```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   4:54 AM

INPUT INSTRUCTIONS

TITLE:      this is an example of longitudinal modeling using a
cross-classified data approach where observations
are nested within the cross-classification of
time and subjects
DATA:       FILE = ex9.27.dat;
VARIABLE:   NAMES = y1-y3 time subject;
USEVARIABLES = y1-y3 timescor;
CLUSTER = subject time;
WITHIN = timescor (time) y1-y3;
DEFINE:     timescor = (time-1)/100;
ANALYSIS:   TYPE = CROSSCLASSIFIED RANDOM;
ESTIMATOR = BAYES;
PROCESSORS = 2;
BITERATIONS = (1000);
MODEL:      %WITHIN%
s1-s3 | f BY y1-y3;
f@1;
s | f ON timescor;
y1-y3; [y1-y3@0];
%BETWEEN time% ! time variation
s1-s3; [s1-s3];
y1-y3; [y1-y3@0];
s@0; [s@0];
%BETWEEN subject% ! subject variation
f; [f];
s1-s3@0; [s1-s3@0];
s; [s];
OUTPUT:     TECH1 TECH8;

this is an example of longitudinal modeling using a
cross-classified data approach where observations
are nested within the cross-classification of
time and subjects

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        7500

Number of dependent variables                                    3
Number of independent variables                                  1
Number of continuous latent variables                            5

Observed dependent variables

Continuous
Y1          Y2          Y3

Observed independent variables
TIMESCOR

Continuous latent variables
F           S1          S2          S3          S

Variables with special functions

Cluster variables     SUBJECT   TIME

Within variables
TIMESCOR

Level 1 and level 2a between variables
Y1          Y2          Y3

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)
ex9.27.dat
Input data format  FREE

SUMMARY OF DATA

Cluster information for TIME

Number of clusters                      100

Size (s)    Cluster ID with Size s

75        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

Cluster information for SUBJECT

Number of clusters                       75

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

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                    0.514       0.086      -7.678    0.01%      -1.364     -0.048      0.486
7500.000       5.097       0.207       9.189    0.01%       1.049      2.346
Y2                    0.495       0.044      -8.905    0.01%      -1.399     -0.115      0.450
7500.000       5.303       0.204      10.089    0.01%       1.067      2.387
Y3                    0.484       0.046      -9.549    0.01%      -1.359     -0.077      0.461
7500.000       5.107       0.219       9.331    0.01%       1.018      2.322
TIMESCOR              0.495       0.000       0.000    1.00%       0.190      0.390      0.495
7500.000       0.083      -1.200       0.990    1.00%       0.590      0.790

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                              16

Information Criteria

Deviance (DIC)                        81194.682
Estimated Number of Parameters (pD)     614.784

MODEL RESULTS

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

Within Level

Intercepts
Y1                 0.000       0.000      1.000       0.000       0.000
Y2                 0.000       0.000      1.000       0.000       0.000
Y3                 0.000       0.000      1.000       0.000       0.000

Residual Variances
Y1                 1.200       0.028      0.000       1.148       1.258      *
Y2                 1.180       0.028      0.000       1.125       1.236      *
Y3                 1.197       0.028      0.000       1.144       1.253      *
F                  1.000       0.000      0.000       1.000       1.000

Between TIME Level

Means
Y1                 0.000       0.000      1.000       0.000       0.000
Y2                 0.000       0.000      1.000       0.000       0.000
Y3                 0.000       0.000      1.000       0.000       0.000
S1                 1.306       0.034      0.000       1.243       1.374      *
S2                 1.347       0.034      0.000       1.280       1.416      *
S3                 1.307       0.037      0.000       1.232       1.383      *
S                  0.000       0.000      1.000       0.000       0.000

Variances
Y1                 0.452       0.074      0.000       0.335       0.618      *
Y2                 0.468       0.076      0.000       0.344       0.648      *
Y3                 0.442       0.070      0.000       0.332       0.607      *
S1                 0.088       0.016      0.000       0.064       0.125      *
S2                 0.098       0.017      0.000       0.070       0.138      *
S3                 0.114       0.019      0.000       0.083       0.160      *
S                  0.000       0.000      0.000       0.000       0.000

Between SUBJECT Level

Means
F                  0.347       0.129      0.004       0.085       0.602      *
S1                 0.000       0.000      1.000       0.000       0.000
S2                 0.000       0.000      1.000       0.000       0.000
S3                 0.000       0.000      1.000       0.000       0.000
S                  0.057       0.096      0.306      -0.123       0.235

Variances
F                  0.965       0.174      0.000       0.699       1.379      *
S1                 0.000       0.000      0.000       0.000       0.000
S2                 0.000       0.000      0.000       0.000       0.000
S3                 0.000       0.000      0.000       0.000       0.000
S                  0.013       0.013      0.000       0.000       0.052      *

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

NU
Y1            Y2            Y3            TIMESCOR
________      ________      ________      ________
0             0             0             0

LAMBDA
F%W           TIMESCOR
________      ________
Y1                 0             0
Y2                 0             0
Y3                 0             0
TIMESCOR           0             0

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

ALPHA
F%W           TIMESCOR
________      ________
0             0

BETA
F%W           TIMESCOR
________      ________
F%W                0             0
TIMESCOR           0             0

PSI
F%W           TIMESCOR
________      ________
F%W                0
TIMESCOR           0             0

PARAMETER SPECIFICATION FOR BETWEEN TIME

NU
Y1            Y2            Y3
________      ________      ________
0             0             0

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

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

ALPHA
F%2a          S1%2a         S2%2a         S3%2a         S%2a
________      ________      ________      ________      ________
0             7             8             9             0

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

PSI
F%2a          S1%2a         S2%2a         S3%2a         S%2a
________      ________      ________      ________      ________
F%2a               0
S1%2a              0            10
S2%2a              0             0            11
S3%2a              0             0             0            12
S%2a               0             0             0             0             0

PARAMETER SPECIFICATION FOR BETWEEN SUBJECT

ALPHA
F%2b          S1%2b         S2%2b         S3%2b         S%2b
________      ________      ________      ________      ________
13             0             0             0            14

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

PSI
F%2b          S1%2b         S2%2b         S3%2b         S%2b
________      ________      ________      ________      ________
F%2b              15
S1%2b              0             0
S2%2b              0             0             0
S3%2b              0             0             0             0
S%2b               0             0             0             0            16

STARTING VALUES FOR WITHIN

NU
Y1            Y2            Y3            TIMESCOR
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
F%W           TIMESCOR
________      ________
Y1             0.000         0.000
Y2             0.000         0.000
Y3             0.000         0.000
TIMESCOR       0.000         1.000

THETA
Y1            Y2            Y3            TIMESCOR
________      ________      ________      ________
Y1             2.548
Y2             0.000         2.652
Y3             0.000         0.000         2.553
TIMESCOR       0.000         0.000         0.000         0.000

ALPHA
F%W           TIMESCOR
________      ________
0.000         0.000

BETA
F%W           TIMESCOR
________      ________
F%W            0.000         0.000
TIMESCOR       0.000         0.000

PSI
F%W           TIMESCOR
________      ________
F%W            1.000
TIMESCOR       0.000         0.042

STARTING VALUES FOR BETWEEN TIME

NU
Y1            Y2            Y3
________      ________      ________
0.000         0.000         0.000

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

THETA
Y1            Y2            Y3
________      ________      ________
Y1             2.548
Y2             0.000         2.652
Y3             0.000         0.000         2.553

ALPHA
F%2a          S1%2a         S2%2a         S3%2a         S%2a
________      ________      ________      ________      ________
0.000         1.000         1.000         1.000         0.000

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

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

STARTING VALUES FOR BETWEEN SUBJECT

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

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

PSI
F%2b          S1%2b         S2%2b         S3%2b         S%2b
________      ________      ________      ________      ________
F%2b           1.000
S1%2b          0.000         0.000
S2%2b          0.000         0.000         0.000
S3%2b          0.000         0.000         0.000         0.000
S%2b           0.000         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~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~N(0.000,infinity)           0.0000            infinity            infinity
Parameter 9~N(0.000,infinity)           0.0000            infinity            infinity
Parameter 10~IG(-1.000,0.000)         infinity            infinity            infinity
Parameter 11~IG(-1.000,0.000)         infinity            infinity            infinity
Parameter 12~IG(-1.000,0.000)         infinity            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

TECHNICAL 8 OUTPUT

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

Parameter   KS Statistic P-value
Parameter 14    0.4600    0.0000

THE KOLMOGOROV-SMIRNOV DISTRIBUTION TEST FOR PARAMETER 14 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 13    0.1800    0.0691
Parameter 15    0.0800    0.8938
Parameter 5    0.0700    0.9610
Parameter 6    0.0700    0.9610
Parameter 8    0.0600    0.9921
Parameter 16    0.0500    0.9995
Parameter 4    0.0300    1.0000
Parameter 7    0.0200    1.0000
Parameter 9    0.0200    1.0000
Parameter 2    0.0200    1.0000
Parameter 3    0.0200    1.0000
Parameter 10    0.0200    1.0000
Parameter 12    0.0100    1.0000
Parameter 1    0.0100    1.0000
Parameter 11    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

TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

CHAIN    BSEED
1        0
2        285380

POTENTIAL       PARAMETER WITH
ITERATION    SCALE REDUCTION      HIGHEST PSR
100              3.010               14
200              1.359               16
300              1.224               16
400              1.046               14
500              1.164               14
600              1.456               14
700              1.877               14
800              2.051               14
900              2.092               14
1000             2.004               14
1100             1.690               14
1200             1.524               14
1300             1.540               14
1400             1.588               14
1500             1.486               14
1600             1.553               14
1700             1.639               14
1800             1.467               14
1900             1.256               14
2000             1.233               14
2100             1.311               14
2200             1.338               14
2300             1.313               14
2400             1.267               14
2500             1.079               14

Beginning Time:  04:54:23
Ending Time:  05:02:56
Elapsed Time:  00:08:33

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