Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:03 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, random factor loadings,
      and a factor varying across both subjects and time
  DATA:	FILE = ex9.40part2.dat;
  VARIABLE:	NAMES = y1-y3 time subject;
  	CLUSTER = subject time;
  ANALYSIS:	TYPE = CROSSCLASSIFIED RANDOM;
  	ESTIMATOR = BAYES;
  	PROCESSORS = 2;
  	BITERATIONS = (1000);
  MODEL:	%WITHIN%
  	s1-s3 | f BY y1-y3 (&1);
  	f@1;
  	f ON f&1;
  	%BETWEEN subject%
  	f;
      %BETWEEN time%
  	f;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;



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, random factor loadings,
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                            5

Observed dependent variables

  Continuous
   Y1          Y2          Y3

Continuous latent variables
   F           F&1         S1          S2          S3

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

Input data file(s)
  ex9.40part2.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                    1.195       0.102     -11.151    0.01%      -1.151      0.448      1.139
           20000.000       7.995       0.117      14.271    0.01%       1.824      3.521
     Y2                    1.139       0.033      -9.327    0.01%      -1.183      0.473      1.143
           20000.000       7.757       0.079      13.259    0.01%       1.842      3.440
     Y3                    1.128       0.104     -12.656    0.01%      -1.278      0.392      1.126
           20000.000       8.701       0.566      14.264    0.01%       1.821      3.466


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)                       198648.054
          Estimated Number of Parameters (pD)   17112.577



MODEL RESULTS

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

Within Level

 F          ON
    F&1                0.306       0.009      0.000       0.290       0.323      *

 Residual Variances
    Y1                 1.220       0.018      0.000       1.184       1.254      *
    Y2                 1.184       0.018      0.000       1.150       1.219      *
    Y3                 1.217       0.018      0.000       1.181       1.253      *
    F                  1.000       0.000      0.000       1.000       1.000

Between TIME Level

 Variances
    Y1                 0.316       0.054      0.000       0.228       0.443      *
    Y2                 0.265       0.046      0.000       0.194       0.373      *
    Y3                 0.344       0.059      0.000       0.247       0.479      *
    F                  0.489       0.078      0.000       0.367       0.668      *

Between SUBJECT Level

 Means
    Y1                 1.086       0.088      0.000       0.918       1.252      *
    Y2                 1.072       0.106      0.000       0.852       1.258      *
    Y3                 0.999       0.098      0.000       0.822       1.196      *
    S1                 1.315       0.027      0.000       1.266       1.368      *
    S2                 1.316       0.025      0.000       1.266       1.364      *
    S3                 1.317       0.025      0.000       1.269       1.365      *

 Variances
    Y1                 0.606       0.090      0.000       0.454       0.808      *
    Y2                 0.567       0.080      0.000       0.430       0.745      *
    Y3                 0.360       0.066      0.000       0.246       0.502      *
    F                  0.878       0.101      0.000       0.712       1.097      *
    S1                 0.111       0.014      0.000       0.088       0.143      *
    S2                 0.102       0.012      0.000       0.081       0.130      *
    S3                 0.097       0.012      0.000       0.076       0.124      *


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              F%W           F&1
              ________      ________
 Y1                 0             0
 Y2                 0             0
 Y3                 0             0


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                 1
 Y2                 0             2
 Y3                 0             0             3


           ALPHA
              F%W           F&1
              ________      ________
                    0             0


           BETA
              F%W           F&1
              ________      ________
 F%W                0             4
 F&1                0             0


           PSI
              F%W           F&1
              ________      ________
 F%W                0
 F&1                0             0


     PARAMETER SPECIFICATION FOR BETWEEN TIME


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    0             0             0


           LAMBDA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y3                 0             0             0             0


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


           ALPHA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
                    0             0             0             0


           BETA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a               0             0             0             0
 S1%2a              0             0             0             0
 S2%2a              0             0             0             0
 S3%2a              0             0             0             0


           PSI
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a               8
 S1%2a              0             0
 S2%2a              0             0             0
 S3%2a              0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN SUBJECT


           NU
              Y1            Y2            Y3
              ________      ________      ________
                    9            10            11


           LAMBDA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 Y1                 0             0             0             0
 Y2                 0             0             0             0
 Y3                 0             0             0             0


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1                12
 Y2                 0            13
 Y3                 0             0            14


           ALPHA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
                    0            15            16            17


           BETA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b               0             0             0             0
 S1%2b              0             0             0             0
 S2%2b              0             0             0             0
 S3%2b              0             0             0             0


           PSI
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b              18
 S1%2b              0            19
 S2%2b              0             0            20
 S3%2b              0             0             0            21


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%W           F&1
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 Y3             0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             3.997
 Y2             0.000         3.878
 Y3             0.000         0.000         4.351


           ALPHA
              F%W           F&1
              ________      ________
                0.000         0.000


           BETA
              F%W           F&1
              ________      ________
 F%W            0.000         0.000
 F&1            0.000         0.000


           PSI
              F%W           F&1
              ________      ________
 F%W            1.000
 F&1            0.000         1.000


     STARTING VALUES FOR BETWEEN TIME


           NU
              Y1            Y2            Y3
              ________      ________      ________
                0.000         0.000         0.000


           LAMBDA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             3.997
 Y2             0.000         3.878
 Y3             0.000         0.000         4.351


           ALPHA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           BETA
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           0.000         0.000         0.000         0.000
 S1%2a          0.000         0.000         0.000         0.000
 S2%2a          0.000         0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


           PSI
              F%2a          S1%2a         S2%2a         S3%2a
              ________      ________      ________      ________
 F%2a           1.000
 S1%2a          0.000         0.000
 S2%2a          0.000         0.000         0.000
 S3%2a          0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN SUBJECT


           NU
              Y1            Y2            Y3
              ________      ________      ________
                1.195         1.139         1.128


           LAMBDA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 Y1             0.000         0.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000


           THETA
              Y1            Y2            Y3
              ________      ________      ________
 Y1             3.997
 Y2             0.000         3.878
 Y3             0.000         0.000         4.351


           ALPHA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
                0.000         1.000         1.000         1.000


           BETA
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           0.000         0.000         0.000         0.000
 S1%2b          0.000         0.000         0.000         0.000
 S2%2b          0.000         0.000         0.000         0.000
 S3%2b          0.000         0.000         0.000         0.000


           PSI
              F%2b          S1%2b         S2%2b         S3%2b
              ________      ________      ________      ________
 F%2b           1.000
 S1%2b          0.000         1.000
 S2%2b          0.000         0.000         1.000
 S3%2b          0.000         0.000         0.000         1.000



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

     Parameter 1~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 2~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 3~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 4~N(0.000,infinity)           0.0000            infinity            infinity
     Parameter 5~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 6~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 7~IG(-1.000,0.000)          infinity            infinity            infinity
     Parameter 8~IG(-1.000,0.000)          infinity            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~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 13~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 14~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 15~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 16~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 17~N(0.000,infinity)          0.0000            infinity            infinity
     Parameter 18~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 19~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 20~IG(-1.000,0.000)         infinity            infinity            infinity
     Parameter 21~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 10    0.2400    0.0050
     Parameter 11    0.2300    0.0082
     Parameter 12    0.2200    0.0131
     Parameter 14    0.2000    0.0314
     Parameter 13    0.1900    0.0470
     Parameter 9    0.1800    0.0691
     Parameter 8    0.1400    0.2606
     Parameter 7    0.1100    0.5560
     Parameter 16    0.0900    0.7942
     Parameter 5    0.0900    0.7942
     Parameter 18    0.0800    0.8938
     Parameter 6    0.0700    0.9610
     Parameter 15    0.0400    1.0000
     Parameter 17    0.0200    1.0000
     Parameter 21    0.0100    1.0000
     Parameter 20    0.0100    1.0000
     Parameter 2    0.0100    1.0000
     Parameter 3    0.0000    1.0000
     Parameter 19    0.0000    1.0000
     Parameter 4    0.0000    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
     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              1.500               11
     200              1.506               9
     300              1.307               14
     400              1.476               12
     500              1.454               12
     600              1.616               11
     700              1.594               11
     800              1.713               11
     900              1.373               11
     1000             1.339               11
     1100             1.314               11
     1200             1.259               10
     1300             1.170               12
     1400             1.156               12
     1500             1.118               12
     1600             1.079               10


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:  17:03:00
        Ending Time:  17:05:32
       Elapsed Time:  00:02:32



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