Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix8
Duda & Hart (1973) data, n=25.
Unequal variances - Everitt & Hand (1981), pp. 41-42
(note that p. 42 gives estimates for s.d.s', not variances)
Source: Everitt, B.S. & Hand, D.J. (1981). Finite
mixture distributions. London: Chapman & Hall
DATA: FILE IS dudahart.dat;
VARIABLE: NAMES ARE y;
USEVAR = y;
CLASSES = c(2);
ANALYSIS: TYPE = MIXTURE;
MITERATIONS=50;
MODEL:
%OVERALL%
y*.5;
[y*-1];
%c#1%
[y*-1];
%c#2%
[y*+1];
y*.5;
! the last statement above relaxes the default
! of class-invariant variances
output: tech1 tech8;
*** WARNING in MODEL command
All variables are uncorrelated with all other variables within class.
Check that this is what is intended.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
mix8
Duda & Hart (1973) data, n=25.
Unequal variances - Everitt & Hand (1981), pp. 41-42
(note that p. 42 gives estimates for s.d.s', not variances)
Source: Everitt, B.S. & Hand, D.J. (1981). Finite
mixture distributions. London: Chapman & Hall
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 25
Number of dependent variables 1
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y
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 50
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)
dudahart.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:
-50.303 195873 6
-50.303 127215 9
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -50.303
H0 Scaling Correction Factor 0.870
for MLR
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 110.606
Bayesian (BIC) 116.700
Sample-Size Adjusted BIC 101.195
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 6.69060 0.26762
2 18.30940 0.73238
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 6.69059 0.26762
2 18.30941 0.73238
CLASSIFICATION QUALITY
Entropy 0.923
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 7 0.28000
2 18 0.72000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.950 0.050
2 0.002 0.998
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Means
Y -2.404 0.235 -10.249 0.000
Variances
Y 0.332 0.186 1.784 0.074
Latent Class 2
Means
Y 1.491 0.341 4.366 0.000
Variances
Y 1.790 0.532 3.367 0.001
Categorical Latent Variables
Means
C#1 -1.007 0.478 -2.105 0.035
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.289E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y
________
1 1
THETA
Y
________
Y 2
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y
________
1 3
THETA
Y
________
Y 4
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 5 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y
________
1 -1.000
THETA
Y
________
Y 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
Y
________
1 1.000
THETA
Y
________
Y 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 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 -0.77647911D+02 0.0000000 0.0000000 9.020 15.980 EM
2 -0.51878238D+02 25.7696729 0.3318785 8.467 16.533 EM
3 -0.51595335D+02 0.2829034 0.0054532 8.014 16.986 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.58472252D+02 0.0000000 0.0000000 7.879 17.121 EM
2 -0.50877125D+02 7.5951274 0.1298928 7.378 17.622 EM
3 -0.50546709D+02 0.3304159 0.0064944 7.091 17.909 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.43487328D+03 0.0000000 0.0000000 0.411 24.589 EM
2 -0.53655462D+02 381.2178134 0.8766182 0.646 24.354 EM
3 -0.53356660D+02 0.2988018 0.0055689 1.109 23.891 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.15595281D+03 0.0000000 0.0000000 16.180 8.820 EM
2 -0.51845874D+02 104.1069330 0.6675541 16.583 8.417 EM
3 -0.51604400D+02 0.2414736 0.0046575 16.994 8.006 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.15717879D+03 0.0000000 0.0000000 9.542 15.458 EM
2 -0.53912997D+02 103.2657911 0.6569957 9.542 15.458 EM
3 -0.53912226D+02 0.0007709 0.0000143 9.543 15.457 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.13733814D+03 0.0000000 0.0000000 19.630 5.370 EM
2 -0.52746726D+02 84.5914102 0.6159353 19.772 5.228 EM
3 -0.52591924D+02 0.1548016 0.0029348 19.867 5.133 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.14760558D+03 0.0000000 0.0000000 7.372 17.628 EM
2 -0.50509372D+02 97.0962121 0.6578085 7.061 17.939 EM
3 -0.50370239D+02 0.1391338 0.0027546 6.893 18.107 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.14536639D+03 0.0000000 0.0000000 0.398 24.602 EM
2 -0.53915069D+02 91.4513210 0.6291091 0.399 24.601 EM
3 -0.53914885D+02 0.0001841 0.0000034 0.399 24.601 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.94805395D+02 0.0000000 0.0000000 8.234 16.766 EM
2 -0.51256667D+02 43.5487273 0.4593486 7.672 17.328 EM
3 -0.50815586D+02 0.4410813 0.0086053 7.310 17.690 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.10706306D+03 0.0000000 0.0000000 6.282 18.718 EM
2 -0.50378186D+02 56.6848732 0.5294531 6.455 18.545 EM
3 -0.50321747D+02 0.0564389 0.0011203 6.560 18.440 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.15265114D+03 0.0000000 0.0000000 14.080 10.920 EM
2 -0.53124331D+02 99.5268049 0.6519886 14.069 10.931 EM
3 -0.52837794D+02 0.2865374 0.0053937 13.913 11.087 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
3 -0.50321747D+02 0.0564389 0.0011203 6.560 18.440 EM
4 -0.50308872D+02 0.0128751 0.0002559 6.619 18.381 EM
5 -0.50304763D+02 0.0041090 0.0000817 6.652 18.348 EM
6 -0.50303502D+02 0.0012607 0.0000251 6.670 18.330 EM
7 -0.50303129D+02 0.0003733 0.0000074 6.680 18.320 EM
8 -0.50303021D+02 0.0001085 0.0000022 6.685 18.315 EM
9 -0.50302989D+02 0.0000312 0.0000006 6.687 18.313 EM
10 -0.50302980D+02 0.0000089 0.0000002 6.689 18.311 EM
11 -0.50302978D+02 0.0000026 0.0000001 6.690 18.310 EM
12 -0.50302977D+02 0.0000007 0.0000000 6.690 18.310 EM
13 -0.50302977D+02 0.0000002 0.0000000 6.690 18.310 EM
14 -0.50302977D+02 0.0000001 0.0000000 6.690 18.310 EM
15 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
16 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
17 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
18 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
3 -0.50370239D+02 0.1391338 0.0027546 6.893 18.107 EM
4 -0.50321897D+02 0.0483416 0.0009597 6.800 18.200 EM
5 -0.50308000D+02 0.0138970 0.0002762 6.749 18.251 EM
6 -0.50304333D+02 0.0036665 0.0000729 6.722 18.278 EM
7 -0.50303352D+02 0.0009812 0.0000195 6.707 18.293 EM
8 -0.50303082D+02 0.0002700 0.0000054 6.700 18.300 EM
9 -0.50303007D+02 0.0000756 0.0000015 6.695 18.305 EM
10 -0.50302985D+02 0.0000213 0.0000004 6.693 18.307 EM
11 -0.50302979D+02 0.0000060 0.0000001 6.692 18.308 EM
12 -0.50302978D+02 0.0000017 0.0000000 6.691 18.309 EM
13 -0.50302977D+02 0.0000005 0.0000000 6.691 18.309 EM
14 -0.50302977D+02 0.0000001 0.0000000 6.691 18.309 EM
15 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
16 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
17 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
18 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
19 -0.50302977D+02 0.0000000 0.0000000 6.691 18.309 EM
Beginning Time: 22:58:13
Ending Time: 22:58:13
Elapsed Time: 00:00:00
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