```Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:22 PM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-level CFA
with categorical factor indicators, a random
intercept factor, and covariates

montecarlo:
names are u1-u4 x1 x2 w;
generate = u1-u4(1);
categorical = u1-u4;
nobservations = 1000;
ncsizes = 3;
csizes = 40 (5) 50 (10) 20 (15);
seed = 58459;
nreps = 1;
save = ex9.7.dat;
within = x1 x2;
between = w;

ANALYSIS:
TYPE IS TWOLEVEL;

MODEL POPULATION:

%Within%
x1-x2@1;

fw BY u1@1
u2*1
u3*1
u4*1;
fw ON x1*1 x2*.5;
fw*1;

%Between%
[w@0]; w@.7;

fb BY u1@1
u2*1
u3*1
u4*1;
fb ON w*.5;
fb*.4;

MODEL:

%Within%

fw BY u1@1
u2*1
u3*1
u4*1;
fw ON x1*1 x2*.5;
fw*1;

%Between%

fb BY u1@1
u2*1
u3*1
u4*1;
fb ON w*.5;
fb*.4;

output:
tech8 tech9;

INPUT READING TERMINATED NORMALLY

this is an example of a two-level CFA
with categorical factor indicators, a random
intercept factor, and covariates

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                58459

Number of dependent variables                                    4
Number of independent variables                                  3
Number of continuous latent variables                            2

Observed dependent variables

Binary and ordered categorical (ordinal)
U1          U2          U3          U4

Observed independent variables
X1          X2          W

Continuous latent variables
FW          FB

Variables with special functions

Within variables
X1          X2

Between variables
W

Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations                                 100
Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations                                 500
Convergence criteria
Loglikelihood change                                 0.100D-02
Relative loglikelihood change                        0.100D-05
Derivative                                           0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations                                    1
M step convergence criterion                           0.100D-02
Basis for M step termination                           ITERATION
Maximum value for logit thresholds                            15
Minimum value for logit thresholds                           -15
Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA
Integration Specifications
Type                                                    STANDARD
Number of integration points                                  15
Dimensions of numerical integration                            2
Cholesky                                                        ON

SUMMARY OF DATA FOR THE FIRST REPLICATION

Cluster information

Size (s)    Number of clusters of Size s

5            40
10            50
15            20

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means
X1            X2            W
________      ________      ________
1              0.021        -0.007        -0.154

Covariances
X1            X2            W
________      ________      ________
X1             0.952
X2            -0.006         1.088
W             -0.004         0.025         0.615

Correlations
X1            X2            W
________      ________      ________
X1             1.000
X2            -0.006         1.000
W             -0.005         0.030         1.000

MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

H0 Value

Mean                             -2352.335
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000        -2352.335      -2352.335
0.980       0.000        -2352.335      -2352.335
0.950       0.000        -2352.335      -2352.335
0.900       0.000        -2352.335      -2352.335
0.800       0.000        -2352.335      -2352.335
0.700       0.000        -2352.335      -2352.335
0.500       0.000        -2352.335      -2352.335
0.300       0.000        -2352.335      -2352.335
0.200       0.000        -2352.335      -2352.335
0.100       0.000        -2352.335      -2352.335
0.050       0.000        -2352.335      -2352.335
0.020       0.000        -2352.335      -2352.335
0.010       0.000        -2352.335      -2352.335

Information Criteria

Akaike (AIC)

Mean                              4734.669
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         4734.669       4734.669
0.980       0.000         4734.669       4734.669
0.950       0.000         4734.669       4734.669
0.900       0.000         4734.669       4734.669
0.800       0.000         4734.669       4734.669
0.700       0.000         4734.669       4734.669
0.500       0.000         4734.669       4734.669
0.300       0.000         4734.669       4734.669
0.200       0.000         4734.669       4734.669
0.100       0.000         4734.669       4734.669
0.050       0.000         4734.669       4734.669
0.020       0.000         4734.669       4734.669
0.010       0.000         4734.669       4734.669

Bayesian (BIC)

Mean                              4808.286
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         4808.286       4808.286
0.980       0.000         4808.286       4808.286
0.950       0.000         4808.286       4808.286
0.900       0.000         4808.286       4808.286
0.800       0.000         4808.286       4808.286
0.700       0.000         4808.286       4808.286
0.500       0.000         4808.286       4808.286
0.300       0.000         4808.286       4808.286
0.200       0.000         4808.286       4808.286
0.100       0.000         4808.286       4808.286
0.050       0.000         4808.286       4808.286
0.020       0.000         4808.286       4808.286
0.010       0.000         4808.286       4808.286

Sample-Size Adjusted BIC (n* = (n + 2) / 24)

Mean                              4760.645
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         4760.645       4760.645
0.980       0.000         4760.645       4760.645
0.950       0.000         4760.645       4760.645
0.900       0.000         4760.645       4760.645
0.800       0.000         4760.645       4760.645
0.700       0.000         4760.645       4760.645
0.500       0.000         4760.645       4760.645
0.300       0.000         4760.645       4760.645
0.200       0.000         4760.645       4760.645
0.100       0.000         4760.645       4760.645
0.050       0.000         4760.645       4760.645
0.020       0.000         4760.645       4760.645
0.010       0.000         4760.645       4760.645

MODEL RESULTS

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

FW       BY
U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U2                  1.000     1.2344     0.0000     0.1769     0.0549 1.000 1.000
U3                  1.000     1.3080     0.0000     0.1705     0.0949 1.000 1.000
U4                  1.000     1.2960     0.0000     0.1675     0.0876 1.000 1.000

FW         ON
X1                  1.000     0.8344     0.0000     0.0890     0.0274 1.000 1.000
X2                  0.500     0.3870     0.0000     0.0471     0.0128 0.000 1.000

Residual Variances
FW                  1.000     0.6605     0.0000     0.1353     0.1152 0.000 1.000

Between Level

FB       BY
U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
U2                  1.000     1.5645     0.0000     0.5985     0.3187 1.000 1.000
U3                  1.000     1.3676     0.0000     0.4245     0.1351 1.000 1.000
U4                  1.000     1.7137     0.0000     0.5953     0.5094 1.000 1.000

FB         ON
W                   0.500     0.2428     0.0000     0.0828     0.0662 0.000 1.000

Thresholds
U1\$1                0.000     0.0106     0.0000     0.0870     0.0001 1.000 0.000
U2\$1                0.000     0.1350     0.0000     0.0962     0.0182 1.000 0.000
U3\$1                0.000     0.0634     0.0000     0.0938     0.0040 1.000 0.000
U4\$1                0.000    -0.0165     0.0000     0.1113     0.0003 1.000 0.000

Residual Variances
FB                  0.400     0.1103     0.0000     0.0618     0.0839 0.000 0.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.160E-02
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1                  0             0             0             0

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1                  0             0             0             0             0

NU
X2            W
________      ________
1                  0             0

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1                 0             0             0             0             0
U2                 1             0             0             0             0
U3                 2             0             0             0             0
U4                 3             0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0
U4                 0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

THETA
X2            W
________      ________
X2                 0
W                  0             0

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1                  0             0             0             0             0

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW                 0             0             4             5             0
FB                 0             0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW                 6
FB                 0             0
X1                 0             0             0
X2                 0             0             0             0
W                  0             0             0             0             0

PARAMETER SPECIFICATION FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1                 12            13            14            15

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1                  0             0             0             0             0

NU
X2            W
________      ________
1                  0             0

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1                 0             0             0             0             0
U2                 0             7             0             0             0
U3                 0             8             0             0             0
U4                 0             9             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1                 0
U2                 0             0
U3                 0             0             0
U4                 0             0             0             0
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

THETA
X2            W
________      ________
X2                 0
W                  0             0

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1                  0             0             0             0             0

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW                 0             0             0             0             0
FB                 0             0             0             0            10
X1                 0             0             0             0             0
X2                 0             0             0             0             0
W                  0             0             0             0             0

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW                 0
FB                 0            11
X1                 0             0             0
X2                 0             0             0             0
W                  0             0             0             0             0

STARTING VALUES FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

NU
X2            W
________      ________
1              0.000         0.000

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1             1.000         0.000         0.000         0.000         0.000
U2             1.000         0.000         0.000         0.000         0.000
U3             1.000         0.000         0.000         0.000         0.000
U4             1.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1             1.000
U2             0.000         1.000
U3             0.000         0.000         1.000
U4             0.000         0.000         0.000         1.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

THETA
X2            W
________      ________
X2             0.000
W              0.000         0.000

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000         0.000         1.000         0.500         0.000
FB             0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             1.000
FB             0.000         0.000
X1             0.000         0.000         0.500
X2             0.000         0.000         0.000         0.500
W              0.000         0.000         0.000         0.000         0.000

STARTING VALUES FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

NU
X2            W
________      ________
1              0.000         0.000

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1             0.000         1.000         0.000         0.000         0.000
U2             0.000         1.000         0.000         0.000         0.000
U3             0.000         1.000         0.000         0.000         0.000
U4             0.000         1.000         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

THETA
X2            W
________      ________
X2             0.000
W              0.000         0.000

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000         0.000         0.000         0.000         0.000
FB             0.000         0.000         0.000         0.000         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000
FB             0.000         0.400
X1             0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.500

POPULATION VALUES FOR WITHIN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

NU
X2            W
________      ________
1              0.000         0.000

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1             1.000         0.000         0.000         0.000         0.000
U2             1.000         0.000         0.000         0.000         0.000
U3             1.000         0.000         0.000         0.000         0.000
U4             1.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

THETA
X2            W
________      ________
X2             0.000
W              0.000         0.000

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000         0.000         1.000         0.500         0.000
FB             0.000         0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             1.000
FB             0.000         0.000
X1             0.000         0.000         1.000
X2             0.000         0.000         0.000         1.000
W              0.000         0.000         0.000         0.000         0.000

POPULATION VALUES FOR BETWEEN

TAU
U1\$1          U2\$1          U3\$1          U4\$1
________      ________      ________      ________
1              0.000         0.000         0.000         0.000

NU
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

NU
X2            W
________      ________
1              0.000         0.000

LAMBDA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
U1             0.000         1.000         0.000         0.000         0.000
U2             0.000         1.000         0.000         0.000         0.000
U3             0.000         1.000         0.000         0.000         0.000
U4             0.000         1.000         0.000         0.000         0.000
X1             0.000         0.000         1.000         0.000         0.000
X2             0.000         0.000         0.000         1.000         0.000
W              0.000         0.000         0.000         0.000         1.000

THETA
U1            U2            U3            U4            X1
________      ________      ________      ________      ________
U1             0.000
U2             0.000         0.000
U3             0.000         0.000         0.000
U4             0.000         0.000         0.000         0.000
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

THETA
X2            W
________      ________
X2             0.000
W              0.000         0.000

ALPHA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
1              0.000         0.000         0.000         0.000         0.000

BETA
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000         0.000         0.000         0.000         0.000
FB             0.000         0.000         0.000         0.000         0.500
X1             0.000         0.000         0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.000

PSI
FW            FB            X1            X2            W
________      ________      ________      ________      ________
FW             0.000
FB             0.000         0.400
X1             0.000         0.000         0.000
X2             0.000         0.000         0.000         0.000
W              0.000         0.000         0.000         0.000         0.700

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.23613274D+04    0.0000000    0.0000000  EM
2 -0.23540324D+04    7.2949791    0.0030894  EM
3 -0.23528562D+04    1.1762740    0.0004997  EM
4 -0.23525291D+04    0.3271132    0.0001390  EM
5 -0.23524202D+04    0.1088548    0.0000463  EM
6 -0.23523760D+04    0.0441996    0.0000188  EM
7 -0.23523554D+04    0.0206495    0.0000088  EM
8 -0.23523450D+04    0.0103375    0.0000044  EM
9 -0.23523397D+04    0.0053316    0.0000023  EM
10 -0.23523369D+04    0.0027870    0.0000012  EM
11 -0.23523354D+04    0.0014677    0.0000006  EM
12 -0.23523347D+04    0.0007772    0.0000003  EM

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
U2
U3
U4
X1
X2
W
CLUSTER

Save file
ex9.7.dat

Save file format           Free
Save file record length    10000

Beginning Time:  17:22:08
Ending Time:  17:22:10
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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) 1998-2014 Muthen & Muthen
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