Mplus VERSION 6
MUTHEN & MUTHEN
04/22/2010 6:14 PM
INPUT INSTRUCTIONS
TITLE: this is an example of CFA with a non-parametric
representation of a non-normal factor
DATA: FILE IS ex7.26.dat;
VARIABLE: NAMES ARE y1-y5 c;
USEV = y1-y5;
CLASSES = c(3);
ANALYSIS: TYPE = MIXTURE;
MODEL: %OVERALL%
f BY y1-y5;
f@0;
OUTPUT: TECH1 TECH8;
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 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
Random Starts Specifications
Number of initial stage random starts 10
Number of final stage optimizations 2
Number of initial stage iterations 10
Initial stage convergence criterion 0.100D+01
Random starts scale 0.500D+01
Random seed for generating random starts 0
Input data file(s)
ex7.26.dat
Input data format FREE
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
-2183.081 939021 8
-2183.081 127215 9
WARNING: WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE
NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION
TO AVOID LOCAL MAXIMA.
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2183.081
H0 Scaling Correction Factor 0.963
for MLR
Information Criteria
Number of Free Parameters 18
Akaike (AIC) 4402.163
Bayesian (BIC) 4478.026
Sample-Size Adjusted BIC 4420.893
(n* = (n + 2) / 24)
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 CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 32.00001 0.06400
2 85.06896 0.17014
3 382.93103 0.76586
CLASSIFICATION QUALITY
Entropy 0.999
CLASSIFICATION OF INDIVIDUALS 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
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
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
F BY
Y1 1.000 0.000 999.000 999.000
Y2 0.748 0.027 27.443 0.000
Y3 0.766 0.026 29.572 0.000
Y4 0.776 0.024 32.185 0.000
Y5 0.748 0.023 32.147 0.000
Means
F 3.928 0.079 49.817 0.000
Intercepts
Y1 -0.019 0.025 -0.765 0.444
Y2 -0.020 0.027 -0.740 0.459
Y3 0.015 0.026 0.570 0.569
Y4 -0.048 0.025 -1.958 0.050
Y5 0.005 0.025 0.202 0.840
Variances
F 0.000 0.000 999.000 999.000
Residual Variances
Y1 0.245 0.014 17.051 0.000
Y2 0.277 0.018 15.453 0.000
Y3 0.271 0.016 17.306 0.000
Y4 0.238 0.014 17.454 0.000
Y5 0.250 0.015 16.453 0.000
Latent Class 2
F BY
Y1 1.000 0.000 999.000 999.000
Y2 0.748 0.027 27.443 0.000
Y3 0.766 0.026 29.572 0.000
Y4 0.776 0.024 32.185 0.000
Y5 0.748 0.023 32.147 0.000
Means
F 1.963 0.047 41.669 0.000
Intercepts
Y1 -0.019 0.025 -0.765 0.444
Y2 -0.020 0.027 -0.740 0.459
Y3 0.015 0.026 0.570 0.569
Y4 -0.048 0.025 -1.958 0.050
Y5 0.005 0.025 0.202 0.840
Variances
F 0.000 0.000 999.000 999.000
Residual Variances
Y1 0.245 0.014 17.051 0.000
Y2 0.277 0.018 15.453 0.000
Y3 0.271 0.016 17.306 0.000
Y4 0.238 0.014 17.454 0.000
Y5 0.250 0.015 16.453 0.000
Latent Class 3
F BY
Y1 1.000 0.000 999.000 999.000
Y2 0.748 0.027 27.443 0.000
Y3 0.766 0.026 29.572 0.000
Y4 0.776 0.024 32.185 0.000
Y5 0.748 0.023 32.147 0.000
Means
F 0.000 0.000 999.000 999.000
Intercepts
Y1 -0.019 0.025 -0.765 0.444
Y2 -0.020 0.027 -0.740 0.459
Y3 0.015 0.026 0.570 0.569
Y4 -0.048 0.025 -1.958 0.050
Y5 0.005 0.025 0.202 0.840
Variances
F 0.000 0.000 999.000 999.000
Residual Variances
Y1 0.245 0.014 17.051 0.000
Y2 0.277 0.018 15.453 0.000
Y3 0.271 0.016 17.306 0.000
Y4 0.238 0.014 17.454 0.000
Y5 0.250 0.015 16.453 0.000
Categorical Latent Variables
Means
C#1 -2.482 0.184 -13.489 0.000
C#2 -1.504 0.120 -12.542 0.000
QUALITY OF NUMERICAL RESULTS
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 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
________
1 15
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 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
________
1 16
BETA
F
________
F 0
PSI
F
________
F 0
PARAMETER SPECIFICATION FOR LATENT CLASS 3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 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
________
1 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
________ ________ ________
1 17 18 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 0.566 0.418 0.463 0.406 0.443
LAMBDA
F
________
Y1 1.000
Y2 1.000
Y3 1.000
Y4 1.000
Y5 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.774
Y2 0.000 0.504
Y3 0.000 0.000 0.518
Y4 0.000 0.000 0.000 0.511
Y5 0.000 0.000 0.000 0.000 0.490
ALPHA
F
________
1 0.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 0.566 0.418 0.463 0.406 0.443
LAMBDA
F
________
Y1 1.000
Y2 1.000
Y3 1.000
Y4 1.000
Y5 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.774
Y2 0.000 0.504
Y3 0.000 0.000 0.518
Y4 0.000 0.000 0.000 0.511
Y5 0.000 0.000 0.000 0.000 0.490
ALPHA
F
________
1 0.000
BETA
F
________
F 0.000
PSI
F
________
F 0.000
STARTING VALUES FOR LATENT CLASS 3
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 0.566 0.418 0.463 0.406 0.443
LAMBDA
F
________
Y1 1.000
Y2 1.000
Y3 1.000
Y4 1.000
Y5 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.774
Y2 0.000 0.504
Y3 0.000 0.000 0.518
Y4 0.000 0.000 0.000 0.511
Y5 0.000 0.000 0.000 0.000 0.490
ALPHA
F
________
1 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
________ ________ ________
1 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
INITIAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.40461082D+04 0.0000000 0.0000000 166.667 166.667 EM
166.667
2 -0.36650397D+04 381.0685162 0.0941815 166.667 166.667 EM
166.667
3 -0.36650397D+04 0.0000000 0.0000000 166.667 166.667 EM
166.667
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.89182076D+04 0.0000000 0.0000000 11.459 0.000 EM
488.541
2 -0.36625157D+04 5255.6918653 0.5893215 13.951 0.000 EM
486.049
3 -0.36612162D+04 1.2994731 0.0003548 17.698 0.000 EM
482.302
4 -0.36600039D+04 1.2123521 0.0003311 22.633 0.000 EM
477.367
5 -0.36584357D+04 1.5681962 0.0004285 29.050 0.000 EM
470.950
6 -0.36562905D+04 2.1452127 0.0005864 37.432 0.000 EM
462.568
7 -0.36532133D+04 3.0771954 0.0008416 48.648 0.000 EM
451.352
8 -0.36488672D+04 4.3460926 0.0011897 63.751 0.000 EM
436.249
9 -0.36423551D+04 6.5120540 0.0017847 84.393 0.000 EM
415.607
10 -0.36320000D+04 10.3551169 0.0028430 112.675 0.000 EM
387.325
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.29473029D+05 0.0000000 0.0000000 0.000 8.870 EM
491.130
2 -0.33526368D+04 ************ 0.8862473 0.000 33.704 EM
466.296
3 -0.31906643D+04 161.9724761 0.0483120 0.000 49.194 EM
450.806
4 -0.31052707D+04 85.3935719 0.0267636 0.000 73.054 EM
426.946
5 -0.29924675D+04 112.8031850 0.0363264 0.000 98.858 EM
401.142
6 -0.29179335D+04 74.5340011 0.0249072 0.000 111.886 EM
388.114
7 -0.29045731D+04 13.3604283 0.0045787 0.000 114.057 EM
385.943
8 -0.29040357D+04 0.5373678 0.0001850 0.000 114.376 EM
385.624
9 -0.29040263D+04 0.0094689 0.0000033 0.000 114.423 EM
385.577
10 -0.29038464D+04 0.1799046 0.0000620 0.000 114.446 EM
385.554
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.21426041D+05 0.0000000 0.0000000 4.543 0.000 EM
495.457
2 -0.34842218D+04 ************ 0.8373838 36.365 0.000 EM
463.635
3 -0.31782715D+04 305.9502980 0.0878102 55.477 0.000 EM
444.523
4 -0.30707353D+04 107.5362191 0.0338348 80.733 0.000 EM
419.267
5 -0.29657040D+04 105.0312985 0.0342040 104.522 0.000 EM
395.478
6 -0.29092328D+04 56.4711738 0.0190414 113.047 0.000 EM
386.953
7 -0.29041507D+04 5.0821798 0.0017469 114.228 0.000 EM
385.772
8 -0.29040348D+04 0.1158295 0.0000399 114.433 0.000 EM
385.567
9 -0.29040168D+04 0.0180334 0.0000062 114.488 0.000 EM
385.512
10 -0.29039899D+04 0.0269016 0.0000093 114.469 0.000 EM
385.531
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.98263592D+04 0.0000000 0.0000000 492.147 0.000 EM
7.853
2 -0.36651748D+04 6161.1843178 0.6270058 492.167 0.000 EM
7.833
3 -0.36633092D+04 1.8656068 0.0005090 490.439 0.000 EM
9.561
4 -0.36627249D+04 0.5842875 0.0001595 488.226 0.000 EM
11.774
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.12442598D+05 0.0000000 0.0000000 382.091 0.000 EM
117.909
2 -0.25884142D+04 9854.1834647 0.7919716 383.276 0.000 EM
116.724
3 -0.25870318D+04 1.3824496 0.0005341 383.251 0.000 EM
116.749
4 -0.25870317D+04 0.0001110 0.0000000 383.249 0.000 EM
116.751
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.30435455D+05 0.0000000 0.0000000 0.000 66.704 EM
433.296
2 -0.27844552D+04 ************ 0.9085128 0.000 98.633 EM
401.367
3 -0.26129978D+04 171.4574163 0.0615766 0.000 114.773 EM
385.227
4 -0.25874288D+04 25.5689640 0.0097853 0.000 116.627 EM
383.373
5 -0.25870335D+04 0.3953131 0.0001528 0.000 116.744 EM
383.256
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.21827407D+05 0.0000000 0.0000000 0.002 0.000 EM
499.998
2 -0.36111199D+04 ************ 0.8345603 17.047 0.000 EM
482.953
3 -0.31095416D+04 501.5782352 0.1388983 33.738 0.000 EM
466.262
4 -0.30055277D+04 104.0139656 0.0334499 47.953 0.000 EM
452.047
5 -0.28986806D+04 106.8470263 0.0355502 76.036 0.000 EM
423.964
6 -0.27094761D+04 189.2045611 0.0652726 105.292 0.000 EM
394.708
7 -0.25979726D+04 111.5035020 0.0411532 115.656 0.000 EM
384.344
8 -0.25871644D+04 10.8081722 0.0041602 116.684 0.000 EM
383.316
9 -0.25870322D+04 0.1321935 0.0000511 116.747 0.000 EM
383.253
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.79859948D+04 0.0000000 0.0000000 0.687 2.175 EM
497.137
2 -0.33039520D+04 4682.0427991 0.5862817 10.788 24.134 EM
465.078
3 -0.29847387D+04 319.2132663 0.0966156 11.386 43.688 EM
444.926
4 -0.27719902D+04 212.7484922 0.0712788 21.297 71.784 EM
406.919
5 -0.23303500D+04 441.6401667 0.1593224 31.946 84.719 EM
383.335
6 -0.21831115D+04 147.2385240 0.0631830 32.000 85.063 EM
382.937
7 -0.21830814D+04 0.0300845 0.0000138 32.000 85.069 EM
382.931
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.15162411D+05 0.0000000 0.0000000 116.786 28.097 EM
355.117
2 -0.22792714D+04 ************ 0.8496762 86.461 32.000 EM
381.538
3 -0.21833750D+04 95.8963666 0.0420733 85.104 32.000 EM
382.896
4 -0.21830816D+04 0.2933635 0.0001344 85.070 32.000 EM
382.930
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.16547893D+05 0.0000000 0.0000000 0.000 0.000 EM
500.000
2 -0.36650397D+04 ************ 0.7785193 0.000 0.000 EM
500.000
3 -0.36650397D+04 0.0000000 0.0000000 0.000 0.000 EM
500.000
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
7 -0.21830814D+04 0.0300845 0.0000138 32.000 85.069 EM
382.931
8 -0.21830814D+04 0.0000060 0.0000000 32.000 85.069 EM
382.931
9 -0.21830814D+04 0.0000000 0.0000000 32.000 85.069 EM
382.931
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
4 -0.21830816D+04 0.2933635 0.0001344 85.070 32.000 EM
382.930
5 -0.21830814D+04 0.0002134 0.0000001 85.069 32.000 EM
382.931
6 -0.21830814D+04 0.0000001 0.0000000 85.069 32.000 EM
382.931
7 -0.21830814D+04 0.0000000 0.0000000 85.069 32.000 EM
382.931
Beginning Time: 18:14:56
Ending Time: 18:14:56
Elapsed Time: 00:00:00
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