Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:22 PM
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
Adaptive quadrature ON
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: 22:22:35
Ending Time: 22:22:36
Elapsed Time: 00:00:01
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