Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:19 AM

INPUT INSTRUCTIONS

  TITLE:	cross-classified time series analysis with a univariate first-order
      autoregressive AR(1) model for a continuous dependent variable with a
      covariate, random intercept, and random slope
  DATA:	FILE = ex9.38.dat;
  VARIABLE:	NAMES = w xm y x time subject;
  	CLUSTER = subject time;
  	WITHIN = x;
  	BETWEEN = (subject)w xm;
  	LAGGED = y(1);
  DEFINE:	CENTER x (GROUPMEAN subject);
  ANALYSIS:	TYPE = CROSSCLASSIFIED RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (2000);
  MODEL:	%WITHIN%
  	sx | y ON x;
  	y ON y&1;
  	%BETWEEN subject%
  	y sx ON w xm;
  	y WITH sx;
  	%BETWEEN time%
  	y WITH sx;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;
  	FACTORS = ALL;



INPUT READING TERMINATED NORMALLY



cross-classified time series analysis with a univariate first-order
autoregressive AR(1) model for a continuous dependent variable with a
covariate, random intercept, and random slope

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

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

Observed dependent variables

  Continuous
   Y

Observed independent variables
   W           XM          X           Y&1

Continuous latent variables
   SX

Variables with special functions

  Cluster variables     SUBJECT   TIME

  Within variables
   X           Y&1

  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
Specifications for Bayes Factor Score Estimation
  Number of imputed data sets                                   50
  Iteration intervals for thinning                               1

Input data file(s)
  ex9.38.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



SUMMARY OF MISSING DATA PATTERNS

     Number of missing data patterns             2


     MISSING DATA PATTERNS (x = not missing)

           1  2
 Y         x  x
 X         x  x
 Y&1       x
 W         x  x
 XM        x  x


     MISSING DATA PATTERN FREQUENCIES

    Pattern   Frequency     Pattern   Frequency
          1       19800           2         200


COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100


     PROPORTION OF DATA PRESENT


           Covariance Coverage
              Y             X             W             XM
              ________      ________      ________      ________
 Y              1.000
 X              1.000         1.000
 W              1.000         1.000         1.000
 XM             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                     1.999       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
     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                              14

Information Criteria

          Deviance (DIC)                        58961.829
          Estimated Number of Parameters (pD)     616.189



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                0.365       0.005      0.000       0.354       0.375      *

 Residual Variances
    Y                  1.083       0.011      0.000       1.061       1.105      *

Between TIME Level

 Y        WITH
    SX                -0.008       0.035      0.416      -0.077       0.063

 Variances
    Y                  0.522       0.081      0.000       0.389       0.708      *
    SX                 0.198       0.031      0.000       0.150       0.269      *

Between SUBJECT Level

 SX         ON
    W                  0.222       0.036      0.000       0.148       0.291      *
    XM                 0.252       0.035      0.000       0.183       0.323      *

 Y          ON
    W                  0.315       0.060      0.000       0.199       0.426      *
    XM                 0.395       0.060      0.000       0.278       0.512      *

 Y        WITH
    SX                -0.014       0.026      0.299      -0.065       0.037

 Intercepts
    Y                  2.103       0.089      0.000       1.942       2.285      *
    SX                 0.621       0.056      0.000       0.510       0.718      *

 Residual Variances
    Y                  0.552       0.059      0.000       0.453       0.686      *
    SX                 0.203       0.023      0.000       0.164       0.253      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


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


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


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


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


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


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


     PARAMETER SPECIFICATION FOR BETWEEN TIME


           NU
              Y
              ________
                    0


           LAMBDA
              SX%2a         Y
              ________      ________
 Y                  0             0


           THETA
              Y
              ________
 Y                  0


           ALPHA
              SX%2a         Y
              ________      ________
                    0             0


           BETA
              SX%2a         Y
              ________      ________
 SX%2a              0             0
 Y                  0             0


           PSI
              SX%2a         Y
              ________      ________
 SX%2a              3
 Y                  4             5


     PARAMETER SPECIFICATION FOR BETWEEN SUBJECT


           NU
              Y             W             XM
              ________      ________      ________
                    0             0             0


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


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


           ALPHA
              SX%2b         Y             W             XM
              ________      ________      ________      ________
                    6             7             0             0


           BETA
              SX%2b         Y             W             XM
              ________      ________      ________      ________
 SX%2b              0             0             8             9
 Y                  0             0            10            11
 W                  0             0             0             0
 XM                 0             0             0             0


           PSI
              SX%2b         Y             W             XM
              ________      ________      ________      ________
 SX%2b             12
 Y                 13            14
 W                  0             0             0
 XM                 0             0             0             0


     STARTING VALUES FOR WITHIN


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


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


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


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


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


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


     STARTING VALUES FOR BETWEEN TIME


           NU
              Y
              ________
                0.000


           LAMBDA
              SX%2a         Y
              ________      ________
 Y              0.000         1.000


           THETA
              Y
              ________
 Y              0.000


           ALPHA
              SX%2a         Y
              ________      ________
                0.000         0.000


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


           PSI
              SX%2a         Y
              ________      ________
 SX%2a          1.000
 Y              0.000         1.832


     STARTING VALUES FOR BETWEEN SUBJECT


           NU
              Y             W             XM
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              SX%2b         Y             W             XM
              ________      ________      ________      ________
 Y              0.000         1.000         0.000         0.000
 W              0.000         0.000         1.000         0.000
 XM             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
              SX%2b         Y             W             XM
              ________      ________      ________      ________
                0.000         1.999         0.000         0.000


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


           PSI
              SX%2b         Y             W             XM
              ________      ________      ________      ________
 SX%2b          1.000
 Y              0.000         1.832
 W              0.000         0.000         0.547
 XM             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~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 4~IW(0.000,-3)              infinity            infinity            infinity
     Parameter 5~IW(0.000,-3)              infinity            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~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 13~IW(0.000,-3)             infinity            infinity            infinity
     Parameter 14~IW(0.000,-3)             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 5    0.0900    0.7942
     Parameter 10    0.0700    0.9610
     Parameter 7    0.0700    0.9610
     Parameter 14    0.0600    0.9921
     Parameter 3    0.0500    0.9995
     Parameter 6    0.0500    0.9995
     Parameter 11    0.0400    1.0000
     Parameter 12    0.0400    1.0000
     Parameter 9    0.0300    1.0000
     Parameter 8    0.0200    1.0000
     Parameter 2    0.0100    1.0000
     Parameter 13    0.0100    1.0000
     Parameter 4    0.0100    1.0000
     Parameter 1    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.047               6
     200              1.679               6
     300              1.292               7
     400              1.242               7
     500              1.054               6
     600              1.038               6
     700              1.074               6
     800              1.160               6
     900              1.119               6
     1000             1.162               6
     1100             1.177               6
     1200             1.134               6
     1300             1.044               6
     1400             1.022               6
     1500             1.027               6
     1600             1.018               6
     1700             1.028               6
     1800             1.040               6
     1900             1.011               7
     2000             1.001               2


SUMMARIES OF PLAUSIBLE VALUES (N = NUMBER OF OBSERVATIONS * NUMBER OF IMPUTATIONS)


     SAMPLE STATISTICS


           Means
              SX%2a         SX%2b         B2a_Y         B2b_Y
              ________      ________      ________      ________
               -0.102         0.615        -0.053         2.048


           Covariances
              SX%2a         SX%2b         B2a_Y         B2b_Y
              ________      ________      ________      ________
 SX%2a          0.182
 SX%2b         -0.001         0.384
 B2a_Y         -0.009        -0.001         0.491
 B2b_Y         -0.001         0.271        -0.003         0.953


           Correlations
              SX%2a         SX%2b         B2a_Y         B2b_Y
              ________      ________      ________      ________
 SX%2a          1.000
 SX%2b         -0.002         1.000
 B2a_Y         -0.029        -0.003         1.000
 B2b_Y         -0.002         0.449        -0.005         1.000


SUMMARY OF PLAUSIBLE STANDARD DEVIATION (N = NUMBER OF OBSERVATIONS)


     SAMPLE STATISTICS


           Means
              SX%2a_SD      SX%2b_SD      B2a_Y_SD      B2b_Y_SD
              ________      ________      ________      ________
                0.079         0.106         0.097         0.170


           Covariances
              SX%2a_SD      SX%2b_SD      B2a_Y_SD      B2b_Y_SD
              ________      ________      ________      ________
 SX%2a_SD       0.000
 SX%2b_SD       0.000         0.000
 B2a_Y_SD       0.000         0.000         0.000
 B2b_Y_SD       0.000         0.000         0.000         0.000


           Correlations
              SX%2a_SD      SX%2b_SD      B2a_Y_SD      B2b_Y_SD
              ________      ________      ________      ________
 SX%2a_SD       1.000
 SX%2b_SD       0.000         1.000
 B2a_Y_SD      -0.144         0.000         1.000
 B2b_Y_SD       0.000         0.134         0.000         1.000


PLOT INFORMATION

The following plots are available:

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

     Beginning Time:  05:19:10
        Ending Time:  05:19:40
       Elapsed Time:  00:00:30



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