```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:32 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

montecarlo:
names are y1-y3;
nobservations = 7500;
nreps = 1;
csizes = 75[100(1)];! 75 subjects (2b), 100 time points (2a)
ncsize = 1[1];
within = (level2a) y1-y3;
save = ex9.27.dat;

analysis:
type = cross random;
estimator = bayes;
proc = 2;

model population:
%within%
s1-s3 | f by y1-y3;
f@1;
y1-y3*1.2; [y1-y3@0];

%between level2a% ! across time variation
s1-s3*0.1;
[s1-s3*1.3];
y1-y3*.5; [y1-y3@0];

%between level2b% ! across subjects variation
f*1; [f*.5];
s1-s3@0;
[s1-s3@0];

model:
%within%
s1-s3 | f by y1-y3;
f@1;
y1-y3*1.2; [y1-y3@0];

%between level2a% ! across time variation
s1-s3*0.1;
[s1-s3*1.3];
y1-y3*.5; [y1-y3@0];

%between level2b% ! across subjects variation
f*1; [f*.5];
s1-s3@0;
[s1-s3@0];

output:
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 replications
Requested                                                    1
Completed                                                    1
Value of seed                                                    0

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           S1          S2          S3

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

SUMMARY OF DATA FOR THE FIRST REPLICATION

Cluster information

Number of level 2a clusters          100
Number of level 2b clusters           75

MODEL FIT INFORMATION

Number of Free Parameters                       14

Information Criteria

Deviance (DIC)

Mean                             81153.044
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        81153.044      81153.044
0.980       0.000        81153.044      81153.044
0.950       0.000        81153.044      81153.044
0.900       0.000        81153.044      81153.044
0.800       0.000        81153.044      81153.044
0.700       0.000        81153.044      81153.044
0.500       0.000        81153.044      81153.044
0.300       0.000        81153.044      81153.044
0.200       0.000        81153.044      81153.044
0.100       0.000        81153.044      81153.044
0.050       0.000        81153.044      81153.044
0.020       0.000        81153.044      81153.044
0.010       0.000        81153.044      81153.044

Estimated Number of Parameters (pD)

Mean                               581.304
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000          581.304        581.304
0.980       0.000          581.304        581.304
0.950       0.000          581.304        581.304
0.900       0.000          581.304        581.304
0.800       0.000          581.304        581.304
0.700       0.000          581.304        581.304
0.500       0.000          581.304        581.304
0.300       0.000          581.304        581.304
0.200       0.000          581.304        581.304
0.100       0.000          581.304        581.304
0.050       0.000          581.304        581.304
0.020       0.000          581.304        581.304
0.010       0.000          581.304        581.304

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
Within Level

Intercepts
Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Variances
F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Residual Variances
Y1                  1.200     1.1980     0.0000     0.0297     0.0000 1.000 1.000
Y2                  1.200     1.1837     0.0000     0.0282     0.0003 1.000 1.000
Y3                  1.200     1.1944     0.0000     0.0256     0.0000 1.000 1.000

Between LEVEL2A Level

Means
Y1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
Y3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S1                  1.300     1.3074     0.0000     0.0302     0.0001 1.000 1.000
S2                  1.300     1.3576     0.0000     0.0381     0.0033 1.000 1.000
S3                  1.300     1.3122     0.0000     0.0350     0.0001 1.000 1.000

Variances
Y1                  0.500     0.4401     0.0000     0.0681     0.0036 1.000 1.000
Y2                  0.500     0.4717     0.0000     0.0746     0.0008 1.000 1.000
Y3                  0.500     0.4477     0.0000     0.0717     0.0027 1.000 1.000
S1                  0.100     0.0867     0.0000     0.0148     0.0002 1.000 1.000
S2                  0.100     0.0972     0.0000     0.0184     0.0000 1.000 1.000
S3                  0.100     0.1143     0.0000     0.0188     0.0002 1.000 1.000

Between LEVEL2B Level

Means
F                   0.500     0.4116     0.0000     0.1128     0.0078 1.000 1.000
S1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Variances
F                   1.000     0.9407     0.0000     0.1594     0.0035 1.000 1.000
S1                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

CORRELATIONS AND MEAN SQUARE ERROR OF THE TRUE FACTOR VALUES AND THE FACTOR SCORES

CORRELATIONS                MEAN SQUARE ERROR
Average    Std. Dev.           Average    Std. Dev.
F%2a                0.000       0.000              0.031       0.000
S1%2a               0.935       0.000              0.107       0.000
S2%2a               0.942       0.000              0.108       0.000
S3%2a               0.920       0.000              0.132       0.000
F%2b                0.992       0.000              0.138       0.000
S1%2b               0.000       0.000              0.035       0.000
S2%2b               0.000       0.000              0.036       0.000
S3%2b               0.000       0.000              0.033       0.000
B2a_Y1              0.965       0.000              0.198       0.000
B2a_Y2              0.962       0.000              0.210       0.000
B2a_Y3              0.964       0.000              0.187       0.000

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

NU
Y1            Y2            Y3
________      ________      ________
0             0             0

LAMBDA
F%W
________
Y1                 0
Y2                 0
Y3                 0

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

ALPHA
F%W
________
0

BETA
F%W
________
F%W                0

PSI
F%W
________
F%W                0

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A

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                 4
Y2                 0             5
Y3                 0             0             6

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

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               0
S1%2a              0            10
S2%2a              0             0            11
S3%2a              0             0             0            12

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B

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

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              14
S1%2b              0             0
S2%2b              0             0             0
S3%2b              0             0             0             0

STARTING VALUES FOR WITHIN

NU
Y1            Y2            Y3
________      ________      ________
0.000         0.000         0.000

LAMBDA
F%W
________
Y1             0.000
Y2             0.000
Y3             0.000

THETA
Y1            Y2            Y3
________      ________      ________
Y1             1.200
Y2             0.000         1.200
Y3             0.000         0.000         1.200

ALPHA
F%W
________
0.000

BETA
F%W
________
F%W            0.000

PSI
F%W
________
F%W            1.000

STARTING VALUES FOR BETWEEN LEVEL2A

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             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500

ALPHA
F%2a          S1%2a         S2%2a         S3%2a
________      ________      ________      ________
0.000         1.300         1.300         1.300

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           0.000
S1%2a          0.000         0.100
S2%2a          0.000         0.000         0.100
S3%2a          0.000         0.000         0.000         0.100

STARTING VALUES FOR BETWEEN LEVEL2B

ALPHA
F%2b          S1%2b         S2%2b         S3%2b
________      ________      ________      ________
0.500         0.000         0.000         0.000

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         0.000
S2%2b          0.000         0.000         0.000
S3%2b          0.000         0.000         0.000         0.000

POPULATION VALUES FOR WITHIN

NU
Y1            Y2            Y3
________      ________      ________
0.000         0.000         0.000

LAMBDA
F%W
________
Y1             0.000
Y2             0.000
Y3             0.000

THETA
Y1            Y2            Y3
________      ________      ________
Y1             1.200
Y2             0.000         1.200
Y3             0.000         0.000         1.200

ALPHA
F%W
________
0.000

BETA
F%W
________
F%W            0.000

PSI
F%W
________
F%W            1.000

POPULATION VALUES FOR BETWEEN LEVEL2A

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             0.500
Y2             0.000         0.500
Y3             0.000         0.000         0.500

ALPHA
F%2a          S1%2a         S2%2a         S3%2a
________      ________      ________      ________
0.000         1.300         1.300         1.300

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           0.000
S1%2a          0.000         0.100
S2%2a          0.000         0.000         0.100
S3%2a          0.000         0.000         0.000         0.100

POPULATION VALUES FOR BETWEEN LEVEL2B

ALPHA
F%2b          S1%2b         S2%2b         S3%2b
________      ________      ________      ________
0.500         0.000         0.000         0.000

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         0.000
S2%2b          0.000         0.000         0.000
S3%2b          0.000         0.000         0.000         0.000

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~IG(-1.000,0.000)         infinity            infinity            infinity

TECHNICAL 8 OUTPUT

REPLICATION 1:

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

Parameter   KS Statistic P-value
Parameter 1    0.1300    0.3439
Parameter 4    0.1200    0.4431
Parameter 8    0.1000    0.6766
Parameter 9    0.1000    0.6766
Parameter 14    0.1000    0.6766
Parameter 13    0.0900    0.7942
Parameter 6    0.0700    0.9610
Parameter 5    0.0500    0.9995
Parameter 10    0.0400    1.0000
Parameter 2    0.0300    1.0000
Parameter 7    0.0100    1.0000
Parameter 12    0.0100    1.0000
Parameter 3    0.0100    1.0000
Parameter 11    0.0100    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

REPLICATION 1:

POTENTIAL       PARAMETER WITH
ITERATION    SCALE REDUCTION      HIGHEST PSR
100              1.164               3
200              1.045               1

SAVEDATA INFORMATION

Order of variables

Y1
Y2
Y3
LEVEL2A
LEVEL2B

Save file
ex9.27.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:32:14
Ending Time:  03:32:40
Elapsed Time:  00:00:26

MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2017 Muthen & Muthen
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