```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:33 AM

INPUT INSTRUCTIONS

TITLE:      this is an example of two-level univariate first-order
autoregressive AR(1) model with a random intercept,
random AR(1), and random residual variance

Step 1: although we are interested in a twolevel model
we generate data using cross-classified analysis
with an empty Between time model to be able to
save data with subject and time variables.
Missing data on y is created by Model Missing

MONTECARLO:  NAMES ARE y w z u;
NOBS = 20000;
NREPS = 1;
CSIZES = 200[100(1)];
NCSIZES = 1[1];
lagged = y(1);
between = (level2b) w z;
missing = y;
! u is needed if there are several y's to make all of them
! have missing at the same time
generate = u(1);
categorical = u;
within = u;
save = ex9.30step1.dat;

MODEL MISSING:
[y@-15]; ! no MCAR missing
y on u@30; ! missing 50% on y;

ANALYSIS:   TYPE = CROSSCLASSIFIED RANDOM;
estimator=bayes;
proc=2;
fbiter=(200); ! full convergence not needed to save the right data

MODEL POPULATION:

%WITHIN%
s | y on y&1;
logv | y;
[u\$1*0];

%BETWEEN level2a%  ! empty
y@0; s@0;

%BETWEEN level2b%
w*1;
y on w*.3;
y*0.09;
s on w*.1;
s*.01; [s*.3];
logv on w*.3;
logv*0; [logv*0];
z on y*.5 s*.7 logv*.3;
z*0.05;

MODEL:

%WITHIN%
s | y on y&1;
logv | y;
[u\$1*0];

%BETWEEN level2a%  ! empty
y@0; s@0;

%BETWEEN level2b%

y on w*.3;
y*0.09;
s on w*.1;
s*.01; [s*.3];
logv on w*.3;
logv*0; [logv*0];
z on y*.5 s*.7 logv*.3;
z*0.05;

OUTPUT:
tech8;

*** WARNING in MODEL command
Variable is uncorrelated with all other variables: U
*** WARNING in MODEL command
At least one variable is uncorrelated with all other variables in the model.
Check that this is what is intended.
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS

this is an example of two-level univariate first-order
autoregressive AR(1) model with a random intercept,
random AR(1), and random residual variance

Step 1: although we are interested in a twolevel model
we generate data using cross-classified analysis
with an empty Between time model to be able to
save data with subject and time variables.
Missing data on y is created by Model Missing

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                                    3
Number of independent variables                                  2
Number of continuous latent variables                            2

Observed dependent variables

Continuous
Z           Y

Binary and ordered categorical (ordinal)
U

Observed independent variables
W           Y&1

Continuous latent variables
S           LOGV

Variables with special functions

Within variables
U           Y&1

Level 2b between variables
W           Z

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

SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION

Number of missing data patterns             4

MISSING DATA PATTERNS (x = not missing)

1  2  3  4
U         x  x  x  x
Z         x  x  x  x
Y         x     x
Y&1       x  x
W         x  x  x  x

MISSING DATA PATTERN FREQUENCIES

Pattern   Frequency     Pattern   Frequency     Pattern   Frequency
1        9936           3          58
2        9963           4          43

COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION

Minimum covariance coverage value   0.100

PROPORTION OF DATA PRESENT

Covariance Coverage
U             Z             Y             W
________      ________      ________      ________
U              1.000
Z              1.000         1.000
Y              0.500         0.500         0.500
W              1.000         1.000         0.500         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       15

MODEL RESULTS

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

Thresholds
U\$1                 0.000    -0.0009     0.0000     0.0086     0.0000 1.000 0.000

Between LEVEL2A Level

Variances
Y                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
S                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

Between LEVEL2B Level

S          ON
W                   0.100     0.1254     0.0000     0.0134     0.0006 1.000 1.000

LOGV       ON
W                   0.300     0.2968     0.0000     0.0125     0.0000 1.000 1.000

Z          ON
S                   0.700     0.6285     0.0000     0.2694     0.0051 1.000 1.000
LOGV                0.300     0.3233     0.0000     0.1333     0.0005 1.000 1.000

Y          ON
W                   0.300     0.2859     0.0000     0.0245     0.0002 1.000 1.000

Z          ON
Y                   0.500     0.4899     0.0000     0.0587     0.0001 1.000 1.000

Intercepts
Z                   0.000     0.0264     0.0000     0.0815     0.0007 1.000 0.000
Y                   0.000    -0.0216     0.0000     0.0303     0.0005 1.000 0.000
S                   0.300     0.2937     0.0000     0.0162     0.0000 1.000 1.000
LOGV                0.000    -0.0261     0.0000     0.0128     0.0007 1.000 0.000

Residual Variances
Z                   0.050     0.0470     0.0000     0.0068     0.0000 1.000 1.000
Y                   0.090     0.1032     0.0000     0.0122     0.0002 1.000 1.000
S                   0.010     0.0128     0.0000     0.0029     0.0000 1.000 1.000
LOGV                0.000     0.0058     0.0000     0.0020     0.0000 0.000 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.
S%2a                0.000       0.000              0.029       0.000
LOGV%2a             0.000       0.000              0.034       0.000
S%2b                0.821       0.000              0.091       0.000
LOGV%2b             0.991       0.000              0.055       0.000
B2a_Y               0.356       0.000              0.028       0.000
B2b_Y               0.940       0.000              0.150       0.000

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

TAU
U\$1
________
15

NU
U             Y             Y&1
________      ________      ________
0             0             0

LAMBDA
Y             Y&1
________      ________
U                  0             0
Y                  0             0
Y&1                0             0

THETA
U             Y             Y&1
________      ________      ________
U                  0
Y                  0             0
Y&1                0             0             0

ALPHA
Y             Y&1
________      ________
0             0

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

PSI
Y             Y&1
________      ________
Y                  0
Y&1                0             0

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2A

NU
Y
________
0

LAMBDA
S%2a          LOGV%2a       Y
________      ________      ________
Y                  0             0             0

THETA
Y
________
Y                  0

ALPHA
S%2a          LOGV%2a       Y
________      ________      ________
0             0             0

BETA
S%2a          LOGV%2a       Y
________      ________      ________
S%2a               0             0             0
LOGV%2a            0             0             0
Y                  0             0             0

PSI
S%2a          LOGV%2a       Y
________      ________      ________
S%2a               0
LOGV%2a            0             0
Y                  0             0             0

PARAMETER SPECIFICATION FOR BETWEEN LEVEL2B

NU
Z             Y             W
________      ________      ________
0             0             0

LAMBDA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
Z                  0             0             0             0             0
Y                  0             0             0             0             0
W                  0             0             0             0             0

THETA
Z             Y             W
________      ________      ________
Z                  0
Y                  0             0
W                  0             0             0

ALPHA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
1             2             3             4             0

BETA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b               0             0             0             0             5
LOGV%2b            0             0             0             0             6
Z                  7             8             0             9             0
Y                  0             0             0             0            10
W                  0             0             0             0             0

PSI
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b              11
LOGV%2b            0            12
Z                  0             0            13
Y                  0             0             0            14
W                  0             0             0             0             0

STARTING VALUES FOR WITHIN

TAU
U\$1
________
0.000

NU
U             Y             Y&1
________      ________      ________
0.000         0.000         0.000

LAMBDA
Y             Y&1
________      ________
U              0.000         0.000
Y              1.000         0.000
Y&1            0.000         1.000

THETA
U             Y             Y&1
________      ________      ________
U              1.000
Y              0.000         0.000
Y&1            0.000         0.000         0.000

ALPHA
Y             Y&1
________      ________
0.000         0.000

BETA
Y             Y&1
________      ________
Y              0.000         0.000
Y&1            0.000         0.000

PSI
Y             Y&1
________      ________
Y              0.000
Y&1            0.000         0.500

STARTING VALUES FOR BETWEEN LEVEL2A

NU
Y
________
0.000

LAMBDA
S%2a          LOGV%2a       Y
________      ________      ________
Y              0.000         0.000         1.000

THETA
Y
________
Y              0.000

ALPHA
S%2a          LOGV%2a       Y
________      ________      ________
0.000         0.000         0.000

BETA
S%2a          LOGV%2a       Y
________      ________      ________
S%2a           0.000         0.000         0.000
LOGV%2a        0.000         0.000         0.000
Y              0.000         0.000         0.000

PSI
S%2a          LOGV%2a       Y
________      ________      ________
S%2a           0.000
LOGV%2a        0.000         0.000
Y              0.000         0.000         0.000

STARTING VALUES FOR BETWEEN LEVEL2B

NU
Z             Y             W
________      ________      ________
0.000         0.000         0.000

LAMBDA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
Z              0.000         0.000         1.000         0.000         0.000
Y              0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
Z             Y             W
________      ________      ________
Z              0.000
Y              0.000         0.000
W              0.000         0.000         0.000

ALPHA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
0.300         0.000         0.000         0.000         0.000

BETA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b           0.000         0.000         0.000         0.000         0.100
LOGV%2b        0.000         0.000         0.000         0.000         0.300
Z              0.700         0.300         0.000         0.500         0.000
Y              0.000         0.000         0.000         0.000         0.300
W              0.000         0.000         0.000         0.000         0.000

PSI
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b           0.010
LOGV%2b        0.000         0.000
Z              0.000         0.000         0.050
Y              0.000         0.000         0.000         0.090
W              0.000         0.000         0.000         0.000         0.500

POPULATION VALUES FOR WITHIN

TAU
U\$1
________
0.000

NU
U             Y             Y&1
________      ________      ________
0.000         0.000         0.000

LAMBDA
Y             Y&1
________      ________
U              0.000         0.000
Y              1.000         0.000
Y&1            0.000         1.000

THETA
U             Y             Y&1
________      ________      ________
U              0.000
Y              0.000         0.000
Y&1            0.000         0.000         0.000

ALPHA
Y             Y&1
________      ________
0.000         0.000

BETA
Y             Y&1
________      ________
Y              0.000         0.000
Y&1            0.000         0.000

PSI
Y             Y&1
________      ________
Y              0.000
Y&1            0.000         1.000

POPULATION VALUES FOR BETWEEN LEVEL2A

NU
Y
________
0.000

LAMBDA
S%2a          LOGV%2a       Y
________      ________      ________
Y              0.000         0.000         1.000

THETA
Y
________
Y              0.000

ALPHA
S%2a          LOGV%2a       Y
________      ________      ________
0.000         0.000         0.000

BETA
S%2a          LOGV%2a       Y
________      ________      ________
S%2a           0.000         0.000         0.000
LOGV%2a        0.000         0.000         0.000
Y              0.000         0.000         0.000

PSI
S%2a          LOGV%2a       Y
________      ________      ________
S%2a           0.000
LOGV%2a        0.000         0.000
Y              0.000         0.000         0.000

POPULATION VALUES FOR BETWEEN LEVEL2B

NU
Z             Y             W
________      ________      ________
0.000         0.000         0.000

LAMBDA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
Z              0.000         0.000         1.000         0.000         0.000
Y              0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
Z             Y             W
________      ________      ________
Z              0.000
Y              0.000         0.000
W              0.000         0.000         0.000

ALPHA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
0.300         0.000         0.000         0.000         0.000

BETA
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b           0.000         0.000         0.000         0.000         0.100
LOGV%2b        0.000         0.000         0.000         0.000         0.300
Z              0.700         0.300         0.000         0.500         0.000
Y              0.000         0.000         0.000         0.000         0.300
W              0.000         0.000         0.000         0.000         0.000

PSI
S%2b          LOGV%2b       Z             Y             W
________      ________      ________      ________      ________
S%2b           0.010
LOGV%2b        0.000         0.000
Z              0.000         0.000         0.050
Y              0.000         0.000         0.000         0.090
W              0.000         0.000         0.000         0.000         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~N(0.000,infinity)           0.0000            infinity            infinity
Parameter 5~N(0.000,infinity)           0.0000            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~IG(-1.000,0.000)         infinity            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(0.000,5.000)             0.0000              5.0000              2.2361

TECHNICAL 8 OUTPUT

REPLICATION 1:

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

Parameter   KS Statistic P-value
Parameter 6    0.1100    0.5560
Parameter 3    0.1100    0.5560
Parameter 7    0.1000    0.6766
Parameter 9    0.0900    0.7942
Parameter 2    0.0700    0.9610
Parameter 8    0.0700    0.9610
Parameter 5    0.0500    0.9995
Parameter 10    0.0400    1.0000
Parameter 1    0.0300    1.0000
Parameter 4    0.0100    1.0000
Parameter 14    0.0000    1.0000
Parameter 11    0.0000    1.0000
Parameter 12    0.0000    1.0000
Parameter 13    0.0000    1.0000
Parameter 15    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         0.0050          4.9231          2.2188

TECHNICAL 8 OUTPUT FOR BAYES ESTIMATION

CHAIN    BSEED
1        0
2        285380

REPLICATION 1:

POTENTIAL       PARAMETER WITH
ITERATION    SCALE REDUCTION      HIGHEST PSR
100              1.221               8
200              1.113               6

SAVEDATA INFORMATION

Order of variables

U
Z
Y
W
LEVEL2A
LEVEL2B
Y&1

Save file
ex9.30step1.dat

Save file format           Free
Save file record length    10000
Missing designated by 999

Beginning Time:  03:33:27
Ending Time:  03:40:51
Elapsed Time:  00:07:24

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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