Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of a factor mixture analysis
with binary latent class indicators
montecarlo:
names are u1-u8;
generate = u1-u8(1);
categorical = u1-u8;
genclasses = c(2);
classes = c(2);
nobs = 2000;
seed = 3454367;
nrep = 1;
save = ex7.27.dat;
model population:
%overall%
f by u1@1 u2-u8*1;
[f@0];
[c#1*0];
%c#1%
f by u2-u4*1 u5-u8*.5;
f*3;
[u1$1*2 u2$1*2 u3$1*2 u4$1*2 u5$1*-2 u6$1*-2 u7$1*-2 u8$1*-2];
%c#2%
f by u2-u4*.5 u5-u8*1;
f*2;
[u1$1*-2 u2$1*-2 u3$1*-2 u4$1*-2 u5$1*2 u6$1*2 u7$1*2 u8$1*2];
analysis:
type = mixture;
algorithm = integration;
! estimator = mlf;
! adaptive = off;
model:
%overall%
f by u1@1 u2-u8*1;
[f@0];
[c#1*0];
%c#1%
f by u2-u4*1 u5-u8*.5;
f*3;
[u1$1*2 u2$1*2 u3$1*2 u4$1*2 u5$1*-2 u6$1*-2 u7$1*-2 u8$1*-2];
%c#2%
f by u2-u4*.5 u5-u8*1;
f*2;
[u1$1*-2 u2$1*-2 u3$1*-2 u4$1*-2 u5$1*2 u6$1*2 u7$1*2 u8$1*2];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a factor mixture analysis
with binary latent class indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 2000
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 33
Loglikelihood
H0 Value
Mean -8193.989
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -8193.989 -8193.989
0.980 0.000 -8193.989 -8193.989
0.950 0.000 -8193.989 -8193.989
0.900 0.000 -8193.989 -8193.989
0.800 0.000 -8193.989 -8193.989
0.700 0.000 -8193.989 -8193.989
0.500 0.000 -8193.989 -8193.989
0.300 0.000 -8193.989 -8193.989
0.200 0.000 -8193.989 -8193.989
0.100 0.000 -8193.989 -8193.989
0.050 0.000 -8193.989 -8193.989
0.020 0.000 -8193.989 -8193.989
0.010 0.000 -8193.989 -8193.989
Information Criteria
Akaike (AIC)
Mean 16453.978
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16453.978 16453.978
0.980 0.000 16453.978 16453.978
0.950 0.000 16453.978 16453.978
0.900 0.000 16453.978 16453.978
0.800 0.000 16453.978 16453.978
0.700 0.000 16453.978 16453.978
0.500 0.000 16453.978 16453.978
0.300 0.000 16453.978 16453.978
0.200 0.000 16453.978 16453.978
0.100 0.000 16453.978 16453.978
0.050 0.000 16453.978 16453.978
0.020 0.000 16453.978 16453.978
0.010 0.000 16453.978 16453.978
Bayesian (BIC)
Mean 16638.808
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16638.808 16638.808
0.980 0.000 16638.808 16638.808
0.950 0.000 16638.808 16638.808
0.900 0.000 16638.808 16638.808
0.800 0.000 16638.808 16638.808
0.700 0.000 16638.808 16638.808
0.500 0.000 16638.808 16638.808
0.300 0.000 16638.808 16638.808
0.200 0.000 16638.808 16638.808
0.100 0.000 16638.808 16638.808
0.050 0.000 16638.808 16638.808
0.020 0.000 16638.808 16638.808
0.010 0.000 16638.808 16638.808
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 16533.965
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 16533.965 16533.965
0.980 0.000 16533.965 16533.965
0.950 0.000 16533.965 16533.965
0.900 0.000 16533.965 16533.965
0.800 0.000 16533.965 16533.965
0.700 0.000 16533.965 16533.965
0.500 0.000 16533.965 16533.965
0.300 0.000 16533.965 16533.965
0.200 0.000 16533.965 16533.965
0.100 0.000 16533.965 16533.965
0.050 0.000 16533.965 16533.965
0.020 0.000 16533.965 16533.965
0.010 0.000 16533.965 16533.965
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 221.727
Std Dev 0.000
Degrees of freedom 222
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 175.939 221.727
0.980 1.000 180.899 221.727
0.950 1.000 188.514 221.727
0.900 1.000 195.460 221.727
0.800 1.000 204.100 221.727
0.700 1.000 210.486 221.727
0.500 1.000 221.334 221.727
0.300 0.000 232.548 221.727
0.200 0.000 239.512 221.727
0.100 0.000 249.396 221.727
0.050 0.000 257.758 221.727
0.020 0.000 267.389 221.727
0.010 0.000 273.939 221.727
Likelihood Ratio Chi-Square
Mean 227.347
Std Dev 0.000
Degrees of freedom 222
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 175.939 227.347
0.980 1.000 180.899 227.347
0.950 1.000 188.514 227.347
0.900 1.000 195.460 227.347
0.800 1.000 204.100 227.347
0.700 1.000 210.486 227.347
0.500 1.000 221.334 227.347
0.300 0.000 232.548 227.347
0.200 0.000 239.512 227.347
0.100 0.000 249.396 227.347
0.050 0.000 257.758 227.347
0.020 0.000 267.389 227.347
0.010 0.000 273.939 227.347
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 981.43219 0.49072
2 1018.56781 0.50928
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 981.43219 0.49072
2 1018.56781 0.50928
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 1005 0.50250
2 995 0.49750
CLASSIFICATION QUALITY
Entropy 0.935
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.967 0.033
2 0.010 0.990
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 0.990 0.010
2 0.032 0.968
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 4.627 0.000
2 -3.394 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 1.2129 0.0000 0.2268 0.0453 1.000 1.000
U3 1.000 1.2882 0.0000 0.2678 0.0831 1.000 1.000
U4 1.000 0.9309 0.0000 0.1689 0.0048 1.000 1.000
U5 0.500 0.7132 0.0000 0.1594 0.0455 1.000 1.000
U6 0.500 0.5914 0.0000 0.1412 0.0084 1.000 1.000
U7 0.500 0.5917 0.0000 0.1462 0.0084 1.000 1.000
U8 0.500 0.7255 0.0000 0.1664 0.0508 1.000 1.000
Means
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Thresholds
U1$1 2.000 1.9601 0.0000 0.1526 0.0016 1.000 1.000
U2$1 2.000 2.3526 0.0000 0.2052 0.1243 1.000 1.000
U3$1 2.000 2.1781 0.0000 0.2082 0.0317 1.000 1.000
U4$1 2.000 1.7916 0.0000 0.1409 0.0434 1.000 1.000
U5$1 -2.000 -2.0216 0.0000 0.1513 0.0005 1.000 1.000
U6$1 -2.000 -2.0871 0.0000 0.1390 0.0076 1.000 1.000
U7$1 -2.000 -1.9888 0.0000 0.1436 0.0001 1.000 1.000
U8$1 -2.000 -2.1454 0.0000 0.1611 0.0212 1.000 1.000
Variances
F 3.000 2.2196 0.0000 0.5946 0.6090 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 0.500 0.4957 0.0000 0.1394 0.0000 1.000 1.000
U3 0.500 0.3582 0.0000 0.1197 0.0201 1.000 1.000
U4 0.500 0.4177 0.0000 0.1270 0.0068 1.000 1.000
U5 1.000 0.8541 0.0000 0.2053 0.0213 1.000 1.000
U6 1.000 0.8674 0.0000 0.2237 0.0176 1.000 1.000
U7 1.000 0.9562 0.0000 0.2079 0.0019 1.000 1.000
U8 1.000 0.8299 0.0000 0.1945 0.0289 1.000 1.000
Means
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Thresholds
U1$1 -2.000 -2.0569 0.0000 0.2196 0.0032 1.000 1.000
U2$1 -2.000 -2.0777 0.0000 0.1342 0.0060 1.000 1.000
U3$1 -2.000 -1.9384 0.0000 0.1153 0.0038 1.000 1.000
U4$1 -2.000 -1.9680 0.0000 0.1242 0.0010 1.000 1.000
U5$1 2.000 1.9606 0.0000 0.1526 0.0015 1.000 1.000
U6$1 2.000 1.9283 0.0000 0.1554 0.0051 1.000 1.000
U7$1 2.000 1.9118 0.0000 0.1630 0.0078 1.000 1.000
U8$1 2.000 1.8279 0.0000 0.1412 0.0296 1.000 1.000
Variances
F 2.000 2.8248 0.0000 1.0112 0.6804 1.000 1.000
Categorical Latent Variables
Means
C#1 0.000 -0.0371 0.0000 0.0475 0.0014 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.720E-02
(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 4
U6 5
U7 6
U8 7
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 8
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 9
U3 10
U4 11
U5 12
U6 13
U7 14
U8 15
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 16
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
17 18 19 20 21
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
22 23 24
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
25 26 27 28 29
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
30 31 32
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
33 0
GAMMA(C)
F
________
C#1 0
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 0.500
U6 0.500
U7 0.500
U8 0.500
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 3.000
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 0.500
U3 0.500
U4 0.500
U5 1.000
U6 1.000
U7 1.000
U8 1.000
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 2.000
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
2.000 2.000 2.000 2.000 -2.000
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
-2.000 -2.000 -2.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
-2.000 -2.000 -2.000 -2.000 2.000
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
2.000 2.000 2.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
F
________
C#1 0.000
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 0.500
U6 0.500
U7 0.500
U8 0.500
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 3.000
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 0.500
U3 0.500
U4 0.500
U5 1.000
U6 1.000
U7 1.000
U8 1.000
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 2.000
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
2.000 2.000 2.000 2.000 -2.000
TAU(U) FOR LATENT CLASS 1
U6$1 U7$1 U8$1
________ ________ ________
-2.000 -2.000 -2.000
TAU(U) FOR LATENT CLASS 2
U1$1 U2$1 U3$1 U4$1 U5$1
________ ________ ________ ________ ________
-2.000 -2.000 -2.000 -2.000 2.000
TAU(U) FOR LATENT CLASS 2
U6$1 U7$1 U8$1
________ ________ ________
2.000 2.000 2.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
F
________
C#1 0.000
C#2 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.82053538D+04 0.0000000 0.0000000 EM
2 -0.81969685D+04 8.3853452 0.0010219 EM
3 -0.81955929D+04 1.3755714 0.0001678 EM
4 -0.81949384D+04 0.6544593 0.0000799 EM
5 -0.81945862D+04 0.3522584 0.0000430 EM
6 -0.81943822D+04 0.2039316 0.0000249 EM
7 -0.81942570D+04 0.1251896 0.0000153 EM
8 -0.81941764D+04 0.0806378 0.0000098 EM
9 -0.81941225D+04 0.0539301 0.0000066 EM
10 -0.81940854D+04 0.0370985 0.0000045 EM
11 -0.81940593D+04 0.0260553 0.0000032 EM
12 -0.81940407D+04 0.0185839 0.0000023 EM
13 -0.81940273D+04 0.0134118 0.0000016 EM
14 -0.81940176D+04 0.0097696 0.0000012 EM
15 -0.81940104D+04 0.0071710 0.0000009 EM
16 -0.81939915D+04 0.0188402 0.0000023 FS
17 -0.81939895D+04 0.0020056 0.0000002 FS
18 -0.81939892D+04 0.0003745 0.0000000 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
ex7.27.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:34
Ending Time: 22:24:35
Elapsed Time: 00:00:01
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