Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title:
this is an example of CFA with a non-parametric
representation of a non-normal factor
montecarlo:
names are y1-y5;
genclasses = c(3);
classes = c(3);
nobs = 500;
seed = 3454367;
nrep = 1;
save = ex7.26.dat;
analysis:
type = mixture;
model population:
%overall%
y1-y5*.25;
f by y1@1 y2-y5*.75;
[f@0];
f@0;
[c#1*-2.5 c#2*-1.5];
%c#1%
[f*4];
%c#2%
[f*2];
model:
%overall%
%overall%
y1-y5*.25;
f by y1@1 y2-y5*.75;
[f@0];
f@0;
[c#1*-2.5 c#2*-1.5];
%c#1%
[f*4];
%c#2%
[f*2];
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of CFA with a non-parametric
representation of a non-normal factor
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 3454367
Number of dependent variables 5
Number of independent variables 0
Number of continuous latent variables 1
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5
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-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
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-05
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-05
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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.566 0.418 0.463 0.406 0.443
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.545
Y2 0.967 1.005
Y3 1.012 0.739 1.033
Y4 1.023 0.757 0.761 1.020
Y5 0.960 0.718 0.718 0.760 0.978
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.776 1.000
Y3 0.800 0.726 1.000
Y4 0.814 0.747 0.741 1.000
Y5 0.781 0.724 0.714 0.761 1.000
MODEL FIT INFORMATION
Number of Free Parameters 18
Loglikelihood
H0 Value
Mean -2183.081
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -2183.081 -2183.081
0.980 0.000 -2183.081 -2183.081
0.950 0.000 -2183.081 -2183.081
0.900 0.000 -2183.081 -2183.081
0.800 0.000 -2183.081 -2183.081
0.700 0.000 -2183.081 -2183.081
0.500 0.000 -2183.081 -2183.081
0.300 0.000 -2183.081 -2183.081
0.200 0.000 -2183.081 -2183.081
0.100 0.000 -2183.081 -2183.081
0.050 0.000 -2183.081 -2183.081
0.020 0.000 -2183.081 -2183.081
0.010 0.000 -2183.081 -2183.081
Information Criteria
Akaike (AIC)
Mean 4402.163
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4402.163 4402.163
0.980 0.000 4402.163 4402.163
0.950 0.000 4402.163 4402.163
0.900 0.000 4402.163 4402.163
0.800 0.000 4402.163 4402.163
0.700 0.000 4402.163 4402.163
0.500 0.000 4402.163 4402.163
0.300 0.000 4402.163 4402.163
0.200 0.000 4402.163 4402.163
0.100 0.000 4402.163 4402.163
0.050 0.000 4402.163 4402.163
0.020 0.000 4402.163 4402.163
0.010 0.000 4402.163 4402.163
Bayesian (BIC)
Mean 4478.026
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4478.026 4478.026
0.980 0.000 4478.026 4478.026
0.950 0.000 4478.026 4478.026
0.900 0.000 4478.026 4478.026
0.800 0.000 4478.026 4478.026
0.700 0.000 4478.026 4478.026
0.500 0.000 4478.026 4478.026
0.300 0.000 4478.026 4478.026
0.200 0.000 4478.026 4478.026
0.100 0.000 4478.026 4478.026
0.050 0.000 4478.026 4478.026
0.020 0.000 4478.026 4478.026
0.010 0.000 4478.026 4478.026
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 4420.893
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4420.893 4420.893
0.980 0.000 4420.893 4420.893
0.950 0.000 4420.893 4420.893
0.900 0.000 4420.893 4420.893
0.800 0.000 4420.893 4420.893
0.700 0.000 4420.893 4420.893
0.500 0.000 4420.893 4420.893
0.300 0.000 4420.893 4420.893
0.200 0.000 4420.893 4420.893
0.100 0.000 4420.893 4420.893
0.050 0.000 4420.893 4420.893
0.020 0.000 4420.893 4420.893
0.010 0.000 4420.893 4420.893
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 32.00001 0.06400
2 85.06896 0.17014
3 382.93103 0.76586
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 32.00001 0.06400
2 85.06896 0.17014
3 382.93103 0.76586
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 32 0.06400
2 85 0.17000
3 383 0.76600
CLASSIFICATION QUALITY
Entropy 0.999
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2 3
1 1.000 0.000 0.000
2 0.000 1.000 0.000
3 0.000 0.000 1.000
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2 3
1 1.000 0.000 0.000
2 0.000 0.999 0.001
3 0.000 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2 3
1 13.816 0.000 0.000
2 -6.702 7.112 0.000
3 -13.816 -13.816 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
F BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.750 0.7485 0.0000 0.0273 0.0000 1.000 1.000
Y3 0.750 0.7658 0.0000 0.0259 0.0002 1.000 1.000
Y4 0.750 0.7757 0.0000 0.0241 0.0007 1.000 1.000
Y5 0.750 0.7482 0.0000 0.0233 0.0000 1.000 1.000
Means
F 4.000 3.9278 0.0000 0.0788 0.0052 1.000 1.000
Intercepts
Y1 0.000 -0.0191 0.0000 0.0250 0.0004 1.000 0.000
Y2 0.000 -0.0201 0.0000 0.0271 0.0004 1.000 0.000
Y3 0.000 0.0147 0.0000 0.0258 0.0002 1.000 0.000
Y4 0.000 -0.0480 0.0000 0.0245 0.0023 1.000 0.000
Y5 0.000 0.0051 0.0000 0.0252 0.0000 1.000 0.000
Variances
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.250 0.2452 0.0000 0.0144 0.0000 1.000 1.000
Y2 0.250 0.2766 0.0000 0.0179 0.0007 1.000 1.000
Y3 0.250 0.2708 0.0000 0.0156 0.0004 1.000 1.000
Y4 0.250 0.2380 0.0000 0.0136 0.0001 1.000 1.000
Y5 0.250 0.2500 0.0000 0.0152 0.0000 1.000 1.000
Latent Class 2
F BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.750 0.7485 0.0000 0.0273 0.0000 1.000 1.000
Y3 0.750 0.7658 0.0000 0.0259 0.0002 1.000 1.000
Y4 0.750 0.7757 0.0000 0.0241 0.0007 1.000 1.000
Y5 0.750 0.7482 0.0000 0.0233 0.0000 1.000 1.000
Means
F 2.000 1.9628 0.0000 0.0471 0.0014 1.000 1.000
Intercepts
Y1 0.000 -0.0191 0.0000 0.0250 0.0004 1.000 0.000
Y2 0.000 -0.0201 0.0000 0.0271 0.0004 1.000 0.000
Y3 0.000 0.0147 0.0000 0.0258 0.0002 1.000 0.000
Y4 0.000 -0.0480 0.0000 0.0245 0.0023 1.000 0.000
Y5 0.000 0.0051 0.0000 0.0252 0.0000 1.000 0.000
Variances
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.250 0.2452 0.0000 0.0144 0.0000 1.000 1.000
Y2 0.250 0.2766 0.0000 0.0179 0.0007 1.000 1.000
Y3 0.250 0.2708 0.0000 0.0156 0.0004 1.000 1.000
Y4 0.250 0.2380 0.0000 0.0136 0.0001 1.000 1.000
Y5 0.250 0.2500 0.0000 0.0152 0.0000 1.000 1.000
Latent Class 3
F BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.750 0.7485 0.0000 0.0273 0.0000 1.000 1.000
Y3 0.750 0.7658 0.0000 0.0259 0.0002 1.000 1.000
Y4 0.750 0.7757 0.0000 0.0241 0.0007 1.000 1.000
Y5 0.750 0.7482 0.0000 0.0233 0.0000 1.000 1.000
Means
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Intercepts
Y1 0.000 -0.0191 0.0000 0.0250 0.0004 1.000 0.000
Y2 0.000 -0.0201 0.0000 0.0271 0.0004 1.000 0.000
Y3 0.000 0.0147 0.0000 0.0258 0.0002 1.000 0.000
Y4 0.000 -0.0480 0.0000 0.0245 0.0023 1.000 0.000
Y5 0.000 0.0051 0.0000 0.0252 0.0000 1.000 0.000
Variances
F 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
Y1 0.250 0.2452 0.0000 0.0144 0.0000 1.000 1.000
Y2 0.250 0.2766 0.0000 0.0179 0.0007 1.000 1.000
Y3 0.250 0.2708 0.0000 0.0156 0.0004 1.000 1.000
Y4 0.250 0.2380 0.0000 0.0136 0.0001 1.000 1.000
Y5 0.250 0.2500 0.0000 0.0152 0.0000 1.000 1.000
Categorical Latent Variables
Means
C#1 -2.500 -2.4821 0.0000 0.1840 0.0003 1.000 1.000
C#2 -1.500 -1.5044 0.0000 0.1199 0.0000 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.761E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
LAMBDA
F
________
Y1 0
Y2 6
Y3 7
Y4 8
Y5 9
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 10
Y2 0 11
Y3 0 0 12
Y4 0 0 0 13
Y5 0 0 0 0 14
ALPHA
F
________
15
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
LAMBDA
F
________
Y1 0
Y2 6
Y3 7
Y4 8
Y5 9
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 10
Y2 0 11
Y3 0 0 12
Y4 0 0 0 13
Y5 0 0 0 0 14
ALPHA
F
________
16
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR LATENT CLASS 3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
LAMBDA
F
________
Y1 0
Y2 6
Y3 7
Y4 8
Y5 9
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 10
Y2 0 11
Y3 0 0 12
Y4 0 0 0 13
Y5 0 0 0 0 14
ALPHA
F
________
0
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
17 18 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
4.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
2.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
STARTING VALUES FOR LATENT CLASS 3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
-2.500 -1.500 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
4.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
2.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
POPULATION VALUES FOR LATENT CLASS 3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
F
________
Y1 1.000
Y2 0.750
Y3 0.750
Y4 0.750
Y5 0.750
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.250
Y2 0.000 0.250
Y3 0.000 0.000 0.250
Y4 0.000 0.000 0.000 0.250
Y5 0.000 0.000 0.000 0.000 0.250
ALPHA
F
________
0.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
-2.500 -1.500 0.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.21905381D+04 0.0000000 0.0000000 EM
2 -0.21830815D+04 7.4565552 0.0034040 EM
3 -0.21830813D+04 0.0001745 0.0000001 EM
4 -0.21830813D+04 0.0000001 0.0000000 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
C
Save file
ex7.26.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:34
Ending Time: 22:24:34
Elapsed Time: 00:00:00
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