```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:57 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a cross-classified time series analysis
with a univariate first-order autoregressive AR(1) model for a
continuous dependent variable with a covariate, linear trend, and random slope
Same as mcex9.38
Montecarlo:
names are y x w xm;
nobservations = 20000;
nreps = 1;
CSIZES = 200[100(1)];
ncsize = 1[1];
lagged = y(1);
Between = (level2b)w (level2b)xm;
within = x;
save = ex9.39.dat;

ANALYSIS:  TYPE = CROSS random;
estimator=bayes; process=2;
fbiter = 200; ! full convergence not needed to generate the data

model population:
%within%
sx | y ON x;
sy | y ON y&1;
y*1; x*1;

%between LEVEL2A%  ! time
y*.5; sx*.2; sy@0;

%between LEVEL2B%  ! subject
y*.5; [y*2];
w*1; xm*1;
w with xm*.5;
[sx*.5]; sx*.2;
[sy*.3]; sy*.02;
y on w*.3 xm*.4;
sx on w*.2 xm*.3;
sy on w*.05 xm*.05;

model:
%within%
sx | y ON x;
sy | y ON y&1;
y*1; x*1;
%between LEVEL2A%  ! time
y*.5; sx*.2; sy@0; ! random AR over time takes a long time

%between LEVEL2B%  ! subject
y*.5; [y*2];
w*1; xm*1;
w with xm*.5;
[sx*.5]; sx*.2;
[sy*.3]; sy*.02;
y on w*.3 xm*.4;
sx on w*.2 xm*.3;
sy on w*.05 xm*.05;

output: tech8 tech9;

INPUT READING TERMINATED NORMALLY

this is an example of a cross-classified time series analysis
with a univariate first-order autoregressive AR(1) model for a
continuous dependent variable with a covariate, linear trend, and random slope
Same as mcex9.38

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                       20000

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                    0

Number of dependent variables                                    1
Number of independent variables                                  4
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Y

Observed independent variables
X           W           XM          Y&1

Continuous latent variables
SX          SY

Variables with special functions

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)
Fixed number of iterations                                   200
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          200

MODEL FIT INFORMATION

Number of Free Parameters                       22

Information Criteria

Deviance (DIC)

Mean                            114463.038
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000       114463.038     114463.038
0.980       0.000       114463.038     114463.038
0.950       0.000       114463.038     114463.038
0.900       0.000       114463.038     114463.038
0.800       0.000       114463.038     114463.038
0.700       0.000       114463.038     114463.038
0.500       0.000       114463.038     114463.038
0.300       0.000       114463.038     114463.038
0.200       0.000       114463.038     114463.038
0.100       0.000       114463.038     114463.038
0.050       0.000       114463.038     114463.038
0.020       0.000       114463.038     114463.038
0.010       0.000       114463.038     114463.038

Estimated Number of Parameters (pD)

Mean                               760.591
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000          760.591        760.591
0.980       0.000          760.591        760.591
0.950       0.000          760.591        760.591
0.900       0.000          760.591        760.591
0.800       0.000          760.591        760.591
0.700       0.000          760.591        760.591
0.500       0.000          760.591        760.591
0.300       0.000          760.591        760.591
0.200       0.000          760.591        760.591
0.100       0.000          760.591        760.591
0.050       0.000          760.591        760.591
0.020       0.000          760.591        760.591
0.010       0.000          760.591        760.591

MODEL RESULTS

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

Means
X                   0.000    -0.0038     0.0000     0.0068     0.0000 1.000 0.000

Variances
X                   1.000     0.9929     0.0000     0.0091     0.0001 1.000 1.000

Residual Variances
Y                   1.000     1.0150     0.0000     0.0100     0.0002 1.000 1.000

Between LEVEL2A Level

Variances
Y                   0.500     0.5024     0.0000     0.0700     0.0000 1.000 1.000
SX                  0.200     0.1857     0.0000     0.0248     0.0002 1.000 1.000
SY                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2B Level

SX         ON
W                   0.200     0.2355     0.0000     0.0350     0.0013 1.000 1.000
XM                  0.300     0.2710     0.0000     0.0320     0.0008 1.000 1.000

SY         ON
W                   0.050     0.0745     0.0000     0.0116     0.0006 0.000 1.000
XM                  0.050     0.0346     0.0000     0.0112     0.0002 1.000 1.000

Y          ON
W                   0.300     0.3186     0.0000     0.0510     0.0003 1.000 1.000
XM                  0.400     0.4338     0.0000     0.0547     0.0011 1.000 1.000

W        WITH
XM                  0.500     0.5761     0.0000     0.0982     0.0058 1.000 1.000

Means
W                   0.000    -0.0659     0.0000     0.0814     0.0043 1.000 0.000
XM                  0.000    -0.0685     0.0000     0.0808     0.0047 1.000 0.000

Intercepts
Y                   2.000     2.0397     0.0000     0.0664     0.0016 1.000 1.000
SX                  0.500     0.5650     0.0000     0.0466     0.0042 1.000 1.000
SY                  0.300     0.3246     0.0000     0.0111     0.0006 0.000 1.000

Variances
W                   1.000     1.1255     0.0000     0.1198     0.0157 1.000 1.000
XM                  1.000     1.1720     0.0000     0.1241     0.0296 1.000 1.000

Residual Variances
Y                   0.500     0.5223     0.0000     0.0571     0.0005 1.000 1.000
SX                  0.200     0.2049     0.0000     0.0199     0.0000 1.000 1.000
SY                  0.020     0.0173     0.0000     0.0023     0.0000 1.000 1.000

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

CORRELATIONS                MEAN SQUARE ERROR
Average    Std. Dev.           Average    Std. Dev.
SX%2a               0.986       0.000              0.070       0.000
SY%2a               0.000       0.000              0.034       0.000
SX%2b               0.989       0.000              0.099       0.000
SY%2b               0.910       0.000              0.066       0.000
B2a_Y               0.994       0.000              0.088       0.000
B2b_Y               0.988       0.000              0.169       0.000

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             1             0

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

PSI
Y             X             Y&1
________      ________      ________
Y                  2
X                  0             3
Y&1                0             0             0

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A

NU
Y
________
0

LAMBDA
SX%2a         SY%2a         Y
________      ________      ________
Y                  0             0             0

THETA
Y
________
Y                  0

ALPHA
SX%2a         SY%2a         Y
________      ________      ________
0             0             0

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

PSI
SX%2a         SY%2a         Y
________      ________      ________
SX%2a              4
SY%2a              0             0
Y                  0             0             5

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B

NU
W             XM            Y
________      ________      ________
0             0             0

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

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

ALPHA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
6             7             8             9            10

BETA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b              0             0            11            12             0
SY%2b              0             0            13            14             0
W                  0             0             0             0             0
XM                 0             0             0             0             0
Y                  0             0            15            16             0

PSI
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b             17
SY%2b              0            18
W                  0             0            19
XM                 0             0            20            21
Y                  0             0             0             0            22

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              1.000
X              0.000         1.000
Y&1            0.000         0.000         0.500

STARTING VALUES FOR BETWEEN LEVEL2A

NU
Y
________
0.000

LAMBDA
SX%2a         SY%2a         Y
________      ________      ________
Y              0.000         0.000         1.000

THETA
Y
________
Y              0.000

ALPHA
SX%2a         SY%2a         Y
________      ________      ________
0.000         0.000         0.000

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

PSI
SX%2a         SY%2a         Y
________      ________      ________
SX%2a          0.200
SY%2a          0.000         0.000
Y              0.000         0.000         0.500

STARTING VALUES FOR BETWEEN LEVEL2B

NU
W             XM            Y
________      ________      ________
0.000         0.000         0.000

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

THETA
W             XM            Y
________      ________      ________
W              0.000
XM             0.000         0.000
Y              0.000         0.000         0.000

ALPHA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
0.500         0.300         0.000         0.000         2.000

BETA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b          0.000         0.000         0.200         0.300         0.000
SY%2b          0.000         0.000         0.050         0.050         0.000
W              0.000         0.000         0.000         0.000         0.000
XM             0.000         0.000         0.000         0.000         0.000
Y              0.000         0.000         0.300         0.400         0.000

PSI
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b          0.200
SY%2b          0.000         0.020
W              0.000         0.000         1.000
XM             0.000         0.000         0.500         1.000
Y              0.000         0.000         0.000         0.000         0.500

POPULATION 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              1.000
X              0.000         1.000
Y&1            0.000         0.000         1.000

POPULATION VALUES FOR BETWEEN LEVEL2A

NU
Y
________
0.000

LAMBDA
SX%2a         SY%2a         Y
________      ________      ________
Y              0.000         0.000         1.000

THETA
Y
________
Y              0.000

ALPHA
SX%2a         SY%2a         Y
________      ________      ________
0.000         0.000         0.000

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

PSI
SX%2a         SY%2a         Y
________      ________      ________
SX%2a          0.200
SY%2a          0.000         0.000
Y              0.000         0.000         0.500

POPULATION VALUES FOR BETWEEN LEVEL2B

NU
W             XM            Y
________      ________      ________
0.000         0.000         0.000

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

THETA
W             XM            Y
________      ________      ________
W              0.000
XM             0.000         0.000
Y              0.000         0.000         0.000

ALPHA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
0.500         0.300         0.000         0.000         2.000

BETA
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b          0.000         0.000         0.200         0.300         0.000
SY%2b          0.000         0.000         0.050         0.050         0.000
W              0.000         0.000         0.000         0.000         0.000
XM             0.000         0.000         0.000         0.000         0.000
Y              0.000         0.000         0.300         0.400         0.000

PSI
SX%2b         SY%2b         W             XM            Y
________      ________      ________      ________      ________
SX%2b          0.200
SY%2b          0.000         0.020
W              0.000         0.000         1.000
XM             0.000         0.000         0.500         1.000
Y              0.000         0.000         0.000         0.000         0.500

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~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~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~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~N(0.000,infinity)          0.0000            infinity            infinity
Parameter 16~N(0.000,infinity)          0.0000            infinity            infinity
Parameter 17~IG(-1.000,0.000)         infinity            infinity            infinity
Parameter 18~IG(-1.000,0.000)         infinity            infinity            infinity
Parameter 19~IW(0.000,-3)             infinity            infinity            infinity
Parameter 20~IW(0.000,-3)             infinity            infinity            infinity
Parameter 21~IW(0.000,-3)             infinity            infinity            infinity
Parameter 22~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 5    0.1300    0.3439
Parameter 10    0.1200    0.4431
Parameter 20    0.1200    0.4431
Parameter 9    0.1100    0.5560
Parameter 21    0.1100    0.5560
Parameter 19    0.0900    0.7942
Parameter 15    0.0900    0.7942
Parameter 11    0.0600    0.9921
Parameter 8    0.0600    0.9921
Parameter 16    0.0500    0.9995
Parameter 22    0.0500    0.9995
Parameter 6    0.0400    1.0000
Parameter 12    0.0400    1.0000
Parameter 17    0.0200    1.0000
Parameter 13    0.0100    1.0000
Parameter 4    0.0100    1.0000
Parameter 3    0.0000    1.0000
Parameter 2    0.0000    1.0000
Parameter 14    0.0000    1.0000
Parameter 7    0.0000    1.0000
Parameter 18    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
Parameter 22 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              1.372               6
200              1.045               13

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

W
XM
Y
X
LEVEL2A
LEVEL2B
Y&1

Save file
ex9.39.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:57:15
Ending Time:  04:03:07
Elapsed Time:  00:05:52

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
```