Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix4
stouffer & toby data.
3 classes - non-identified model
model h2 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;
USEV ARE u1-u4;
CATEGORICAL ARE u1-u4;
CLASSES = c(3);
ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 9000;
MODEL:
%OVERALL%
! c#1 BY u1*2 u2*2 u3*2 u4*2;
! c#2 BY u1*1 u2*1 u3*1 u4*1;
! c#3 BY u1*0 u2*0 u3*0 u4*0;
[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];
%c#3%
[u1$1*0 u2$1*0 u3$1*0 u4$1*0];
! this is the 3-class model labelled H2 on page 222
! with these starting values the iterations move towards
! goodman's H2'' estimates
! for comments on parameter specifications and starting
! values, see the file mix1.inp
OUTPUT:
TECH1;
INPUT READING TERMINATED NORMALLY
mix4
stouffer & toby data.
3 classes - non-identified model
model h2 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 9000
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:
-503.301 195873 6
-503.301 608496 4
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 STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING
VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE
CONDITION NUMBER IS -0.125D-15. PROBLEM INVOLVING PARAMETER 14.
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -503.301
H0 Scaling Correction Factor 0.946
for MLR
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 1034.602
Bayesian (BIC) 1081.856
Sample-Size Adjusted BIC 1037.492
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.423
Degrees of Freedom 1
P-Value 0.5157
Likelihood Ratio Chi-Square
Value 0.387
Degrees of Freedom 1
P-Value 0.5340
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 47.08275 0.21798
2 25.16870 0.11652
3 143.74856 0.66550
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 47.08273 0.21798
2 25.16870 0.11652
3 143.74856 0.66550
CLASSIFICATION QUALITY
Entropy 0.660
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 0.916 0.000 0.084
2 0.000 0.616 0.384
3 0.056 0.083 0.861
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 -5.421 8.336 -0.650 0.516
U2$1 -3.436 3.137 -1.095 0.273
U3$1 -3.764 4.846 -0.777 0.437
U4$1 -1.870 1.627 -1.150 0.250
Latent Class 2
Thresholds
U1$1 0.796 3.593 0.222 0.825
U2$1 4.682 19.329 0.242 0.809
U3$1 1.135 1.303 0.871 0.384
U4$1 2.770 3.179 0.871 0.384
Latent Class 3
Thresholds
U1$1 -1.444 0.445 -3.244 0.001
U2$1 0.272 0.735 0.370 0.711
U3$1 0.366 0.450 0.814 0.415
U4$1 1.572 0.646 2.433 0.015
Categorical Latent Variables
Means
C#1 -1.116 0.545 -2.048 0.041
C#2 -1.742 1.561 -1.116 0.264
RESULTS IN PROBABILITY SCALE
Latent Class 1
U1
Category 1 0.004 0.037 0.120 0.904
Category 2 0.996 0.037 27.237 0.000
U2
Category 1 0.031 0.095 0.329 0.742
Category 2 0.969 0.095 10.218 0.000
U3
Category 1 0.023 0.107 0.211 0.833
Category 2 0.977 0.107 9.105 0.000
U4
Category 1 0.133 0.188 0.709 0.478
Category 2 0.867 0.188 4.604 0.000
Latent Class 2
U1
Category 1 0.689 0.770 0.895 0.371
Category 2 0.311 0.770 0.404 0.686
U2
Category 1 0.991 0.176 5.638 0.000
Category 2 0.009 0.176 0.052 0.958
U3
Category 1 0.757 0.240 3.154 0.002
Category 2 0.243 0.240 1.014 0.311
U4
Category 1 0.941 0.176 5.334 0.000
Category 2 0.059 0.176 0.334 0.738
Latent Class 3
U1
Category 1 0.191 0.069 2.777 0.005
Category 2 0.809 0.069 11.766 0.000
U2
Category 1 0.568 0.180 3.147 0.002
Category 2 0.432 0.180 2.397 0.017
U3
Category 1 0.591 0.109 5.433 0.000
Category 2 0.409 0.109 3.767 0.000
U4
Category 1 0.828 0.092 9.001 0.000
Category 2 0.172 0.092 1.869 0.062
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 501.233 3723.195 0.135 0.893
U2
Category > 1 3352.713 68183.250 0.049 0.961
U3
Category > 1 134.134 707.378 0.190 0.850
U4
Category > 1 103.592 387.069 0.268 0.789
Latent Class 1 Compared to Latent Class 3
U1
Category > 1 53.347 451.915 0.118 0.906
U2
Category > 1 40.758 126.897 0.321 0.748
U3
Category > 1 62.184 287.023 0.217 0.828
U4
Category > 1 31.258 44.269 0.706 0.480
Latent Class 2 Compared to Latent Class 3
U1
Category > 1 0.106 0.396 0.269 0.788
U2
Category > 1 0.012 0.243 0.050 0.960
U3
Category > 1 0.464 0.728 0.637 0.524
U4
Category > 1 0.302 1.080 0.279 0.780
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix -0.125E-15
(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 1 2 3
U2 4 5 6
U3 7 8 9
U4 10 11 12
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3
________ ________ ________
1 13 14 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 2.000 1.000 0.000
U2 2.000 1.000 0.000
U3 2.000 1.000 0.000
U4 2.000 1.000 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
Beginning Time: 22:58:12
Ending Time: 22:58:12
Elapsed Time: 00:00:00
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