Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix5
stouffer-toby data
3-class restricted model H9 in 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;
USEVAR ARE u1 - u4;
CATEGORICAL = u1 - u4;
CLASSES = c(3);
ANALYSIS: TYPE = MIXTURE;
MITERATIONS = 25;
MODEL:
%OVERALL%
! c#1 BY u1@100
! u2@100
! u3@100
! u4@100;
! c#2 BY u1@-100
! u2@-100
! u3@-100
! u4@-100;
! c#3 BY u1*1
! u2*.5(1)
! u3*.5(1)
! u4*0;
[u1$1@-100 u2$1@-100 u3$1@-100 u4$1@-100];
%c#2%
[u1$1@100 u2$1@100 u3$1@100 u4$1@100];
%c#3%
[u1$1*-1 u4$1*0];
[u2$1*-.5 u3$1*-.5](1);
! the conditional u probabilities are fixed at 1 for class 1,
! fixed at zero for class 2,
! and estimated for class 3.
! the class probabilities are free to be estimated by default.
!
! note the relationship between logits and probabilities:
!
! probability = 1/(1+exp(-logit))
!
! logit = elog(probability/(1-probability))
!
! which means that
!
! Probability Logit
! 0 -100 (approximately)
! 0.5 0
! 1 +100 (approximately)
!
! for other comments on parameter specifications and starting
! values, see the file wbart.inp.
OUTPUT:
tech1 tech8;
INPUT READING TERMINATED NORMALLY
mix5
stouffer-toby data
3-class restricted model H9 in 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 25
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:
-504.303 903420 5
-504.303 462953 7
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 -504.303
H0 Scaling Correction Factor 1.013
for MLR
Information Criteria
Number of Free Parameters 5
Akaike (AIC) 1018.607
Bayesian (BIC) 1035.483
Sample-Size Adjusted BIC 1019.639
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 2.421
Degrees of Freedom 10
P-Value 0.9920
Likelihood Ratio Chi-Square
Value 2.391
Degrees of Freedom 10
P-Value 0.9924
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 37.72211 0.17464
2 10.77702 0.04989
3 167.50087 0.77547
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 37.72212 0.17464
2 10.77693 0.04989
3 167.50095 0.77547
CLASSIFICATION QUALITY
Entropy 0.884
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 42 0.19444
2 20 0.09259
3 154 0.71296
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2 3
1 0.898 0.000 0.102
2 0.000 0.539 0.461
3 0.000 0.000 1.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 -100.000 0.000 999.000 999.000
U2$1 -100.000 0.000 999.000 999.000
U3$1 -100.000 0.000 999.000 999.000
U4$1 -100.000 0.000 999.000 999.000
Latent Class 2
Thresholds
U1$1 100.000 0.000 999.000 999.000
U2$1 100.000 0.000 999.000 999.000
U3$1 100.000 0.000 999.000 999.000
U4$1 100.000 0.000 999.000 999.000
Latent Class 3
Thresholds
U1$1 -1.360 0.226 -6.003 0.000
U2$1 0.288 0.128 2.252 0.024
U3$1 0.288 0.128 2.252 0.024
U4$1 1.552 0.223 6.955 0.000
Categorical Latent Variables
Means
C#1 -1.491 0.196 -7.607 0.000
C#2 -2.744 0.495 -5.539 0.000
RESULTS IN PROBABILITY SCALE
Latent Class 1
U1
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
U2
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
U3
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
U4
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
Latent Class 2
U1
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
U2
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
U3
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
U4
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
Latent Class 3
U1
Category 1 0.204 0.037 5.549 0.000
Category 2 0.796 0.037 21.611 0.000
U2
Category 1 0.571 0.031 18.252 0.000
Category 2 0.429 0.031 13.686 0.000
U3
Category 1 0.571 0.031 18.252 0.000
Category 2 0.429 0.031 13.686 0.000
U4
Category 1 0.825 0.032 25.639 0.000
Category 2 0.175 0.032 5.431 0.000
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 ********* 0.000 999.000 999.000
U2
Category > 1 ********* 0.000 999.000 999.000
U3
Category > 1 ********* 0.000 999.000 999.000
U4
Category > 1 ********* 0.000 999.000 999.000
Latent Class 1 Compared to Latent Class 3
U1
Category > 1 ********* ********* 4.415 0.000
U2
Category > 1 ********* ********* 7.821 0.000
U3
Category > 1 ********* ********* 7.821 0.000
U4
Category > 1 ********* ********* 4.481 0.000
Latent Class 2 Compared to Latent Class 3
U1
Category > 1 0.000 0.000 4.415 0.000
U2
Category > 1 0.000 0.000 7.821 0.000
U3
Category > 1 0.000 0.000 7.821 0.000
U4
Category > 1 0.000 0.000 4.481 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.515E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
PARAMETER SPECIFICATION FOR LATENT CLASS 2
PARAMETER SPECIFICATION FOR LATENT CLASS 3
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
LAMBDA(U)
C#1 C#2 C#3
________ ________ ________
U1 0 0 1
U2 0 0 2
U3 0 0 2
U4 0 0 3
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 4 5 0
STARTING VALUES FOR LATENT CLASS 1
STARTING VALUES FOR LATENT CLASS 2
STARTING VALUES FOR LATENT CLASS 3
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
LAMBDA(U)
C#1 C#2 C#3
________ ________ ________
U1 100.000 -100.000 1.000
U2 100.000 -100.000 0.500
U3 100.000 -100.000 0.500
U4 100.000 -100.000 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 -0.64386015D+03 0.0000000 0.0000000 36.790 19.624 EM
159.587
2 -0.50620745D+03 137.6527033 0.2137929 36.734 15.259 EM
164.007
3 -0.50479437D+03 1.4130782 0.0027915 37.077 13.406 EM
165.517
4 -0.50447166D+03 0.3227110 0.0006393 37.333 12.416 EM
166.251
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.57712640D+03 0.0000000 0.0000000 30.516 16.411 EM
169.074
2 -0.50634409D+03 70.7823131 0.1226461 34.517 14.411 EM
167.073
3 -0.50487928D+03 1.4648050 0.0028929 36.368 13.162 EM
166.470
4 -0.50448266D+03 0.3966200 0.0007856 37.120 12.342 EM
166.538
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.92510455D+03 0.0000000 0.0000000 41.292 19.177 EM
155.531
2 -0.50619787D+03 418.9066791 0.4528209 38.187 14.768 EM
163.046
3 -0.50466485D+03 1.5330250 0.0030285 37.581 13.042 EM
165.377
4 -0.50441889D+03 0.2459573 0.0004874 37.519 12.170 EM
166.311
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.84711009D+03 0.0000000 0.0000000 29.720 19.883 EM
166.397
2 -0.50796979D+03 339.1402987 0.4003497 33.740 15.803 EM
166.458
3 -0.50531381D+03 2.6559864 0.0052286 35.947 13.899 EM
166.154
4 -0.50461256D+03 0.7012454 0.0013877 36.920 12.779 EM
166.301
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.72573047D+03 0.0000000 0.0000000 39.918 18.321 EM
157.761
2 -0.50570287D+03 220.0275936 0.3031809 37.849 14.526 EM
163.625
3 -0.50461983D+03 1.0830405 0.0021417 37.494 12.947 EM
165.559
4 -0.50441051D+03 0.2093236 0.0004148 37.499 12.124 EM
166.377
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.65705060D+03 0.0000000 0.0000000 41.783 13.204 EM
161.013
2 -0.50487802D+03 152.1725797 0.2315995 38.686 11.891 EM
165.423
3 -0.50435435D+03 0.5236664 0.0010372 37.931 11.397 EM
166.672
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.17867187D+04 0.0000000 0.0000000 42.000 19.944 EM
154.056
2 -0.50664278D+03 1280.0758945 0.7164395 38.332 15.012 EM
162.656
3 -0.50471338D+03 1.9293990 0.0038082 37.608 13.153 EM
165.239
4 -0.50443023D+03 0.2831489 0.0005610 37.519 12.230 EM
166.250
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.89516627D+03 0.0000000 0.0000000 41.968 11.828 EM
162.205
2 -0.50483069D+03 390.3355874 0.4360481 38.808 11.062 EM
166.130
3 -0.50433653D+03 0.4941550 0.0009789 38.021 10.866 EM
167.114
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.88635433D+03 0.0000000 0.0000000 41.525 19.756 EM
154.719
2 -0.50647287D+03 379.8814634 0.4285887 38.213 14.975 EM
162.811
3 -0.50470401D+03 1.7688626 0.0034925 37.574 13.144 EM
165.281
4 -0.50442968D+03 0.2743319 0.0005436 37.509 12.229 EM
166.262
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.94595199D+03 0.0000000 0.0000000 41.922 1.507 EM
172.570
2 -0.50655603D+03 439.3959555 0.4645013 39.303 1.975 EM
174.722
3 -0.50600965D+03 0.5463837 0.0010786 38.683 2.645 EM
174.672
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.85812483D+03 0.0000000 0.0000000 11.471 19.918 EM
184.611
2 -0.52025384D+03 337.8709868 0.3937317 19.271 16.755 EM
179.974
3 -0.51248966D+03 7.7641784 0.0149238 27.544 15.290 EM
173.166
4 -0.50721847D+03 5.2711907 0.0102855 33.180 14.122 EM
168.698
5 -0.50508775D+03 2.1307175 0.0042008 35.884 13.122 EM
166.994
6 -0.50451908D+03 0.5686773 0.0011259 36.961 12.360 EM
166.679
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
3 -0.50433653D+03 0.4941550 0.0009789 38.021 10.866 EM
167.114
4 -0.50430578D+03 0.0307476 0.0000610 37.805 10.808 EM
167.387
5 -0.50430346D+03 0.0023226 0.0000046 37.745 10.790 EM
167.465
6 -0.50430328D+03 0.0001851 0.0000004 37.728 10.783 EM
167.488
7 -0.50430326D+03 0.0000154 0.0000000 37.723 10.781 EM
167.496
8 -0.50430326D+03 0.0000015 0.0000000 37.722 10.779 EM
167.499
9 -0.50430326D+03 0.0000002 0.0000000 37.722 10.778 EM
167.500
10 -0.50430326D+03 0.0000001 0.0000000 37.722 10.778 EM
167.500
11 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
12 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
13 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
3 -0.50435435D+03 0.5236664 0.0010372 37.931 11.397 EM
166.672
4 -0.50431280D+03 0.0415567 0.0000824 37.742 11.158 EM
167.100
5 -0.50430646D+03 0.0063314 0.0000126 37.702 11.022 EM
167.276
6 -0.50430460D+03 0.0018632 0.0000037 37.699 10.938 EM
167.362
7 -0.50430385D+03 0.0007495 0.0000015 37.704 10.884 EM
167.411
8 -0.50430352D+03 0.0003277 0.0000006 37.709 10.849 EM
167.442
9 -0.50430338D+03 0.0001463 0.0000003 37.713 10.825 EM
167.462
10 -0.50430331D+03 0.0000658 0.0000001 37.716 10.809 EM
167.475
11 -0.50430328D+03 0.0000297 0.0000001 37.718 10.799 EM
167.483
12 -0.50430327D+03 0.0000134 0.0000000 37.719 10.791 EM
167.489
13 -0.50430326D+03 0.0000061 0.0000000 37.720 10.787 EM
167.493
14 -0.50430326D+03 0.0000027 0.0000000 37.721 10.783 EM
167.496
15 -0.50430326D+03 0.0000012 0.0000000 37.721 10.781 EM
167.497
16 -0.50430326D+03 0.0000006 0.0000000 37.722 10.780 EM
167.499
17 -0.50430326D+03 0.0000003 0.0000000 37.722 10.779 EM
167.499
18 -0.50430326D+03 0.0000001 0.0000000 37.722 10.778 EM
167.500
19 -0.50430326D+03 0.0000001 0.0000000 37.722 10.778 EM
167.500
20 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
21 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
22 -0.50430326D+03 0.0000000 0.0000000 37.722 10.777 EM
167.501
Beginning Time: 22:58:12
Ending Time: 22:58:13
Elapsed Time: 00:00:01
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