             0
 X                  0             0             0             0
 TIMEW              0             0             0             0
 Y&1                0             0             0             0


           THETA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y                  0
 X                  0             0
 TIMEW              0             0             0
 Y&1                0             0             0             0


           ALPHA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y                  0             0             0             1
 X                  0             0             0             0
 TIMEW              0             0             0             0
 Y&1                0             0             0             0


           PSI
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y                  2
 X                  0             0
 TIMEW              0             0             0
 Y&1                0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN TIME


           NU
              Y             TIMET
              ________      ________
                    0             0


           LAMBDA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 Y                  0             0             0             0
 TIMET              0             0             0             0


           THETA
              Y             TIMET
              ________      ________
 Y                  0
 TIMET              0             0


           ALPHA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 S%2a               0             0             0             0
 SX%2a              0             0             0             3
 Y                  0             0             0             0
 TIMET              0             0             0             0


           PSI
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 S%2a               0
 SX%2a              0             4
 Y                  0             5             6
 TIMET              0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN SUBJECT


           NU
              Y             W             XM
              ________      ________      ________
                    0             0             0


           LAMBDA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 Y                  0             0             0             0             0
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


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


           ALPHA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
                    7             8             9             0             0


           BETA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 S%2b               0             0             0            10            11
 SX%2b              0             0             0            12            13
 Y                  0             0             0            14            15
 W                  0             0             0             0             0
 XM                 0             0             0             0             0


           PSI
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 S%2b              16
 SX%2b             17            18
 Y                 19            20            21
 W                  0             0             0             0
 XM                 0             0             0             0             0


     STARTING VALUES FOR WITHIN


           NU
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


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


           THETA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y              0.000
 X              0.000         0.000
 TIMEW          0.000         0.000         0.000
 Y&1            0.000         0.000         0.000         0.000


           ALPHA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y              0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000
 TIMEW          0.000         0.000         0.000         0.000
 Y&1            0.000         0.000         0.000         0.000


           PSI
              Y             X             TIMEW         Y&1
              ________      ________      ________      ________
 Y              1.832
 X              0.000         0.490
 TIMEW          0.000         0.000       416.625
 Y&1            0.000         0.000         0.000         1.836


     STARTING VALUES FOR BETWEEN TIME


           NU
              Y             TIMET
              ________      ________
                0.000         0.000


           LAMBDA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 Y              0.000         0.000         1.000         0.000
 TIMET          0.000         0.000         0.000         1.000


           THETA
              Y             TIMET
              ________      ________
 Y              0.000
 TIMET          0.000         0.000


           ALPHA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 S%2a           0.000         0.000         0.000         0.000
 SX%2a          0.000         0.000         0.000         0.000
 Y              0.000         0.000         0.000         0.000
 TIMET          0.000         0.000         0.000         0.000


           PSI
              S%2a          SX%2a         Y             TIMET
              ________      ________      ________      ________
 S%2a           0.000
 SX%2a          0.000         1.000
 Y              0.000         0.000         1.832
 TIMET          0.000         0.000         0.000       416.625


     STARTING VALUES FOR BETWEEN SUBJECT


           NU
              Y             W             XM
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 Y              0.000         0.000         1.000         0.000         0.000
 W              0.000         0.000         0.000         1.000         0.000
 XM             0.000         0.000         0.000         0.000         1.000


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


           ALPHA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
                0.000         0.000         1.999         0.000         0.000


           BETA
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 S%2b           0.000         0.000         0.000         0.000         0.000
 SX%2b          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


           PSI
              S%2b          SX%2b         Y             W             XM
              ________      ________      ________      ________      ________
 S%2b           1.000
 SX%2b          0.000         1.000
 Y              0.000         0.000         1.832
 W              0.000         0.000         0.000         0.547
 XM             0.000         0.000         0.000         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~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 3~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 4~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 5~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 6~IW(0.000,-3)              infinity            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,-4)             infinity            infinity            infinity
     Parameter 17~IW(0.000,-4)             infinity            infinity            infinity
     Parameter 18~IW(0.000,-4)             infinity            infinity            infinity
     Parameter 19~IW(0.000,-4)             infinity            infinity            infinity
     Parameter 20~IW(0.000,-4)             infinity            infinity            infinity
     Parameter 21~IW(0.000,-4)             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    0.2100    0.0205
     Parameter 6    0.1500    0.1930
     Parameter 8    0.1300    0.3439
     Parameter 21    0.0800    0.8938
     Parameter 12    0.0700    0.9610
     Parameter 15    0.0600    0.9921
     Parameter 5    0.0500    0.9995
     Parameter 20    0.0400    1.0000
     Parameter 14    0.0400    1.0000
     Parameter 4    0.0200    1.0000
     Parameter 18    0.0200    1.0000
     Parameter 13    0.0100    1.0000
     Parameter 19    0.0000    1.0000
     Parameter 7    0.0000    1.0000
     Parameter 2    0.0000    1.0000
     Parameter 17    0.0000    1.0000
     Parameter 1    0.0000    1.0000
     Parameter 16    0.0000    1.0000
     Parameter 10    0.0000    1.0000
     Parameter 11    0.0000    1.0000
     Parameter 3    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              4.050               8
     200              1.451               8
     300              1.172               9
     400              2.075               9
     500              3.104               9
     600              2.403               9
     700              1.790               9
     800              1.730               8
     900              1.792               8
     1000             1.573               8
     1100             1.323               8
     1200             1.416               9
     1300             1.655               9
     1400             1.824               9
     1500             2.141               9
     1600             2.071               9
     1700             2.069               9
     1800             2.072               9
     1900             1.997               9
     2000             2.005               9
     2100             1.883               9
     2200             1.835               9
     2300             1.508               9
     2400             1.369               9
     2500             1.326               9
     2600             1.294               9
     2700             1.277               9
     2800             1.220               9
     2900             1.222               8
     3000             1.298               8
     3100             1.338               8
     3200             1.327               8
     3300             1.381               8
     3400             1.472               8
     3500             1.529               8
     3600             1.566               8
     3700             1.584               8
     3800             1.572               8
     3900             1.494               8
     4000             1.467               8
     4100             1.409               8
     4200             1.305               8
     4300             1.208               9
     4400             1.223               9
     4500             1.233               9
     4600             1.265               9
     4700             1.279               9
     4800             1.277               9
     4900             1.258               9
     5000             1.235               9
     5100             1.243               9
     5200             1.224               9
     5300             1.207               9
     5400             1.186               9
     5500             1.191               9
     5600             1.183               9
     5700             1.188               9
     5800             1.195               9
     5900             1.192               9
     6000             1.183               9
     6100             1.170               9
     6200             1.172               9
     6300             1.155               9
     6400             1.135               9
     6500             1.121               9
     6600             1.096               9
     6700             1.074               9


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:  06:56:09
        Ending Time:  06:57:53
       Elapsed Time:  00:01:44



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