```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   3:27 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a multinomial
logistic regression for an unordered
categorical dependent variable with two
covariates
MONTECARLO:
NAMES = u1 x1 x3;
NOBSERVATIONS = 500;
NREPS = 1;
SEED = 53487;
GENERATE = u1(n 2);
NOMINAL = u1;
SAVE = ex3.6.dat;
MODEL POPULATION:
[x1-x3@0];
x1-x3@1;
u1#1 ON x1*1 x3*2;
u1#2 ON x1*.5 x3*1;
[u1#1*-.5 u1#2*.5];
MODEL:	u1#1 ON x1*1 x3*2;
u1#2 ON x1*.5 x3*1;
[u1#1*-.5 u1#2*.5];
OUTPUT:	TECH8 TECH9;

INPUT READING TERMINATED NORMALLY

this is an example of a multinomial
logistic regression for an unordered
categorical dependent variable with two
covariates

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
Requested                                                    1
Completed                                                    1
Value of seed                                                53487

Number of dependent variables                                    1
Number of independent variables                                  2
Number of continuous latent variables                            0

Observed dependent variables

Unordered categorical (nominal)
U1

Observed independent variables
X1          X3

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                            0
Cholesky                                                       OFF

SAMPLE STATISTICS FOR THE FIRST REPLICATION

SAMPLE STATISTICS

Means
X1            X3
________      ________
0.000        -0.067

Covariances
X1            X3
________      ________
X1             1.041
X3             0.023         0.960

Correlations
X1            X3
________      ________
X1             1.000
X3             0.023         1.000

MODEL FIT INFORMATION

Number of Free Parameters                        6

Loglikelihood

H0 Value

Mean                              -433.426
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000         -433.426       -433.426
0.980       0.000         -433.426       -433.426
0.950       0.000         -433.426       -433.426
0.900       0.000         -433.426       -433.426
0.800       0.000         -433.426       -433.426
0.700       0.000         -433.426       -433.426
0.500       0.000         -433.426       -433.426
0.300       0.000         -433.426       -433.426
0.200       0.000         -433.426       -433.426
0.100       0.000         -433.426       -433.426
0.050       0.000         -433.426       -433.426
0.020       0.000         -433.426       -433.426
0.010       0.000         -433.426       -433.426

Information Criteria

Akaike (AIC)

Mean                               878.853
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000          878.853        878.853
0.980       0.000          878.853        878.853
0.950       0.000          878.853        878.853
0.900       0.000          878.853        878.853
0.800       0.000          878.853        878.853
0.700       0.000          878.853        878.853
0.500       0.000          878.853        878.853
0.300       0.000          878.853        878.853
0.200       0.000          878.853        878.853
0.100       0.000          878.853        878.853
0.050       0.000          878.853        878.853
0.020       0.000          878.853        878.853
0.010       0.000          878.853        878.853

Bayesian (BIC)

Mean                               904.140
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000          904.140        904.140
0.980       0.000          904.140        904.140
0.950       0.000          904.140        904.140
0.900       0.000          904.140        904.140
0.800       0.000          904.140        904.140
0.700       0.000          904.140        904.140
0.500       0.000          904.140        904.140
0.300       0.000          904.140        904.140
0.200       0.000          904.140        904.140
0.100       0.000          904.140        904.140
0.050       0.000          904.140        904.140
0.020       0.000          904.140        904.140
0.010       0.000          904.140        904.140

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

Mean                               885.096
Std Dev                              0.000
Number of successful computations        1

Proportions                   Percentiles
Expected    Observed         Expected       Observed
0.990       0.000          885.096        885.096
0.980       0.000          885.096        885.096
0.950       0.000          885.096        885.096
0.900       0.000          885.096        885.096
0.800       0.000          885.096        885.096
0.700       0.000          885.096        885.096
0.500       0.000          885.096        885.096
0.300       0.000          885.096        885.096
0.200       0.000          885.096        885.096
0.100       0.000          885.096        885.096
0.050       0.000          885.096        885.096
0.020       0.000          885.096        885.096
0.010       0.000          885.096        885.096

MODEL RESULTS

ESTIMATES              S. E.     M. S. E.  95%  % Sig
Population   Average   Std. Dev.   Average             Cover Coeff
U1#1       ON
X1                  1.000     0.7686     0.0000     0.1646     0.0535 1.000 1.000
X3                  2.000     2.2594     0.0000     0.2027     0.0673 1.000 1.000

U1#2       ON
X1                  0.500     0.2799     0.0000     0.1145     0.0485 1.000 1.000
X3                  1.000     0.8851     0.0000     0.1428     0.0132 1.000 1.000

Intercepts
U1#1               -0.500    -0.7489     0.0000     0.1584     0.0619 1.000 1.000
U1#2                0.500     0.2623     0.0000     0.1197     0.0565 0.000 1.000

QUALITY OF NUMERICAL RESULTS

Average Condition Number for the Information Matrix      0.849E-01
(ratio of smallest to largest eigenvalue)

TECHNICAL 1 OUTPUT

PARAMETER SPECIFICATION

NU
U1#1          U1#2          X1            X3
________      ________      ________      ________
0             0             0             0

LAMBDA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1               0             0             0             0
U1#2               0             0             0             0
X1                 0             0             0             0
X3                 0             0             0             0

THETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1               0
U1#2               0             0
X1                 0             0             0
X3                 0             0             0             0

ALPHA
U1#1          U1#2          X1            X3
________      ________      ________      ________
1             2             0             0

BETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1               0             0             3             4
U1#2               0             0             5             6
X1                 0             0             0             0
X3                 0             0             0             0

PSI
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1               0
U1#2               0             0
X1                 0             0             0
X3                 0             0             0             0

STARTING VALUES

NU
U1#1          U1#2          X1            X3
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           1.000         0.000         0.000         0.000
U1#2           0.000         1.000         0.000         0.000
X1             0.000         0.000         1.000         0.000
X3             0.000         0.000         0.000         1.000

THETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000
U1#2           0.000         0.000
X1             0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

ALPHA
U1#1          U1#2          X1            X3
________      ________      ________      ________
-0.500         0.500         0.000         0.000

BETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000         0.000         1.000         2.000
U1#2           0.000         0.000         0.500         1.000
X1             0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

PSI
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000
U1#2           0.000         0.000
X1             0.000         0.000         0.500
X3             0.000         0.000         0.000         0.500

POPULATION VALUES

NU
U1#1          U1#2          X1            X3
________      ________      ________      ________
0.000         0.000         0.000         0.000

LAMBDA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           1.000         0.000         0.000         0.000
U1#2           0.000         1.000         0.000         0.000
X1             0.000         0.000         1.000         0.000
X3             0.000         0.000         0.000         1.000

THETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000
U1#2           0.000         0.000
X1             0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

ALPHA
U1#1          U1#2          X1            X3
________      ________      ________      ________
-0.500         0.500         0.000         0.000

BETA
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000         0.000         1.000         2.000
U1#2           0.000         0.000         0.500         1.000
X1             0.000         0.000         0.000         0.000
X3             0.000         0.000         0.000         0.000

PSI
U1#1          U1#2          X1            X3
________      ________      ________      ________
U1#1           0.000
U1#2           0.000         0.000
X1             0.000         0.000         1.000
X3             0.000         0.000         0.000         1.000

TECHNICAL 8 OUTPUT

TECHNICAL 8 OUTPUT FOR REPLICATION 1

E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
1 -0.43959770D+03    0.0000000    0.0000000  EM
2 -0.43349193D+03    6.1057721    0.0138895  EM
3 -0.43342632D+03    0.0656126    0.0001514  EM
4 -0.43342629D+03    0.0000268    0.0000001  EM

TECHNICAL 9 OUTPUT

Error messages for each replication (if any)

SAVEDATA INFORMATION

Order of variables

U1
X1
X3

Save file
ex3.6.dat

Save file format           Free
Save file record length    10000

Beginning Time:  03:27:50
Ending Time:  03:27:50
Elapsed Time:  00:00:00

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Los Angeles, CA  90066

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Copyright (c) 1998-2017 Muthen & Muthen
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