Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:02 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a cross-classified time series analysis
      with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
      for continuous factor indicators with random intercepts and a factor varying
      across both subjects and time
  DATA:	FILE = ex9.40.dat;
  VARIABLE:	NAMES = y1-y3 time subject;
  	CLUSTER = subject time;
  ANALYSIS:	TYPE = CROSSCLASSIFIED RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (1000);
  MODEL:	%WITHIN%
  	f BY y1-y3* (&1 1-3);
  	f@1;
  	f ON f&1;
  	%BETWEEN subject%
  	fsubj BY y1-y3* (1-3);
  	%BETWEEN time%
  	ftime BY y1-y3* (1-3);
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;
  	FACTORS = ALL;



INPUT READING TERMINATED NORMALLY



this is an example of a cross-classified time series analysis
with a first-order autoregressive AR(1) confirmatory factor analysis (CFA) model
for continuous factor indicators with random intercepts and a factor varying
across both subjects and time

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of dependent variables                                    3
Number of independent variables                                  0
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y1          Y2          Y3

Continuous latent variables
   F           F&1         FTIME       FSUBJ

Variables with special functions

  Cluster variables     SUBJECT   TIME

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)
  ex9.40.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




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                    0.940      -0.020     -10.014    0.01%      -1.121      0.321      0.949
           20000.000       5.992      -0.006      10.079    0.01%       1.564      3.014
     Y2                    0.954      -0.030      -8.184    0.01%      -1.137      0.344      0.958
           20000.000       6.262      -0.016       9.991    0.01%       1.589      3.070
     Y3                    0.783       0.045      -7.819    0.01%      -1.366      0.133      0.792
           20000.000       6.434      -0.013      11.156    0.01%       1.419      2.886


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                              18

Information Criteria

          Deviance (DIC)                       197729.437
          Estimated Number of Parameters (pD)   16490.195



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                 1.280       0.011      0.000       1.258       1.300      *
    Y2                 1.296       0.011      0.000       1.276       1.317      *
    Y3                 1.268       0.011      0.000       1.246       1.289      *

 F          ON
    F&1                0.299       0.008      0.000       0.282       0.316      *

 Residual Variances
    Y1                 1.198       0.018      0.000       1.163       1.234      *
    Y2                 1.173       0.018      0.000       1.137       1.208      *
    Y3                 1.232       0.017      0.000       1.197       1.266      *
    F                  1.000       0.000      0.000       1.000       1.000

Between TIME Level

 FTIME    BY
    Y1                 1.280       0.011      0.000       1.258       1.300      *
    Y2                 1.296       0.011      0.000       1.276       1.317      *
    Y3                 1.268       0.011      0.000       1.246       1.289      *

 Variances
    FTIME              0.617       0.103      0.000       0.452       0.849      *

 Residual Variances
    Y1                 0.129       0.049      0.000       0.049       0.242      *
    Y2                 0.367       0.073      0.000       0.244       0.532      *
    Y3                 0.353       0.071      0.000       0.235       0.516      *

Between SUBJECT Level

 FSUBJ    BY
    Y1                 1.280       0.011      0.000       1.258       1.300      *
    Y2                 1.296       0.011      0.000       1.276       1.317      *
    Y3                 1.268       0.011      0.000       1.246       1.289      *

 Intercepts
    Y1                 0.985       0.187      0.000       0.573       1.289      *
    Y2                 1.022       0.169      0.000       0.609       1.273      *
    Y3                 0.828       0.164      0.000       0.494       1.138      *

 Variances
    FSUBJ              0.890       0.108      0.000       0.713       1.132      *

 Residual Variances
    Y1                 0.538       0.082      0.000       0.397       0.706      *
    Y2                 0.502       0.082      0.000       0.369       0.679      *
    Y3                 0.588       0.088      0.000       0.443       0.782      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


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


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


           ALPHA
              F             F&1
              ________      ________
                    0             0


           BETA
              F             F&1
              ________      ________
 F                  0             7
 F&1                0             0


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


     PARAMETER SPECIFICATION FOR BETWEEN TIME


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              FTIME
              ________
 Y1                 1
 Y2                 2
 Y3                 3


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                 8
 Y2                 0             9
 Y3                 0             0            10


           ALPHA
              FTIME
              ________
                    0


           BETA
              FTIME
              ________
 FTIME              0


           PSI
              FTIME
              ________
 FTIME             11


     PARAMETER SPECIFICATION FOR BETWEEN SUBJECT


           NU
              Y1            Y2            Y3
              ________      ________      ________
                   12            13            14


           LAMBDA
              FSUBJ
              ________
 Y1                 1
 Y2                 2
 Y3                 3


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                15
 Y2                 0            16
 Y3                 0             0            17


           ALPHA
              FSUBJ
              ________
                    0


           BETA
              FSUBJ
              ________
 FSUBJ              0


           PSI
              FSUBJ
              ________
 FSUBJ             18


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                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


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             2.996
 Y2             0.000         3.131
 Y3             0.000         0.000         3.217


           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              1.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN TIME


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              FTIME
              ________
 Y1             1.000
 Y2             1.000
 Y3             1.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             2.996
 Y2             0.000         3.131
 Y3             0.000         0.000         3.217


           ALPHA
              FTIME
              ________
                0.000


           BETA
              FTIME
              ________
 FTIME          0.000


           PSI
              FTIME
              ________
 FTIME          1.000


     STARTING VALUES FOR BETWEEN SUBJECT


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.940         0.954         0.783


           LAMBDA
              FSUBJ
              ________
 Y1             1.000
 Y2             1.000
 Y3             1.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             2.996
 Y2             0.000         3.131
 Y3             0.000         0.000         3.217


           ALPHA
              FSUBJ
              ________
                0.000


           BETA
              FSUBJ
              ________
 FSUBJ          0.000


           PSI
              FSUBJ
              ________
 FSUBJ          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~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 8~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 9~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 11~IG(-1.000,0.000)         infinity            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~IG(-1.000,0.000)         infinity            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


TECHNICAL 8 OUTPUT



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





     Parameter   KS Statistic P-value
     Parameter 13    0.3700    0.0000

     THE KOLMOGOROV-SMIRNOV DISTRIBUTION TEST FOR PARAMETER 13 HAS A P-VALUE 0.0000,
     INDICATING DISCREPANT POSTERIOR DISTRIBUTIONS IN THE DIFFERENT MCMC CHAINS.
     THIS MAY INDICATE NON-CONVERGENCE DUE TO AN INSUFFICIENT NUMBER OF MCMC ITERATIONS OR IT MAY
     INDICATE A NON-IDENTIFIED MODEL. SPECIFY A LARGER NUMBER OF MCMC ITERATIONS USING THE FBITER
     OPTION OF THE ANALYSIS COMMAND TO INVESTIGATE THE PROBLEM.

     Parameter 12    0.3500    0.0000
     Parameter 14    0.2600    0.0018
     Parameter 15    0.1200    0.4431
     Parameter 16    0.1100    0.5560
     Parameter 11    0.1000    0.6766
     Parameter 8    0.0900    0.7942
     Parameter 17    0.0800    0.8938
     Parameter 9    0.0500    0.9995
     Parameter 10    0.0500    0.9995
     Parameter 6    0.0300    1.0000
     Parameter 18    0.0300    1.0000
     Parameter 5    0.0200    1.0000
     Parameter 1    0.0100    1.0000
     Parameter 3    0.0100    1.0000
     Parameter 4    0.0100    1.0000
     Parameter 7    0.0000    1.0000
     Parameter 2    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


   TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

     CHAIN    BSEED
     1        0
     2        285380

                     POTENTIAL       PARAMETER WITH
     ITERATION    SCALE REDUCTION      HIGHEST PSR
     100              1.178               16
     200              1.178               8
     300              1.282               13
     400              1.445               13
     500              1.453               14
     600              1.536               14
     700              1.789               14
     800              1.673               14
     900              1.846               14
     1000             2.036               14
     1100             2.333               12
     1200             2.298               12
     1300             2.065               12
     1400             1.692               12
     1500             1.400               12
     1600             1.216               12
     1700             1.069               13


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


     SAMPLE STATISTICS


           Means
              F             F&1           FTIME         FSUBJ         B2a_Y1
              ________      ________      ________      ________      ________
               -0.006        -0.006         0.029         0.004         0.050


           Means
              B2a_Y2        B2a_Y3        B2b_Y1        B2b_Y2        B2b_Y3
              ________      ________      ________      ________      ________
                0.003         0.022         0.897         0.961         0.771


           Covariances
              F             F&1           FTIME         FSUBJ         B2a_Y1
              ________      ________      ________      ________      ________
 F              1.100
 F&1            0.328         1.100
 FTIME         -0.004        -0.004         0.606
 FSUBJ         -0.001        -0.001         0.000         0.888
 B2a_Y1        -0.005        -0.005         0.755         0.000         1.059
 B2a_Y2        -0.007        -0.006         0.784         0.000         0.971
 B2a_Y3        -0.004        -0.009         0.807         0.000         1.001
 B2b_Y1        -0.003        -0.004         0.000         1.117        -0.001
 B2b_Y2        -0.002        -0.003         0.000         1.120         0.000
 B2b_Y3         0.004         0.004         0.000         1.134         0.000


           Covariances
              B2a_Y2        B2a_Y3        B2b_Y1        B2b_Y2        B2b_Y3
              ________      ________      ________      ________      ________
 B2a_Y2         1.376
 B2a_Y3         1.070         1.397
 B2b_Y1         0.000         0.001         1.960
 B2b_Y2        -0.001        -0.001         1.410         1.893
 B2b_Y3        -0.001        -0.001         1.465         1.433         2.044


           Correlations
              F             F&1           FTIME         FSUBJ         B2a_Y1
              ________      ________      ________      ________      ________
 F              1.000
 F&1            0.298         1.000
 FTIME         -0.005        -0.005         1.000
 FSUBJ         -0.001        -0.001         0.000         1.000
 B2a_Y1        -0.005        -0.005         0.942         0.001         1.000
 B2a_Y2        -0.006        -0.005         0.858         0.000         0.804
 B2a_Y3        -0.003        -0.007         0.877         0.000         0.823
 B2b_Y1        -0.002        -0.003         0.000         0.847         0.000
 B2b_Y2        -0.001        -0.002         0.000         0.864         0.000
 B2b_Y3         0.003         0.003         0.000         0.842         0.000


           Correlations
              B2a_Y2        B2a_Y3        B2b_Y1        B2b_Y2        B2b_Y3
              ________      ________      ________      ________      ________
 B2a_Y2         1.000
 B2a_Y3         0.772         1.000
 B2b_Y1         0.000         0.000         1.000
 B2b_Y2        -0.001         0.000         0.732         1.000
 B2b_Y3         0.000        -0.001         0.732         0.729         1.000


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


     SAMPLE STATISTICS


           Means
              F_SD          F&1_SD        FTIME_SD      FSUBJ_SD      B2a_Y1_S
              ________      ________      ________      ________      ________
                0.456         0.462         0.213         0.339         0.113


           Means
              B2a_Y2_S      B2a_Y3_S      B2b_Y1_S      B2b_Y2_S      B2b_Y3_S
              ________      ________      ________      ________      ________
                0.117         0.120         0.181         0.182         0.183


           Covariances
              F_SD          F&1_SD        FTIME_SD      FSUBJ_SD      B2a_Y1_S
              ________      ________      ________      ________      ________
 F_SD           0.002
 F&1_SD         0.000         0.005
 FTIME_SD       0.000         0.000         0.001
 FSUBJ_SD       0.000         0.000         0.000         0.001
 B2a_Y1_S       0.000         0.000         0.000         0.000         0.000
 B2a_Y2_S       0.000         0.000         0.000         0.000         0.000
 B2a_Y3_S       0.000         0.000         0.000         0.000         0.000
 B2b_Y1_S       0.000         0.000         0.000         0.000         0.000
 B2b_Y2_S       0.000         0.000         0.000         0.000         0.000
 B2b_Y3_S       0.000         0.000         0.000         0.000         0.000


           Covariances
              B2a_Y2_S      B2a_Y3_S      B2b_Y1_S      B2b_Y2_S      B2b_Y3_S
              ________      ________      ________      ________      ________
 B2a_Y2_S       0.000
 B2a_Y3_S       0.000         0.000
 B2b_Y1_S       0.000         0.000         0.001
 B2b_Y2_S       0.000         0.000         0.001         0.001
 B2b_Y3_S       0.000         0.000         0.001         0.001         0.001


           Correlations
              F_SD          F&1_SD        FTIME_SD      FSUBJ_SD      B2a_Y1_S
              ________      ________      ________      ________      ________
 F_SD           1.000
 F&1_SD         0.037         1.000
 FTIME_SD       0.007        -0.021         1.000
 FSUBJ_SD       0.049         0.035         0.000         1.000
 B2a_Y1_S       0.029        -0.040         0.199         0.000         1.000
 B2a_Y2_S       0.019         0.019         0.024         0.000         0.572
 B2a_Y3_S       0.027         0.103         0.038         0.000         0.437
 B2b_Y1_S       0.149         0.092         0.000         0.275         0.000
 B2b_Y2_S       0.139         0.086         0.000         0.267         0.000
 B2b_Y3_S       0.133         0.082         0.000         0.310         0.000


           Correlations
              B2a_Y2_S      B2a_Y3_S      B2b_Y1_S      B2b_Y2_S      B2b_Y3_S
              ________      ________      ________      ________      ________
 B2a_Y2_S       1.000
 B2a_Y3_S       0.614         1.000
 B2b_Y1_S       0.000         0.000         1.000
 B2b_Y2_S       0.000         0.000         0.804         1.000
 B2b_Y3_S       0.000         0.000         0.758         0.827         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:  17:02:40
        Ending Time:  17:03:00
       Elapsed Time:  00:00:20



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