Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix3
stouffer & toby data.
2 classes - H1 model of Goodman (1974), p. 222
Source: Goodman, L. (1974). Exploratory latent structure
analysis using both identifiable and unidentifiable models.
Biometrika, 61, 215-231.
DATA: FILE IS stouf.dat;
VARIABLE: NAMES ARE u1-u4 x1 x2;
USEV ARE u1-u4;
CATEGORICAL ARE u1-u4;
CLASSES = c(2);
ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 100;
MODEL:
%OVERALL%
! c#1 BY u1*2 u2*2 u3*2 u4*2;
! c#2 BY u1*1 u2*1 u3*1 u4*1;
[u1$1*-2 u2$1*-2 u3$1*-2 u4$1*-2];
%C#2%
[u1$1*-1 u2$1*-1 u3$1*-1 u4$1*-1];
! this is the 2-class model labelled H1 on page 222
! for comments on parameter specifications and starting
! values, see the file wbart.inp
OUTPUT:
TECH8;
INPUT READING TERMINATED NORMALLY
mix3
stouffer & toby data.
2 classes - H1 model of Goodman (1974), p. 222
Source: Goodman, L. (1974). Exploratory latent structure
analysis using both identifiable and unidentifiable models.
Biometrika, 61, 215-231.
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 216
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
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
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 100
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
Link LOGIT
Input data file(s)
stouf.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.208 45.000
Category 2 0.792 171.000
U2
Category 1 0.500 108.000
Category 2 0.500 108.000
U3
Category 1 0.486 105.000
Category 2 0.514 111.000
U4
Category 1 0.690 149.000
Category 2 0.310 67.000
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:
-504.468 unperturbed 0
-504.468 127215 9
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -504.468
H0 Scaling Correction Factor 1.011
for MLR
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 1026.935
Bayesian (BIC) 1057.313
Sample-Size Adjusted BIC 1028.793
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 2.720
Degrees of Freedom 6
P-Value 0.8431
Likelihood Ratio Chi-Square
Value 2.720
Degrees of Freedom 6
P-Value 0.8431
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 60.31718 0.27925
2 155.68282 0.72075
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 60.31718 0.27925
2 155.68282 0.72075
CLASSIFICATION QUALITY
Entropy 0.719
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 71 0.32870
2 145 0.67130
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.777 0.223
2 0.035 0.965
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 -4.983 3.741 -1.332 0.183
U2$1 -2.747 1.187 -2.314 0.021
U3$1 -2.535 0.992 -2.554 0.011
U4$1 -1.203 0.553 -2.176 0.030
Latent Class 2
Thresholds
U1$1 -0.913 0.205 -4.457 0.000
U2$1 0.710 0.231 3.075 0.002
U3$1 0.601 0.214 2.805 0.005
U4$1 1.880 0.338 5.556 0.000
Categorical Latent Variables
Means
C#1 -0.948 0.300 -3.162 0.002
RESULTS IN PROBABILITY SCALE
Latent Class 1
U1
Category 1 0.007 0.025 0.269 0.788
Category 2 0.993 0.025 39.267 0.000
U2
Category 1 0.060 0.067 0.896 0.370
Category 2 0.940 0.067 13.985 0.000
U3
Category 1 0.073 0.068 1.088 0.277
Category 2 0.927 0.068 13.716 0.000
U4
Category 1 0.231 0.098 2.351 0.019
Category 2 0.769 0.098 7.833 0.000
Latent Class 2
U1
Category 1 0.286 0.042 6.841 0.000
Category 2 0.714 0.042 17.045 0.000
U2
Category 1 0.670 0.051 13.140 0.000
Category 2 0.330 0.051 6.461 0.000
U3
Category 1 0.646 0.049 13.175 0.000
Category 2 0.354 0.049 7.220 0.000
U4
Category 1 0.868 0.039 22.325 0.000
Category 2 0.132 0.039 3.406 0.001
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 58.566 219.503 0.267 0.790
U2
Category > 1 31.730 37.606 0.844 0.399
U3
Category > 1 23.012 22.799 1.009 0.313
U4
Category > 1 21.836 13.291 1.643 0.100
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.183E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 8 OUTPUT
INITIAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.73705141D+03 0.0000000 0.0000000 64.148 151.852 EM
2 -0.51841398D+03 218.6374281 0.2966380 68.325 147.675 EM
3 -0.50849208D+03 9.9218966 0.0191389 70.276 145.724 EM
4 -0.50546652D+03 3.0255644 0.0059501 70.280 145.720 EM
5 -0.50495483D+03 0.5116936 0.0010123 69.551 146.449 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.71776122D+03 0.0000000 0.0000000 159.298 56.702 EM
2 -0.51641165D+03 201.3495717 0.2805245 156.855 59.145 EM
3 -0.50860136D+03 7.8102880 0.0151242 156.327 59.673 EM
4 -0.50680963D+03 1.7917274 0.0035229 156.579 59.421 EM
5 -0.50596561D+03 0.8440230 0.0016654 156.805 59.195 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.11166724D+04 0.0000000 0.0000000 91.958 124.042 EM
2 -0.55185531D+03 564.8170780 0.5058037 87.798 128.202 EM
3 -0.54744524D+03 4.4100729 0.0079914 85.492 130.508 EM
4 -0.54578235D+03 1.6628870 0.0030375 84.031 131.969 EM
5 -0.54457875D+03 1.2035997 0.0022053 83.169 132.831 EM
6 -0.54286125D+03 1.7175035 0.0031538 83.040 132.960 EM
7 -0.53926633D+03 3.5949124 0.0066222 84.210 131.790 EM
8 -0.53198311D+03 7.2832247 0.0135058 87.334 128.666 EM
9 -0.52200301D+03 9.9801038 0.0187602 91.799 124.201 EM
10 -0.51496725D+03 7.0357588 0.0134784 96.187 119.813 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.75188774D+03 0.0000000 0.0000000 62.232 153.768 EM
2 -0.54934510D+03 202.5426421 0.2693788 59.225 156.775 EM
3 -0.54589506D+03 3.4500397 0.0062803 58.018 157.982 EM
4 -0.54400234D+03 1.8927243 0.0034672 57.795 158.205 EM
5 -0.54180141D+03 2.2009266 0.0040458 58.651 157.349 EM
6 -0.53752946D+03 4.2719511 0.0078847 61.335 154.665 EM
7 -0.52996442D+03 7.5650397 0.0140737 66.346 149.654 EM
8 -0.52172478D+03 8.2396388 0.0155475 72.379 143.621 EM
9 -0.51692782D+03 4.7969572 0.0091944 77.879 138.121 EM
10 -0.51495697D+03 1.9708534 0.0038126 82.644 133.356 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.68259199D+03 0.0000000 0.0000000 43.149 172.851 EM
2 -0.54599704D+03 136.5949536 0.2001122 41.848 174.152 EM
3 -0.54446563D+03 1.5314061 0.0028048 41.368 174.632 EM
4 -0.54347491D+03 0.9907185 0.0018196 41.447 174.553 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.57932024D+03 0.0000000 0.0000000 65.349 150.651 EM
2 -0.51957699D+03 59.7432537 0.1031265 68.583 147.417 EM
3 -0.51787177D+03 1.7052144 0.0032819 70.726 145.274 EM
4 -0.51741763D+03 0.4541491 0.0008770 72.397 143.603 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.12901670D+04 0.0000000 0.0000000 129.715 86.285 EM
2 -0.52642059D+03 763.7463804 0.5919748 127.291 88.709 EM
3 -0.51803909D+03 8.3814982 0.0159217 123.962 92.038 EM
4 -0.51529589D+03 2.7431977 0.0052953 120.542 95.458 EM
5 -0.51382890D+03 1.4669878 0.0028469 116.980 99.020 EM
6 -0.51258720D+03 1.2416974 0.0024166 113.297 102.703 EM
7 -0.51148516D+03 1.1020447 0.0021500 109.591 106.409 EM
8 -0.51054722D+03 0.9379368 0.0018338 105.951 110.049 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.88358535D+03 0.0000000 0.0000000 199.748 16.252 EM
2 -0.54723682D+03 336.3485309 0.3806633 202.895 13.105 EM
3 -0.54268545D+03 4.5513739 0.0083170 202.414 13.586 EM
4 -0.53835326D+03 4.3321875 0.0079829 199.133 16.867 EM
5 -0.53345419D+03 4.8990692 0.0091001 194.470 21.530 EM
6 -0.53025224D+03 3.2019555 0.0060023 190.512 25.488 EM
7 -0.52886167D+03 1.3905686 0.0026225 187.380 28.620 EM
8 -0.52793865D+03 0.9230153 0.0017453 184.343 31.657 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.10464483D+04 0.0000000 0.0000000 173.113 42.887 EM
2 -0.53407838D+03 512.3699431 0.4896276 169.526 46.474 EM
3 -0.52590619D+03 8.1721915 0.0153015 164.413 51.587 EM
4 -0.52253294D+03 3.3732455 0.0064142 160.223 55.777 EM
5 -0.52125329D+03 1.2796564 0.0024489 157.032 58.968 EM
6 -0.52063638D+03 0.6169103 0.0011835 154.425 61.575 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.14112019D+04 0.0000000 0.0000000 184.477 31.523 EM
2 -0.54314111D+03 868.0607499 0.6151216 184.200 31.800 EM
3 -0.53172544D+03 11.4156760 0.0210179 178.199 37.801 EM
4 -0.51684489D+03 14.8805457 0.0279854 170.405 45.595 EM
5 -0.50753003D+03 9.3148568 0.0180225 166.093 49.907 EM
6 -0.50545832D+03 2.0717196 0.0040820 164.597 51.403 EM
7 -0.50518298D+03 0.2753391 0.0005447 164.016 51.984 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.16028630D+04 0.0000000 0.0000000 123.037 92.963 EM
2 -0.51725161D+03 1085.6114008 0.6772952 121.630 94.370 EM
3 -0.51420051D+03 3.0510935 0.0058987 119.561 96.439 EM
4 -0.51316400D+03 1.0365128 0.0020158 117.074 98.926 EM
5 -0.51236122D+03 0.8027779 0.0015644 114.267 101.733 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
5 -0.50495483D+03 0.5116936 0.0010123 69.551 146.449 EM
6 -0.50482547D+03 0.1293526 0.0002562 68.663 147.337 EM
7 -0.50474987D+03 0.0756074 0.0001498 67.798 148.202 EM
8 -0.50469235D+03 0.0575136 0.0001139 67.005 148.995 EM
9 -0.50464694D+03 0.0454111 0.0000900 66.292 149.708 EM
10 -0.50461088D+03 0.0360625 0.0000715 65.655 150.345 EM
11 -0.50458219D+03 0.0286854 0.0000568 65.088 150.912 EM
12 -0.50455935D+03 0.0228394 0.0000453 64.583 151.417 EM
13 -0.50454115D+03 0.0182009 0.0000361 64.134 151.866 EM
14 -0.50452664D+03 0.0145185 0.0000288 63.734 152.266 EM
15 -0.50451504D+03 0.0115935 0.0000230 63.378 152.622 EM
16 -0.50450577D+03 0.0092687 0.0000184 63.060 152.940 EM
17 -0.50449835D+03 0.0074192 0.0000147 62.777 153.223 EM
18 -0.50449241D+03 0.0059463 0.0000118 62.524 153.476 EM
19 -0.50448764D+03 0.0047719 0.0000095 62.299 153.701 EM
20 -0.50448380D+03 0.0038343 0.0000076 62.097 153.903 EM
21 -0.50448072D+03 0.0030848 0.0000061 61.917 154.083 EM
22 -0.50447823D+03 0.0024849 0.0000049 61.756 154.244 EM
23 -0.50447623D+03 0.0020039 0.0000040 61.611 154.389 EM
24 -0.50447461D+03 0.0016179 0.0000032 61.482 154.518 EM
25 -0.50447330D+03 0.0013076 0.0000026 61.365 154.635 EM
26 -0.50447224D+03 0.0010578 0.0000021 61.261 154.739 EM
27 -0.50447139D+03 0.0008566 0.0000017 61.168 154.832 EM
28 -0.50447069D+03 0.0006943 0.0000014 61.084 154.916 EM
29 -0.50447013D+03 0.0005632 0.0000011 61.008 154.992 EM
30 -0.50446967D+03 0.0004572 0.0000009 60.940 155.060 EM
31 -0.50446930D+03 0.0003714 0.0000007 60.879 155.121 EM
32 -0.50446900D+03 0.0003019 0.0000006 60.824 155.176 EM
33 -0.50446875D+03 0.0002456 0.0000005 60.775 155.225 EM
34 -0.50446855D+03 0.0001999 0.0000004 60.730 155.270 EM
35 -0.50446839D+03 0.0001628 0.0000003 60.690 155.310 EM
36 -0.50446826D+03 0.0001326 0.0000003 60.654 155.346 EM
37 -0.50446815D+03 0.0001081 0.0000002 60.621 155.379 EM
38 -0.50446768D+03 0.0004737 0.0000009 60.347 155.653 FS
39 -0.50446767D+03 0.0000069 0.0000000 60.322 155.678 FS
40 -0.50446767D+03 0.0000002 0.0000000 60.318 155.682 FS
41 -0.50446767D+03 0.0000000 0.0000000 60.317 155.683 FS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
7 -0.50518298D+03 0.2753391 0.0005447 164.016 51.984 EM
8 -0.50509586D+03 0.0871208 0.0001725 163.658 52.342 EM
9 -0.50503570D+03 0.0601582 0.0001191 163.353 52.647 EM
10 -0.50498355D+03 0.0521489 0.0001033 163.059 52.941 EM
11 -0.50493314D+03 0.0504059 0.0000998 162.758 53.242 EM
12 -0.50488189D+03 0.0512506 0.0001015 162.441 53.559 EM
13 -0.50482946D+03 0.0524300 0.0001038 162.104 53.896 EM
14 -0.50477701D+03 0.0524549 0.0001039 161.747 54.253 EM
15 -0.50472648D+03 0.0505239 0.0001001 161.373 54.627 EM
16 -0.50467996D+03 0.0465217 0.0000922 160.988 55.012 EM
17 -0.50463905D+03 0.0409151 0.0000811 160.601 55.399 EM
18 -0.50460454D+03 0.0345022 0.0000684 160.219 55.781 EM
19 -0.50457644D+03 0.0281022 0.0000557 159.850 56.150 EM
20 -0.50455412D+03 0.0223217 0.0000442 159.499 56.501 EM
21 -0.50453665D+03 0.0174694 0.0000346 159.169 56.831 EM
22 -0.50452305D+03 0.0135997 0.0000270 158.863 57.137 EM
23 -0.50451244D+03 0.0106112 0.0000210 158.579 57.421 EM
24 -0.50450410D+03 0.0083397 0.0000165 158.318 57.682 EM
25 -0.50449748D+03 0.0066184 0.0000131 158.080 57.920 EM
26 -0.50449218D+03 0.0053060 0.0000105 157.862 58.138 EM
27 -0.50448788D+03 0.0042938 0.0000085 157.663 58.337 EM
28 -0.50448438D+03 0.0035021 0.0000069 157.483 58.517 EM
29 -0.50448151D+03 0.0028742 0.0000057 157.318 58.682 EM
30 -0.50447914D+03 0.0023700 0.0000047 157.169 58.831 EM
31 -0.50447717D+03 0.0019607 0.0000039 157.033 58.967 EM
32 -0.50447555D+03 0.0016257 0.0000032 156.909 59.091 EM
33 -0.50447420D+03 0.0013497 0.0000027 156.797 59.203 EM
34 -0.50447308D+03 0.0011213 0.0000022 156.695 59.305 EM
35 -0.50447215D+03 0.0009316 0.0000018 156.602 59.398 EM
36 -0.50447137D+03 0.0007738 0.0000015 156.517 59.483 EM
37 -0.50447073D+03 0.0006423 0.0000013 156.441 59.559 EM
38 -0.50446772D+03 0.0030096 0.0000060 155.746 60.254 FS
39 -0.50446767D+03 0.0000494 0.0000001 155.695 60.305 FS
40 -0.50446767D+03 0.0000010 0.0000000 155.684 60.316 FS
41 -0.50446767D+03 0.0000000 0.0000000 155.683 60.317 FS
Beginning Time: 22:58:12
Ending Time: 22:58:12
Elapsed Time: 00:00:00
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