Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix14
4-class model representing two 2-class latent variables
proposed by Goodman (1974), pages 229-231.
See also Bartholomew (1987), pages 23-25.
Coleman's panel data on student attitudes (n=3398).
Two points in time, 1 and 2. Measures:
Member = self-perceived membership in the leading crowd?
(Yes=1, No=0)
Attitud = does membership involve sometimes going against
principles? (Yes=0, No=1)
DATA: FILE IS coleman.dat;
VARIABLE:
NAMES ARE membr1 attd1 membr2 attd2;
USEV ARE membr1 attd1 membr2 attd2;
CATEGORICAL ARE membr1 attd1 membr2 attd2;
CLASSES = c(4);
ANALYSIS:
TYPE = MIXTURE;
MITERATIONS = 1000;
MODEL:
%OVERALL%
! c#1 BY
! membr1*1 (1)
! attd1*2 (2)
! membr2*3 (3)
! attd2*2 (4);
! c#2 BY
! membr1*1 (1)
! attd1*-1 (6)
! membr2*3 (3)
! attd2*-1 (8);
! c#3 BY
! membr1*-1.5 (5)
! attd1*2 (2)
! membr2*-2 (7)
! attd2*2 (4);
! c#4 BY
! membr1*-1.5 (5)
! attd1*-1 (6)
! membr2*-2 (7)
! attd2*-1 (8);
[membr1$1*-1] (1);
[attd1$1*-2] (2);
[membr2$1*-3] (3);
[attd2$1*-2] (4);
%c#2%
[membr1$1*-1] (1);
[attd1$1*1] (6);
[membr2$1*-3] (3);
[attd2$1*1] (8);
%c#3%
[membr1$1*1.5] (5);
[attd1$1*-2] (2);
[membr2$1*2] (7);
[attd2$1*-2] (4);
%c#4%
[membr1$1*1.5] (5);
[attd1$1*1] (6);
[membr2$1*2] (7);
[attd2$1*1] (8);
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
mix14
4-class model representing two 2-class latent variables
proposed by Goodman (1974), pages 229-231.
See also Bartholomew (1987), pages 23-25.
Coleman's panel data on student attitudes (n=3398).
Two points in time, 1 and 2. Measures:
Member = self-perceived membership in the leading crowd?
(Yes=1, No=0)
Attitud = does membership involve sometimes going against
principles? (Yes=0, No=1)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 3398
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)
MEMBR1 ATTD1 MEMBR2 ATTD2
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 1000
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)
coleman.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
MEMBR1
Category 1 0.631 2145.000
Category 2 0.369 1253.000
ATTD1
Category 1 0.462 1570.000
Category 2 0.538 1828.000
MEMBR2
Category 1 0.590 2006.000
Category 2 0.410 1392.000
ATTD2
Category 1 0.431 1465.000
Category 2 0.569 1933.000
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:
-8494.674 unperturbed 0
-8494.674 93468 3
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 -8494.674
H0 Scaling Correction Factor 1.003
for MLR
Information Criteria
Number of Free Parameters 11
Akaike (AIC) 17011.349
Bayesian (BIC) 17078.789
Sample-Size Adjusted BIC 17043.837
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 1.281
Degrees of Freedom 4
P-Value 0.8646
Likelihood Ratio Chi-Square
Value 1.270
Degrees of Freedom 4
P-Value 0.8665
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 924.41868 0.27205
2 436.40970 0.12843
3 786.63233 0.23150
4 1250.53929 0.36802
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 924.41868 0.27205
2 436.40970 0.12843
3 786.63233 0.23150
4 1250.53929 0.36802
CLASSIFICATION QUALITY
Entropy 0.563
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 1113 0.32755
2 279 0.08211
3 641 0.18864
4 1365 0.40171
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2 3 4
1 0.731 0.174 0.052 0.043
2 0.098 0.728 0.007 0.167
3 0.088 0.005 0.762 0.145
4 0.020 0.026 0.175 0.779
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
MEMBR1$1 -1.122 0.211 -5.311 0.000
ATTD1$1 -1.421 0.243 -5.839 0.000
MEMBR2$1 -2.312 0.527 -4.390 0.000
ATTD2$1 -1.603 0.266 -6.025 0.000
Latent Class 2
Thresholds
MEMBR1$1 -1.122 0.211 -5.311 0.000
ATTD1$1 1.012 0.200 5.058 0.000
MEMBR2$1 -2.312 0.527 -4.390 0.000
ATTD2$1 0.840 0.185 4.532 0.000
Latent Class 3
Thresholds
MEMBR1$1 2.078 0.232 8.966 0.000
ATTD1$1 -1.421 0.243 -5.839 0.000
MEMBR2$1 2.505 0.470 5.330 0.000
ATTD2$1 -1.603 0.266 -6.025 0.000
Latent Class 4
Thresholds
MEMBR1$1 2.078 0.232 8.966 0.000
ATTD1$1 1.012 0.200 5.058 0.000
MEMBR2$1 2.505 0.470 5.330 0.000
ATTD2$1 0.840 0.185 4.532 0.000
Categorical Latent Variables
Means
C#1 -0.302 0.228 -1.325 0.185
C#2 -1.053 0.188 -5.612 0.000
C#3 -0.464 0.249 -1.862 0.063
RESULTS IN PROBABILITY SCALE
Latent Class 1
MEMBR1
Category 1 0.246 0.039 6.279 0.000
Category 2 0.754 0.039 19.273 0.000
ATTD1
Category 1 0.194 0.038 5.099 0.000
Category 2 0.806 0.038 21.126 0.000
MEMBR2
Category 1 0.090 0.043 2.087 0.037
Category 2 0.910 0.043 21.061 0.000
ATTD2
Category 1 0.168 0.037 4.515 0.000
Category 2 0.832 0.037 22.431 0.000
Latent Class 2
MEMBR1
Category 1 0.246 0.039 6.279 0.000
Category 2 0.754 0.039 19.273 0.000
ATTD1
Category 1 0.733 0.039 18.745 0.000
Category 2 0.267 0.039 6.812 0.000
MEMBR2
Category 1 0.090 0.043 2.087 0.037
Category 2 0.910 0.043 21.061 0.000
ATTD2
Category 1 0.698 0.039 17.891 0.000
Category 2 0.302 0.039 7.723 0.000
Latent Class 3
MEMBR1
Category 1 0.889 0.023 38.791 0.000
Category 2 0.111 0.023 4.854 0.000
ATTD1
Category 1 0.194 0.038 5.099 0.000
Category 2 0.806 0.038 21.126 0.000
MEMBR2
Category 1 0.924 0.033 28.174 0.000
Category 2 0.076 0.033 2.302 0.021
ATTD2
Category 1 0.168 0.037 4.515 0.000
Category 2 0.832 0.037 22.431 0.000
Latent Class 4
MEMBR1
Category 1 0.889 0.023 38.791 0.000
Category 2 0.111 0.023 4.854 0.000
ATTD1
Category 1 0.733 0.039 18.745 0.000
Category 2 0.267 0.039 6.812 0.000
MEMBR2
Category 1 0.924 0.033 28.174 0.000
Category 2 0.076 0.033 2.302 0.021
ATTD2
Category 1 0.698 0.039 17.891 0.000
Category 2 0.302 0.039 7.723 0.000
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
MEMBR1
Category > 1 1.000 0.000 999.000 999.000
ATTD1
Category > 1 11.402 2.899 3.932 0.000
MEMBR2
Category > 1 1.000 0.000 999.000 999.000
ATTD2
Category > 1 11.511 3.048 3.777 0.000
Latent Class 1 Compared to Latent Class 3
MEMBR1
Category > 1 24.532 7.188 3.413 0.001
ATTD1
Category > 1 1.000 0.000 999.000 999.000
MEMBR2
Category > 1 123.488 81.062 1.523 0.128
ATTD2
Category > 1 1.000 0.000 999.000 999.000
Latent Class 1 Compared to Latent Class 4
MEMBR1
Category > 1 24.532 7.188 3.413 0.001
ATTD1
Category > 1 11.402 2.899 3.932 0.000
MEMBR2
Category > 1 123.488 81.062 1.523 0.128
ATTD2
Category > 1 11.511 3.048 3.777 0.000
Latent Class 2 Compared to Latent Class 3
MEMBR1
Category > 1 24.532 7.188 3.413 0.001
ATTD1
Category > 1 0.088 0.022 3.932 0.000
MEMBR2
Category > 1 123.488 81.062 1.523 0.128
ATTD2
Category > 1 0.087 0.023 3.777 0.000
Latent Class 2 Compared to Latent Class 4
MEMBR1
Category > 1 24.532 7.188 3.413 0.001
ATTD1
Category > 1 1.000 0.000 999.000 999.000
MEMBR2
Category > 1 123.488 81.062 1.523 0.128
ATTD2
Category > 1 1.000 0.000 999.000 999.000
Latent Class 3 Compared to Latent Class 4
MEMBR1
Category > 1 1.000 0.000 999.000 999.000
ATTD1
Category > 1 11.402 2.899 3.932 0.000
MEMBR2
Category > 1 1.000 0.000 999.000 999.000
ATTD2
Category > 1 11.511 3.048 3.777 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.490E-02
(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 4
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
LAMBDA(U)
C#1 C#2 C#3 C#4
________ ________ ________ ________
MEMBR1 1 1 2 2
ATTD1 3 4 3 4
MEMBR2 5 5 6 6
ATTD2 7 8 7 8
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3 C#4
________ ________ ________ ________
1 9 10 11 0
STARTING VALUES FOR LATENT CLASS 1
STARTING VALUES FOR LATENT CLASS 2
STARTING VALUES FOR LATENT CLASS 3
STARTING VALUES FOR LATENT CLASS 4
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
LAMBDA(U)
C#1 C#2 C#3 C#4
________ ________ ________ ________
MEMBR1 1.000 1.000 -1.500 -1.500
ATTD1 2.000 -1.000 2.000 -1.000
MEMBR2 3.000 3.000 -2.000 -2.000
ATTD2 2.000 -1.000 2.000 -1.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2 C#3 C#4
________ ________ ________ ________
1 0.000 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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