Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a SEM with a
continuous and a categorical latent
variable
montecarlo:
names are u1-u8;
generate = u1-u8(1);
categorical = u1-u8;
genclasses = c(2);
classes = c(2);
nobs = 1000;
seed = 3454367;
nrep = 1;
save = ex7.19.dat;
analysis:
type = mixture;
algo = int;
model population:
%overall%
f by u1@1 u2-u4*1;
f*1;
c#1 on f*1;
%c#1%
[u5$1-u8$1*-1];
%c#2%
[u5$1-u8$1*1];
model:
%overall%
f by u1@1 u2-u4*1;
f*1;
c#1 on f*1;
%c#1%
[u5$1-u8$1*-1];
%c#2%
[u5$1-u8$1*1];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a SEM with a
continuous and a categorical latent
variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 8
Number of independent variables 0
Number of continuous latent variables 1
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
U7 U8
Continuous latent variables
F
Categorical latent variables
C
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 1
Adaptive quadrature ON
Link LOGIT
Cholesky ON
MODEL FIT INFORMATION
Number of Free Parameters 18
Loglikelihood
H0 Value
Mean -5332.536
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -5332.536 -5332.536
0.980 0.000 -5332.536 -5332.536
0.950 0.000 -5332.536 -5332.536
0.900 0.000 -5332.536 -5332.536
0.800 0.000 -5332.536 -5332.536
0.700 0.000 -5332.536 -5332.536
0.500 0.000 -5332.536 -5332.536
0.300 0.000 -5332.536 -5332.536
0.200 0.000 -5332.536 -5332.536
0.100 0.000 -5332.536 -5332.536
0.050 0.000 -5332.536 -5332.536
0.020 0.000 -5332.536 -5332.536
0.010 0.000 -5332.536 -5332.536
Information Criteria
Akaike (AIC)
Mean 10701.073
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 10701.073 10701.073
0.980 0.000 10701.073 10701.073
0.950 0.000 10701.073 10701.073
0.900 0.000 10701.073 10701.073
0.800 0.000 10701.073 10701.073
0.700 0.000 10701.073 10701.073
0.500 0.000 10701.073 10701.073
0.300 0.000 10701.073 10701.073
0.200 0.000 10701.073 10701.073
0.100 0.000 10701.073 10701.073
0.050 0.000 10701.073 10701.073
0.020 0.000 10701.073 10701.073
0.010 0.000 10701.073 10701.073
Bayesian (BIC)
Mean 10789.412
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 10789.412 10789.412
0.980 0.000 10789.412 10789.412
0.950 0.000 10789.412 10789.412
0.900 0.000 10789.412 10789.412
0.800 0.000 10789.412 10789.412
0.700 0.000 10789.412 10789.412
0.500 0.000 10789.412 10789.412
0.300 0.000 10789.412 10789.412
0.200 0.000 10789.412 10789.412
0.100 0.000 10789.412 10789.412
0.050 0.000 10789.412 10789.412
0.020 0.000 10789.412 10789.412
0.010 0.000 10789.412 10789.412
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 10732.243
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 10732.243 10732.243
0.980 0.000 10732.243 10732.243
0.950 0.000 10732.243 10732.243
0.900 0.000 10732.243 10732.243
0.800 0.000 10732.243 10732.243
0.700 0.000 10732.243 10732.243
0.500 0.000 10732.243 10732.243
0.300 0.000 10732.243 10732.243
0.200 0.000 10732.243 10732.243
0.100 0.000 10732.243 10732.243
0.050 0.000 10732.243 10732.243
0.020 0.000 10732.243 10732.243
0.010 0.000 10732.243 10732.243
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 229.927
Std Dev 0.000
Degrees of freedom 238
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 190.203 229.927
0.980 1.000 195.365 229.927
0.950 1.000 203.286 229.927
0.900 1.000 210.503 229.927
0.800 1.000 219.471 229.927
0.700 1.000 226.094 229.927
0.500 0.000 237.334 229.927
0.300 0.000 248.940 229.927
0.200 0.000 256.141 229.927
0.100 0.000 266.353 229.927
0.050 0.000 274.987 229.927
0.020 0.000 284.922 229.927
0.010 0.000 291.675 229.927
Likelihood Ratio Chi-Square
Mean 242.290
Std Dev 0.000
Degrees of freedom 238
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 190.203 242.290
0.980 1.000 195.365 242.290
0.950 1.000 203.286 242.290
0.900 1.000 210.503 242.290
0.800 1.000 219.471 242.290
0.700 1.000 226.094 242.290
0.500 1.000 237.334 242.290
0.300 0.000 248.940 242.290
0.200 0.000 256.141 242.290
0.100 0.000 266.353 242.290
0.050 0.000 274.987 242.290
0.020 0.000 284.922 242.290
0.010 0.000 291.675 242.290
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 467.59382 0.46759
2 532.40618 0.53241
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 467.56317 0.46756
2 532.43683 0.53244
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 459 0.45900
2 541 0.54100
CLASSIFICATION QUALITY
Entropy 0.516
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.850 0.150
2 0.143 0.857
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.834 0.166
2 0.130 0.870
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.616 0.000
2 -1.905 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
F BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 0.8429 0.0000 0.1972 0.0247 1.000 1.000
U3 1.000 0.8450 0.0000 0.1960 0.0240 1.000 1.000
U4 1.000 1.0771 0.0000 0.2465 0.0059 1.000 1.000
Thresholds
U1$1 0.000 0.0103 0.0000 0.0771 0.0001 1.000 0.000
U2$1 0.000 0.1445 0.0000 0.0738 0.0209 1.000 0.000
U3$1 0.000 -0.0695 0.0000 0.0736 0.0048 1.000 0.000
U4$1 0.000 -0.0296 0.0000 0.0791 0.0009 1.000 0.000
U5$1 -1.000 -1.1227 0.0000 0.1797 0.0150 1.000 1.000
U6$1 -1.000 -1.1975 0.0000 0.1964 0.0390 1.000 1.000
U7$1 -1.000 -0.9222 0.0000 0.1499 0.0061 1.000 1.000
U8$1 -1.000 -1.0460 0.0000 0.1807 0.0021 1.000 1.000
Variances
F 1.000 1.0538 0.0000 0.3300 0.0029 1.000 1.000
Latent Class 2
F BY
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 0.8429 0.0000 0.1972 0.0247 1.000 1.000
U3 1.000 0.8450 0.0000 0.1960 0.0240 1.000 1.000
U4 1.000 1.0771 0.0000 0.2465 0.0059 1.000 1.000
Thresholds
U1$1 0.000 0.0103 0.0000 0.0771 0.0001 1.000 0.000
U2$1 0.000 0.1445 0.0000 0.0738 0.0209 1.000 0.000
U3$1 0.000 -0.0695 0.0000 0.0736 0.0048 1.000 0.000
U4$1 0.000 -0.0296 0.0000 0.0791 0.0009 1.000 0.000
U5$1 1.000 0.8789 0.0000 0.1465 0.0147 1.000 1.000
U6$1 1.000 0.9744 0.0000 0.1534 0.0007 1.000 1.000
U7$1 1.000 0.8765 0.0000 0.1486 0.0153 1.000 1.000
U8$1 1.000 1.0406 0.0000 0.1531 0.0016 1.000 1.000
Variances
F 1.000 1.0538 0.0000 0.3300 0.0029 1.000 1.000
Categorical Latent Variables
C#1 ON
F 1.000 1.1257 0.0000 0.3297 0.0158 1.000 1.000
Intercepts
C#1 0.000 -0.1653 0.0000 0.2193 0.0273 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.198E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8
________ ________ ________
0 0 0
LAMBDA
F
________
U1 0
U2 1
U3 2
U4 3
U5 0
U6 0
U7 0
U8 0
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
U5 0 0 0 0 0
U6 0 0 0 0 0
U7 0 0 0 0 0
U8 0 0 0 0 0
THETA
U6 U7 U8
________ ________ ________
U6 0
U7 0 0
U8 0 0 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 4
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0 0 0 0 0
NU
U6 U7 U8
________ ________ ________
0 0 0
LAMBDA
F
________
U1 0
U2 1
U3 2
U4 3
U5 0
U6 0
U7 0
U8 0
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
U5 0 0 0 0 0
U6 0 0 0 0 0
U7 0 0 0 0 0
U8 0 0 0 0 0
THETA
U6 U7 U8
________ ________ ________
U6 0
U7 0 0
U8 0 0 0
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 4
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
5 6 7 8 9
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
10 11 12
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
5 6 7 8 13
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
14 15 16
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
17 0
GAMMA(C)
F
________
C#1 18
C#2 0
STARTING VALUES FOR LATENT CLASS 1
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8
________ ________ ________
0.000 0.000 0.000
LAMBDA
F
________
U1 1.000
U2 1.000
U3 1.000
U4 1.000
U5 0.000
U6 0.000
U7 0.000
U8 0.000
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
U5 0.000 0.000 0.000 0.000 1.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8
________ ________ ________
U6 1.000
U7 0.000 1.000
U8 0.000 0.000 1.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
STARTING VALUES FOR LATENT CLASS 2
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8
________ ________ ________
0.000 0.000 0.000
LAMBDA
F
________
U1 1.000
U2 1.000
U3 1.000
U4 1.000
U5 0.000
U6 0.000
U7 0.000
U8 0.000
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
U5 0.000 0.000 0.000 0.000 1.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8
________ ________ ________
U6 1.000
U7 0.000 1.000
U8 0.000 0.000 1.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 -1.000
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
-1.000 -1.000 -1.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.000
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
1.000 1.000 1.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
F
________
C#1 1.000
C#2 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8
________ ________ ________
0.000 0.000 0.000
LAMBDA
F
________
U1 1.000
U2 1.000
U3 1.000
U4 1.000
U5 0.000
U6 0.000
U7 0.000
U8 0.000
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8
________ ________ ________
U6 0.000
U7 0.000 0.000
U8 0.000 0.000 0.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U6 U7 U8
________ ________ ________
0.000 0.000 0.000
LAMBDA
F
________
U1 1.000
U2 1.000
U3 1.000
U4 1.000
U5 0.000
U6 0.000
U7 0.000
U8 0.000
THETA
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
U5 0.000 0.000 0.000 0.000 0.000
U6 0.000 0.000 0.000 0.000 0.000
U7 0.000 0.000 0.000 0.000 0.000
U8 0.000 0.000 0.000 0.000 0.000
THETA
U6 U7 U8
________ ________ ________
U6 0.000
U7 0.000 0.000
U8 0.000 0.000 0.000
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 1.000
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 -1.000
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
-1.000 -1.000 -1.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 1.000
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
1.000 1.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
F
________
C#1 1.000
C#2 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.53386637D+04 0.0000000 0.0000000 EM
2 -0.53337186D+04 4.9450697 0.0009263 EM
3 -0.53332560D+04 0.4626760 0.0000867 EM
4 -0.53330206D+04 0.2353792 0.0000441 EM
5 -0.53328855D+04 0.1350804 0.0000253 EM
6 -0.53325513D+04 0.3341773 0.0000627 FS
7 -0.53325371D+04 0.0142217 0.0000027 FS
8 -0.53325363D+04 0.0008135 0.0000002 FS
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
U5
U6
U7
U8
C
Save file
ex7.19.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:30
Ending Time: 22:24:32
Elapsed Time: 00:00:02
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) 1998-2022 Muthen & Muthen
Back to examples