Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix1
DATA: FILE IS bart.dat;
VARIABLE: NAMES ARE u1-u4;
USEV ARE u1-u4;
CATEGORICAL = u1 - u4;
CLASSES = c(2);
ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 100;
! this is a latent class analysis of 4 binary indicators of a
! categorical latent variable with 2 classes
! the default number of E step iterations is reduced from 100
! to 60 because this example converges quickly even with rough
! starting values
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];
! the two lines above refer to the logits of the conditional
! probabilities of u = 1 given latent class 1 and 2, respectively.
! Starting values are required for these parameters.
! Starting values can for example be obtained
! by having lower u probabilities for the first class than for the second
! class. There is no need to provide starting values for the latent class
! probabilities - the default is equal probabilities. As an example of
! giving a starting value with a small probability for class 1 is as
! follows:
!
! [c#1*-2];
!
! The following shows how to set starting values in the logit scale.
! the relationship between logits and probabilities is
!
! probability = 1/(1+exp(-logit))
!
! logit = elog(probability/(1-probability))
!
! which means that
!
! Probability Logit
! 0 -100 (approximately)
! 0.5 0
! 1 +100 (approximately)
OUTPUT:
TECH8;
! tech8 is needed to monitor the convergence of mixture modeling
INPUT READING TERMINATED NORMALLY
mix1
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 142
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)
bart.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.472 67.000
Category 2 0.528 75.000
U2
Category 1 0.514 73.000
Category 2 0.486 69.000
U3
Category 1 0.739 105.000
Category 2 0.261 37.000
U4
Category 1 0.563 80.000
Category 2 0.437 62.000
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:
-331.764 unperturbed 0
-331.764 195873 6
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -331.764
H0 Scaling Correction Factor 1.018
for MLR
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 681.527
Bayesian (BIC) 708.130
Sample-Size Adjusted BIC 679.653
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 9.459
Degrees of Freedom 6
P-Value 0.1494
Likelihood Ratio Chi-Square
Value 8.966
Degrees of Freedom 6
P-Value 0.1755
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 58.70852 0.41344
2 83.29148 0.58656
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 58.70852 0.41344
2 83.29148 0.58656
CLASSIFICATION QUALITY
Entropy 0.754
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 65 0.45775
2 77 0.54225
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.875 0.125
2 0.024 0.976
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 1.333 0.402 3.313 0.001
U2$1 2.613 0.883 2.960 0.003
U3$1 4.004 2.120 1.888 0.059
U4$1 2.898 1.143 2.535 0.011
Latent Class 2
Thresholds
U1$1 -1.117 0.323 -3.455 0.001
U2$1 -1.267 0.402 -3.155 0.002
U3$1 0.275 0.238 1.158 0.247
U4$1 -0.883 0.306 -2.886 0.004
Categorical Latent Variables
Means
C#1 -0.350 0.271 -1.290 0.197
RESULTS IN PROBABILITY SCALE
Latent Class 1
U1
Category 1 0.791 0.066 11.911 0.000
Category 2 0.209 0.066 3.139 0.002
U2
Category 1 0.932 0.056 16.584 0.000
Category 2 0.068 0.056 1.216 0.224
U3
Category 1 0.982 0.037 26.325 0.000
Category 2 0.018 0.037 0.480 0.631
U4
Category 1 0.948 0.057 16.741 0.000
Category 2 0.052 0.057 0.923 0.356
Latent Class 2
U1
Category 1 0.247 0.060 4.105 0.000
Category 2 0.753 0.060 12.543 0.000
U2
Category 1 0.220 0.069 3.191 0.001
Category 2 0.780 0.069 11.332 0.000
U3
Category 1 0.568 0.058 9.748 0.000
Category 2 0.432 0.058 7.402 0.000
U4
Category 1 0.292 0.063 4.617 0.000
Category 2 0.708 0.063 11.169 0.000
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 0.086 0.043 2.025 0.043
U2
Category > 1 0.021 0.019 1.084 0.278
U3
Category > 1 0.024 0.051 0.468 0.639
U4
Category > 1 0.023 0.026 0.875 0.382
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.842E-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 -0.35341784D+03 0.0000000 0.0000000 67.571 74.429 EM
2 -0.33273204D+03 20.6858009 0.0585307 66.296 75.704 EM
3 -0.33232989D+03 0.4021470 0.0012086 65.255 76.745 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48417716D+03 0.0000000 0.0000000 90.980 51.020 EM
2 -0.34687327D+03 137.3038923 0.2835819 88.175 53.825 EM
3 -0.34063962D+03 6.2336522 0.0179710 85.917 56.083 EM
4 -0.33840420D+03 2.2354233 0.0065624 83.463 58.537 EM
5 -0.33645180D+03 1.9523944 0.0057694 80.938 61.062 EM
6 -0.33504185D+03 1.4099537 0.0041907 78.685 63.315 EM
7 -0.33423040D+03 0.8114423 0.0024219 76.797 65.203 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.77768249D+03 0.0000000 0.0000000 46.971 95.029 EM
2 -0.36949672D+03 408.1857690 0.5248746 48.542 93.458 EM
3 -0.35165377D+03 17.8429484 0.0482899 52.522 89.478 EM
4 -0.34077280D+03 10.8809669 0.0309423 55.474 86.526 EM
5 -0.33731967D+03 3.4531338 0.0101332 57.798 84.202 EM
6 -0.33570616D+03 1.6135105 0.0047833 59.878 82.122 EM
7 -0.33481833D+03 0.8878320 0.0026447 61.695 80.305 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.61820111D+03 0.0000000 0.0000000 47.935 94.065 EM
2 -0.37843203D+03 239.7690785 0.3878496 46.882 95.118 EM
3 -0.37601374D+03 2.4182954 0.0063903 46.636 95.364 EM
4 -0.37542767D+03 0.5860713 0.0015586 46.593 95.407 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.48659193D+03 0.0000000 0.0000000 44.898 97.102 EM
2 -0.37742247D+03 109.1694573 0.2243553 44.122 97.878 EM
3 -0.37598331D+03 1.4391617 0.0038131 43.868 98.132 EM
4 -0.37555870D+03 0.4246111 0.0011293 43.774 98.226 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.41231589D+03 0.0000000 0.0000000 45.822 96.178 EM
2 -0.33561386D+03 76.7020372 0.1860274 49.722 92.278 EM
3 -0.33293099D+03 2.6828640 0.0079939 51.046 90.954 EM
4 -0.33258677D+03 0.3442275 0.0010339 51.626 90.374 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.79307525D+03 0.0000000 0.0000000 68.408 73.592 EM
2 -0.33398857D+03 459.0866854 0.5788690 67.718 74.282 EM
3 -0.33273698D+03 1.2515866 0.0037474 66.925 75.075 EM
4 -0.33243624D+03 0.3007386 0.0009038 66.093 75.907 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.52760607D+03 0.0000000 0.0000000 109.495 32.505 EM
2 -0.36030670D+03 167.2993712 0.3170914 107.529 34.471 EM
3 -0.35139501D+03 8.9116866 0.0247336 102.010 39.990 EM
4 -0.34404878D+03 7.3462369 0.0209059 95.968 46.032 EM
5 -0.33924135D+03 4.8074202 0.0139731 91.281 50.719 EM
6 -0.33699025D+03 2.2511054 0.0066357 87.893 54.107 EM
7 -0.33587049D+03 1.1197547 0.0033228 85.335 56.665 EM
8 -0.33522041D+03 0.6500896 0.0019355 83.323 58.677 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.51298960D+03 0.0000000 0.0000000 95.411 46.589 EM
2 -0.34268810D+03 170.3014993 0.3319785 93.883 48.117 EM
3 -0.34021089D+03 2.4772094 0.0072288 91.611 50.389 EM
4 -0.33840223D+03 1.8086548 0.0053163 88.867 53.133 EM
5 -0.33677031D+03 1.6319190 0.0048224 86.145 55.855 EM
6 -0.33563440D+03 1.1359109 0.0033730 83.786 58.214 EM
7 -0.33495725D+03 0.6771488 0.0020175 81.836 60.164 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.65538774D+03 0.0000000 0.0000000 100.101 41.899 EM
2 -0.35243394D+03 302.9537974 0.4622512 95.169 46.831 EM
3 -0.34659260D+03 5.8413457 0.0165743 89.437 52.563 EM
4 -0.34049161D+03 6.1009858 0.0176028 84.429 57.571 EM
5 -0.33642426D+03 4.0673504 0.0119455 80.936 61.064 EM
6 -0.33469993D+03 1.7243285 0.0051255 78.538 63.462 EM
7 -0.33404244D+03 0.6574908 0.0019644 76.742 65.258 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.61777512D+03 0.0000000 0.0000000 126.981 15.019 EM
2 -0.36283884D+03 254.9362853 0.4126684 123.421 18.579 EM
3 -0.35935476D+03 3.4840776 0.0096023 120.617 21.383 EM
4 -0.35742723D+03 1.9275333 0.0053639 117.671 24.329 EM
5 -0.35482527D+03 2.6019530 0.0072797 113.446 28.554 EM
6 -0.35057447D+03 4.2508072 0.0119800 107.466 34.534 EM
7 -0.34500864D+03 5.5658275 0.0158763 100.907 41.093 EM
8 -0.34044954D+03 4.5590949 0.0132144 95.655 46.345 EM
9 -0.33805236D+03 2.3971878 0.0070412 91.960 50.040 EM
10 -0.33683591D+03 1.2164475 0.0035984 89.280 52.720 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
3 -0.33232989D+03 0.4021470 0.0012086 65.255 76.745 EM
4 -0.33216130D+03 0.1685907 0.0005073 64.365 77.635 EM
5 -0.33206162D+03 0.0996882 0.0003001 63.596 78.404 EM
6 -0.33199055D+03 0.0710615 0.0002140 62.931 79.069 EM
7 -0.33193654D+03 0.0540137 0.0001627 62.355 79.645 EM
8 -0.33189488D+03 0.0416624 0.0001255 61.855 80.145 EM
9 -0.33186280D+03 0.0320784 0.0000967 61.423 80.577 EM
10 -0.33183826D+03 0.0245411 0.0000739 61.050 80.950 EM
11 -0.33181961D+03 0.0186462 0.0000562 60.728 81.272 EM
12 -0.33180553D+03 0.0140837 0.0000424 60.449 81.551 EM
13 -0.33179494D+03 0.0105887 0.0000319 60.210 81.790 EM
14 -0.33178700D+03 0.0079344 0.0000239 60.003 81.997 EM
15 -0.33178107D+03 0.0059317 0.0000179 59.825 82.175 EM
16 -0.33177665D+03 0.0044279 0.0000133 59.672 82.328 EM
17 -0.33177334D+03 0.0033023 0.0000100 59.540 82.460 EM
18 -0.33177088D+03 0.0024618 0.0000074 59.426 82.574 EM
19 -0.33176905D+03 0.0018349 0.0000055 59.328 82.672 EM
20 -0.33176768D+03 0.0013678 0.0000041 59.243 82.757 EM
21 -0.33176666D+03 0.0010197 0.0000031 59.171 82.829 EM
22 -0.33176590D+03 0.0007604 0.0000023 59.108 82.892 EM
23 -0.33176533D+03 0.0005673 0.0000017 59.053 82.947 EM
24 -0.33176491D+03 0.0004233 0.0000013 59.007 82.993 EM
25 -0.33176459D+03 0.0003160 0.0000010 58.966 83.034 EM
26 -0.33176436D+03 0.0002359 0.0000007 58.931 83.069 EM
27 -0.33176418D+03 0.0001762 0.0000005 58.901 83.099 EM
28 -0.33176405D+03 0.0001317 0.0000004 58.875 83.125 EM
29 -0.33176395D+03 0.0000984 0.0000003 58.852 83.148 EM
30 -0.33176388D+03 0.0000735 0.0000002 58.833 83.167 EM
31 -0.33176382D+03 0.0000550 0.0000002 58.816 83.184 EM
32 -0.33176378D+03 0.0000411 0.0000001 58.802 83.198 EM
33 -0.33176375D+03 0.0000307 0.0000001 58.789 83.211 EM
34 -0.33176373D+03 0.0000230 0.0000001 58.778 83.222 EM
35 -0.33176371D+03 0.0000172 0.0000001 58.769 83.231 EM
36 -0.33176366D+03 0.0000477 0.0000001 58.719 83.281 FS
37 -0.33176366D+03 0.0000031 0.0000000 58.713 83.287 FS
38 -0.33176366D+03 0.0000003 0.0000000 58.709 83.291 FS
39 -0.33176366D+03 0.0000000 0.0000000 58.709 83.291 FS
40 -0.33176366D+03 0.0000000 0.0000000 58.709 83.291 FS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
4 -0.33243624D+03 0.3007386 0.0009038 66.093 75.907 EM
5 -0.33229059D+03 0.1456529 0.0004381 65.280 76.720 EM
6 -0.33218415D+03 0.1064426 0.0003203 64.513 77.487 EM
7 -0.33209672D+03 0.0874278 0.0002632 63.807 78.193 EM
8 -0.33202424D+03 0.0724758 0.0002182 63.165 78.835 EM
9 -0.33196514D+03 0.0591075 0.0001780 62.591 79.409 EM
10 -0.33191788D+03 0.0472563 0.0001424 62.081 79.919 EM
11 -0.33188077D+03 0.0371104 0.0001118 61.631 80.369 EM
12 -0.33185205D+03 0.0287177 0.0000865 61.238 80.762 EM
13 -0.33183008D+03 0.0219701 0.0000662 60.895 81.105 EM
14 -0.33181342D+03 0.0166642 0.0000502 60.597 81.403 EM
15 -0.33180086D+03 0.0125612 0.0000379 60.339 81.661 EM
16 -0.33179143D+03 0.0094270 0.0000284 60.116 81.884 EM
17 -0.33178438D+03 0.0070539 0.0000213 59.924 82.076 EM
18 -0.33177911D+03 0.0052681 0.0000159 59.757 82.243 EM
19 -0.33177518D+03 0.0039298 0.0000118 59.614 82.386 EM
20 -0.33177225D+03 0.0029296 0.0000088 59.490 82.510 EM
21 -0.33177006D+03 0.0021834 0.0000066 59.383 82.617 EM
22 -0.33176844D+03 0.0016272 0.0000049 59.291 82.709 EM
23 -0.33176722D+03 0.0012129 0.0000037 59.212 82.788 EM
24 -0.33176632D+03 0.0009043 0.0000027 59.143 82.857 EM
25 -0.33176565D+03 0.0006744 0.0000020 59.084 82.916 EM
26 -0.33176514D+03 0.0005032 0.0000015 59.033 82.967 EM
27 -0.33176477D+03 0.0003755 0.0000011 58.989 83.011 EM
28 -0.33176449D+03 0.0002803 0.0000008 58.951 83.049 EM
29 -0.33176428D+03 0.0002093 0.0000006 58.918 83.082 EM
30 -0.33176412D+03 0.0001564 0.0000005 58.890 83.110 EM
31 -0.33176400D+03 0.0001168 0.0000004 58.865 83.135 EM
32 -0.33176392D+03 0.0000873 0.0000003 58.844 83.156 EM
33 -0.33176385D+03 0.0000653 0.0000002 58.826 83.174 EM
34 -0.33176380D+03 0.0000488 0.0000001 58.810 83.190 EM
35 -0.33176377D+03 0.0000365 0.0000001 58.796 83.204 EM
36 -0.33176374D+03 0.0000273 0.0000001 58.784 83.216 EM
37 -0.33176366D+03 0.0000756 0.0000002 58.721 83.279 FS
38 -0.33176366D+03 0.0000050 0.0000000 58.714 83.286 FS
39 -0.33176366D+03 0.0000005 0.0000000 58.710 83.290 FS
40 -0.33176366D+03 0.0000000 0.0000000 58.709 83.291 FS
41 -0.33176366D+03 0.0000000 0.0000000 58.709 83.291 FS
Beginning Time: 22:58:10
Ending Time: 22:58:10
Elapsed Time: 00:00:00
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