Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix9
fisher's iris data
see everitt & hand (1981), pp. 43-44
equal covariance matrices
Source: Everitt, B.S. & Hand, D.J. (1981). Finite
mixture distributions. London: Chapman & Hall
DATA: FILE IS fisher.dat;
VARIABLE: NAMES ARE v1 v2 v3 v4 id;
USEVAR = v1-v4;
CLASSES = c(3);
DEFINE: v1=v1/10; v2=v2/10; v3=v3/10; v4=v4/10;
! variables are divided by 10 to correspond to everitt & hand
ANALYSIS: TYPE = mixture;
MODEL:
%overall%
v1 WITH v2-v4;
v2 WITH v3 v4;
v3 WITH v4;
! the outcome variables v1-v4 are uncorrelated by default
! and are allowed to be correlated by the above 3 statements
[v1*5.0 v2*3.4 v3*1.5 v4*.3];
! starting values are given for the means which would have
! been held equal across classes by default had the
! statements below not been given
%c#2%
[v1*6.0 v2*2.8 v3*4.2 v4*1.3];
%c#3%
[v1*6.5 v2*3.0 v3*5.5 v4*2.0];
OUTPUT:
tech1 tech8;
INPUT READING TERMINATED NORMALLY
mix9
fisher's iris data
see everitt & hand (1981), pp. 43-44
equal covariance matrices
Source: Everitt, B.S. & Hand, D.J. (1981). Finite
mixture distributions. London: Chapman & Hall
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 150
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
V1 V2 V3 V4
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)
fisher.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:
-256.354 unperturbed 0
-267.236 415931 10
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.
WARNING: THE BEST LOGLIKELIHOOD VALUE WAS NOT REPLICATED. THE
SOLUTION MAY NOT BE TRUSTWORTHY DUE TO LOCAL MAXIMA. INCREASE THE
NUMBER OF RANDOM STARTS.
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -256.354
H0 Scaling Correction Factor 1.119
for MLR
Information Criteria
Number of Free Parameters 24
Akaike (AIC) 560.708
Bayesian (BIC) 632.963
Sample-Size Adjusted BIC 557.008
(n* = (n + 2) / 24)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 50.00000 0.33333
2 49.44114 0.32961
3 50.55886 0.33706
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 50.00000 0.33333
2 49.44114 0.32961
3 50.55886 0.33706
CLASSIFICATION QUALITY
Entropy 0.962
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 50 0.33333
2 49 0.32667
3 51 0.34000
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 0.982 0.018
3 0.000 0.026 0.974
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
V1 WITH
V2 0.090 0.016 5.459 0.000
V3 0.170 0.028 5.990 0.000
V4 0.039 0.009 4.159 0.000
V2 WITH
V3 0.051 0.014 3.714 0.000
V4 0.030 0.007 4.503 0.000
V3 WITH
V4 0.042 0.008 5.172 0.000
Means
V1 5.006 0.049 101.442 0.000
V2 3.428 0.053 64.595 0.000
V3 1.462 0.024 60.133 0.000
V4 0.246 0.015 16.673 0.000
Variances
V1 0.264 0.033 7.967 0.000
V2 0.112 0.014 7.813 0.000
V3 0.187 0.030 6.312 0.000
V4 0.040 0.006 6.419 0.000
Latent Class 2
V1 WITH
V2 0.090 0.016 5.459 0.000
V3 0.170 0.028 5.990 0.000
V4 0.039 0.009 4.159 0.000
V2 WITH
V3 0.051 0.014 3.714 0.000
V4 0.030 0.007 4.503 0.000
V3 WITH
V4 0.042 0.008 5.172 0.000
Means
V1 5.942 0.077 77.524 0.000
V2 2.761 0.045 61.374 0.000
V3 4.259 0.083 51.246 0.000
V4 1.319 0.032 41.822 0.000
Variances
V1 0.264 0.033 7.967 0.000
V2 0.112 0.014 7.813 0.000
V3 0.187 0.030 6.312 0.000
V4 0.040 0.006 6.419 0.000
Latent Class 3
V1 WITH
V2 0.090 0.016 5.459 0.000
V3 0.170 0.028 5.990 0.000
V4 0.039 0.009 4.159 0.000
V2 WITH
V3 0.051 0.014 3.714 0.000
V4 0.030 0.007 4.503 0.000
V3 WITH
V4 0.042 0.008 5.172 0.000
Means
V1 6.575 0.095 69.352 0.000
V2 2.981 0.047 63.154 0.000
V3 5.539 0.084 65.599 0.000
V4 2.025 0.050 40.906 0.000
Variances
V1 0.264 0.033 7.967 0.000
V2 0.112 0.014 7.813 0.000
V3 0.187 0.030 6.312 0.000
V4 0.040 0.006 6.419 0.000
Categorical Latent Variables
Means
C#1 -0.011 0.210 -0.053 0.958
C#2 -0.022 0.232 -0.096 0.923
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.295E-04
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
V1 V2 V3 V4
________ ________ ________ ________
1 1 2 3 4
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 5
V2 6 7
V3 8 9 10
V4 11 12 13 14
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
V1 V2 V3 V4
________ ________ ________ ________
1 15 16 17 18
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 5
V2 6 7
V3 8 9 10
V4 11 12 13 14
PARAMETER SPECIFICATION FOR LATENT CLASS 3
NU
V1 V2 V3 V4
________ ________ ________ ________
1 19 20 21 22
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 5
V2 6 7
V3 8 9 10
V4 11 12 13 14
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 23 24 0
STARTING VALUES FOR LATENT CLASS 1
NU
V1 V2 V3 V4
________ ________ ________ ________
1 5.000 3.400 1.500 0.300
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 0.343
V2 0.000 0.095
V3 0.000 0.000 1.558
V4 0.000 0.000 0.000 0.291
STARTING VALUES FOR LATENT CLASS 2
NU
V1 V2 V3 V4
________ ________ ________ ________
1 6.000 2.800 4.200 1.300
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 0.343
V2 0.000 0.095
V3 0.000 0.000 1.558
V4 0.000 0.000 0.000 0.291
STARTING VALUES FOR LATENT CLASS 3
NU
V1 V2 V3 V4
________ ________ ________ ________
1 6.500 3.000 5.500 2.000
THETA
V1 V2 V3 V4
________ ________ ________ ________
V1 0.343
V2 0.000 0.095
V3 0.000 0.000 1.558
V4 0.000 0.000 0.000 0.291
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 -0.53327146D+03 0.0000000 0.0000000 49.961 49.793 EM
50.246
2 -0.27850491D+03 254.7665574 0.4777427 50.000 51.097 EM
48.903
3 -0.26889812D+03 9.6067889 0.0344941 50.000 52.810 EM
47.190
4 -0.26061511D+03 8.2830085 0.0308035 50.000 53.410 EM
46.590
5 -0.25792063D+03 2.6944782 0.0103389 50.000 53.080 EM
46.920
6 -0.25725723D+03 0.6633976 0.0025721 50.000 52.552 EM
47.448
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48315219D+04 0.0000000 0.0000000 149.854 0.000 EM
0.146
2 -0.37992764D+03 4451.5942167 0.9213648 149.866 0.000 EM
0.134
3 -0.37990248D+03 0.0251581 0.0000662 149.854 0.000 EM
0.146
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.33951794D+04 0.0000000 0.0000000 0.000 150.000 EM
0.000
2 -0.37991500D+03 3015.2643554 0.8881016 0.000 150.000 EM
0.000
3 -0.37991463D+03 0.0003672 0.0000010 0.000 150.000 EM
0.000
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.49465299D+04 0.0000000 0.0000000 98.608 11.605 EM
39.787
2 -0.37428322D+03 4572.2466511 0.9243342 98.489 12.411 EM
39.100
3 -0.36081163D+03 13.4715927 0.0359930 99.402 12.892 EM
37.706
4 -0.33089185D+03 29.9197771 0.0829235 100.672 13.033 EM
36.295
5 -0.29626389D+03 34.6279675 0.1046504 100.033 12.784 EM
37.183
6 -0.29295023D+03 3.3136526 0.0111848 100.000 12.597 EM
37.403
7 -0.29291669D+03 0.0335402 0.0001145 100.000 12.381 EM
37.619
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.38012398D+04 0.0000000 0.0000000 150.000 0.000 EM
0.000
2 -0.37991475D+03 3421.3250926 0.9000550 150.000 0.000 EM
0.000
3 -0.37991463D+03 0.0001177 0.0000003 150.000 0.000 EM
0.000
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.49306063D+04 0.0000000 0.0000000 150.000 0.000 EM
0.000
2 -0.37991463D+03 4550.6916810 0.9229477 150.000 0.000 EM
0.000
3 -0.37991463D+03 0.0000000 0.0000000 150.000 0.000 EM
0.000
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.44731753D+04 0.0000000 0.0000000 0.000 0.004 EM
149.996
2 -0.37991215D+03 4093.2631666 0.9150688 0.000 0.006 EM
149.994
3 -0.37990952D+03 0.0026243 0.0000069 0.000 0.011 EM
149.989
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.11448068D+05 0.0000000 0.0000000 147.388 0.817 EM
1.795
2 -0.37861432D+03 ************ 0.9669277 146.668 1.095 EM
2.237
3 -0.37674652D+03 1.8678044 0.0049333 145.962 1.573 EM
2.465
4 -0.37531520D+03 1.4313165 0.0037991 145.359 2.181 EM
2.460
5 -0.37468484D+03 0.6303650 0.0016796 144.616 2.801 EM
2.583
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.26283720D+04 0.0000000 0.0000000 148.734 1.266 EM
0.000
2 -0.37950592D+03 2248.8660534 0.8556118 148.453 1.547 EM
0.000
3 -0.37934925D+03 0.1566743 0.0004128 148.095 1.905 EM
0.000
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.23398887D+04 0.0000000 0.0000000 1.958 148.042 EM
0.000
2 -0.37974590D+03 1960.1428073 0.8377077 1.748 148.252 EM
0.000
3 -0.37945446D+03 0.2914455 0.0007675 1.727 148.273 EM
0.000
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48089506D+04 0.0000000 0.0000000 92.779 57.221 EM
0.000
2 -0.38057956D+03 4428.3710715 0.9208602 85.103 64.895 EM
0.002
3 -0.37599965D+03 4.5799107 0.0120340 80.557 69.416 EM
0.027
4 -0.37357393D+03 2.4257167 0.0064514 76.879 72.879 EM
0.243
5 -0.36981952D+03 3.7544127 0.0100500 73.015 75.808 EM
1.177
6 -0.36366522D+03 6.1543005 0.0166414 67.913 80.069 EM
2.018
7 -0.35457133D+03 9.0938865 0.0250062 60.531 87.100 EM
2.369
8 -0.33264345D+03 21.9278801 0.0618434 52.662 94.461 EM
2.876
9 -0.29676328D+03 35.8801701 0.1078638 50.051 95.450 EM
4.498
10 -0.28330634D+03 13.4569347 0.0453457 50.001 92.065 EM
7.934
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
6 -0.25725723D+03 0.6633976 0.0025721 50.000 52.552 EM
47.448
7 -0.25693752D+03 0.3197127 0.0012428 50.000 52.104 EM
47.896
8 -0.25680298D+03 0.1345359 0.0005236 50.000 51.768 EM
48.232
9 -0.25674233D+03 0.0606576 0.0002362 50.000 51.499 EM
48.501
10 -0.25669706D+03 0.0452611 0.0001763 50.000 51.252 EM
48.748
11 -0.25664889D+03 0.0481778 0.0001877 50.000 51.002 EM
48.998
12 -0.25659325D+03 0.0556337 0.0002168 50.000 50.741 EM
49.259
13 -0.25653175D+03 0.0614986 0.0002397 50.000 50.474 EM
49.526
14 -0.25647148D+03 0.0602747 0.0002350 50.000 50.220 EM
49.780
15 -0.25642193D+03 0.0495510 0.0001932 50.000 49.998 EM
50.002
16 -0.25638852D+03 0.0334073 0.0001303 50.000 49.821 EM
50.179
17 -0.25636978D+03 0.0187464 0.0000731 50.000 49.690 EM
50.310
18 -0.25636068D+03 0.0090967 0.0000355 50.000 49.600 EM
50.400
19 -0.25635670D+03 0.0039822 0.0000155 50.000 49.541 EM
50.459
20 -0.25635507D+03 0.0016284 0.0000064 50.000 49.503 EM
50.497
21 -0.25635443D+03 0.0006376 0.0000025 50.000 49.479 EM
50.521
22 -0.25635419D+03 0.0002430 0.0000009 50.000 49.464 EM
50.536
23 -0.25635410D+03 0.0000911 0.0000004 50.000 49.455 EM
50.545
24 -0.25635406D+03 0.0000338 0.0000001 50.000 49.450 EM
50.550
25 -0.25635405D+03 0.0000125 0.0000000 50.000 49.446 EM
50.554
26 -0.25635405D+03 0.0000046 0.0000000 50.000 49.444 EM
50.556
27 -0.25635404D+03 0.0000017 0.0000000 50.000 49.443 EM
50.557
28 -0.25635404D+03 0.0000006 0.0000000 50.000 49.442 EM
50.558
29 -0.25635404D+03 0.0000002 0.0000000 50.000 49.442 EM
50.558
30 -0.25635404D+03 0.0000001 0.0000000 50.000 49.442 EM
50.558
31 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
32 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
33 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
34 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
35 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
36 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
37 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
38 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
39 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
40 -0.25635404D+03 0.0000000 0.0000000 50.000 49.441 EM
50.559
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
10 -0.28330634D+03 13.4569347 0.0453457 50.001 92.065 EM
7.934
11 -0.27175732D+03 11.5490203 0.0407651 50.001 89.445 EM
10.553
12 -0.26763231D+03 4.1250105 0.0151790 50.002 88.568 EM
11.430
13 -0.26728365D+03 0.3486677 0.0013028 50.002 88.283 EM
11.715
14 -0.26724905D+03 0.0345975 0.0001294 50.002 88.157 EM
11.841
15 -0.26724067D+03 0.0083779 0.0000313 50.002 88.093 EM
11.905
16 -0.26723795D+03 0.0027190 0.0000102 50.002 88.058 EM
11.940
17 -0.26723693D+03 0.0010198 0.0000038 50.001 88.038 EM
11.961
18 -0.26723652D+03 0.0004123 0.0000015 50.001 88.025 EM
11.974
19 -0.26723635D+03 0.0001732 0.0000006 50.001 88.017 EM
11.981
20 -0.26723627D+03 0.0000743 0.0000003 50.001 88.012 EM
11.987
21 -0.26723624D+03 0.0000322 0.0000001 50.001 88.009 EM
11.990
22 -0.26723623D+03 0.0000141 0.0000001 50.001 88.007 EM
11.992
23 -0.26723622D+03 0.0000062 0.0000000 50.001 88.005 EM
11.993
24 -0.26723622D+03 0.0000027 0.0000000 50.001 88.004 EM
11.994
25 -0.26723622D+03 0.0000012 0.0000000 50.001 88.004 EM
11.995
26 -0.26723621D+03 0.0000005 0.0000000 50.001 88.003 EM
11.995
27 -0.26723621D+03 0.0000002 0.0000000 50.001 88.003 EM
11.996
28 -0.26723621D+03 0.0000001 0.0000000 50.001 88.003 EM
11.996
29 -0.26723621D+03 0.0000000 0.0000000 50.001 88.003 EM
11.996
30 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
31 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
32 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
33 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
34 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
35 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
36 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
37 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
38 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
39 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
40 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
41 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
42 -0.26723621D+03 0.0000000 0.0000000 50.001 88.002 EM
11.996
Beginning Time: 22:58:13
Ending Time: 22:58:13
Elapsed Time: 00:00:00
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