Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: mix7
latent class analysis with covariates
DATA: FILE IS full102.dat;
VARIABLE: NAMES ARE y1 y2 y3 y4 y5 u1 u2 u3 u4 u5 x w;
USEV ARE u1 u2 u3 u4 u5 x;
CATEGORICAL = u1 - u5;
CLASSES = c(2);
ANALYSIS: TYPE = MIXTURE;
MODEL:
%OVERALL%
! c#1 BY u1*1 u2*1 u3*0 u4*0 u5*-1;
! c#2 BY u1*0 u2*0 u3*-1 u4*1 u5*1;
[u1$1*-1 u2$1*-1 u3$1*0 u4$1*0 u5$1*1];
! for comments on starting values, see input file
! wbart.inp
c#1 ON x;
%c#2%
[u1$1*0 u2$1*0 u3$1*1 u4$1*-1 u5$1*-1];
! the above statement refers to the multinomial logistic
! regression of c on x. the last c category (#2) cannot
! be referred to because the coresponding coefficients
! are standardized to zero. For information on multinomial
! logistic regression, see, e.g., Agresti's book on
! categorical data analysis.
! a direct effect can easily be specified by adding a
! statement such as u1 on x. Such direct effects can be
! either class-invariant, putting the statement in the
! OVERALL model part, or class-varying, putting the statement
! in the class-specific parts. When direct effects
! are included computations are slower than when
! they are not included.
OUTPUT: tech8;
INPUT READING TERMINATED NORMALLY
mix7
latent class analysis with covariates
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 400
Number of dependent variables 5
Number of independent variables 1
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5
Observed independent variables
X
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 500
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)
full102.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.382 153.000
Category 2 0.618 247.000
U2
Category 1 0.447 179.000
Category 2 0.553 221.000
U3
Category 1 0.610 244.000
Category 2 0.390 156.000
U4
Category 1 0.410 164.000
Category 2 0.590 236.000
U5
Category 1 0.522 209.000
Category 2 0.477 191.000
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:
-1303.585 608496 4
-1303.585 93468 3
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -1303.585
H0 Scaling Correction Factor 1.041
for MLR
Information Criteria
Number of Free Parameters 12
Akaike (AIC) 2631.170
Bayesian (BIC) 2679.068
Sample-Size Adjusted BIC 2640.991
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 32.019
Degrees of Freedom 20
P-Value 0.0431
Likelihood Ratio Chi-Square
Value 34.551
Degrees of Freedom 20
P-Value 0.0226
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 198.22719 0.49557
2 201.77281 0.50443
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 198.22717 0.49557
2 201.77283 0.50443
CLASSIFICATION QUALITY
Entropy 0.573
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 199 0.49750
2 201 0.50250
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.873 0.127
2 0.122 0.878
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
U1$1 -1.060 0.224 -4.733 0.000
U2$1 -0.783 0.208 -3.765 0.000
U3$1 -0.021 0.203 -0.104 0.917
U4$1 0.328 0.172 1.911 0.056
U5$1 1.155 0.261 4.428 0.000
Latent Class 2
Thresholds
U1$1 0.022 0.165 0.133 0.894
U2$1 0.318 0.166 1.923 0.054
U3$1 0.961 0.196 4.899 0.000
U4$1 -1.143 0.238 -4.800 0.000
U5$1 -0.901 0.201 -4.474 0.000
Categorical Latent Variables
C#1 ON
X -2.454 0.738 -3.325 0.001
Intercepts
C#1 -0.048 0.335 -0.143 0.886
RESULTS IN PROBABILITY SCALE
Latent Class 1
U1
Category 1 0.257 0.043 6.012 0.000
Category 2 0.743 0.043 17.353 0.000
U2
Category 1 0.314 0.045 7.007 0.000
Category 2 0.686 0.045 15.329 0.000
U3
Category 1 0.495 0.051 9.751 0.000
Category 2 0.505 0.051 9.960 0.000
U4
Category 1 0.581 0.042 13.916 0.000
Category 2 0.419 0.042 10.024 0.000
U5
Category 1 0.760 0.048 16.002 0.000
Category 2 0.240 0.048 5.044 0.000
Latent Class 2
U1
Category 1 0.505 0.041 12.243 0.000
Category 2 0.495 0.041 11.976 0.000
U2
Category 1 0.579 0.040 14.344 0.000
Category 2 0.421 0.040 10.433 0.000
U3
Category 1 0.723 0.039 18.425 0.000
Category 2 0.277 0.039 7.049 0.000
U4
Category 1 0.242 0.044 5.537 0.000
Category 2 0.758 0.044 17.368 0.000
U5
Category 1 0.289 0.041 6.982 0.000
Category 2 0.711 0.041 17.192 0.000
LATENT CLASS ODDS RATIO RESULTS
Latent Class 1 Compared to Latent Class 2
U1
Category > 1 2.951 0.919 3.212 0.001
U2
Category > 1 3.008 0.885 3.401 0.001
U3
Category > 1 2.670 0.875 3.051 0.002
U4
Category > 1 0.230 0.073 3.160 0.002
U5
Category > 1 0.128 0.043 3.002 0.003
LOGISTIC REGRESSION ODDS RATIO RESULTS
Categorical Latent Variables
C#1 ON
X 0.086
ALTERNATIVE PARAMETERIZATIONS FOR THE CATEGORICAL LATENT VARIABLE REGRESSION
Parameterization using Reference Class 1
C#2 ON
X 2.454 0.738 3.325 0.001
Intercepts
C#2 0.048 0.335 0.143 0.886
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.527E-01
(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 -0.13413569D+04 0.0000000 0.0000000 199.797 200.203 EM
2 -0.13204708D+04 20.8860499 0.0155708 197.952 202.048 EM
3 -0.13125936D+04 7.8772036 0.0059655 196.358 203.642 EM
4 -0.13087129D+04 3.8807209 0.0029565 195.095 204.905 EM
5 -0.13067307D+04 1.9821453 0.0015146 194.178 205.822 EM
6 -0.13056322D+04 1.0984993 0.0008406 193.573 206.427 EM
7 -0.13049737D+04 0.6585332 0.0005044 193.223 206.777 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.16093730D+04 0.0000000 0.0000000 169.670 230.330 EM
2 -0.13593444D+04 250.0285640 0.1553577 203.983 196.017 EM
3 -0.13373799D+04 21.9645439 0.0161582 203.984 196.016 EM
4 -0.13293557D+04 8.0242085 0.0059999 204.817 195.183 EM
5 -0.13234107D+04 5.9449413 0.0044720 205.874 194.126 EM
6 -0.13178307D+04 5.5800358 0.0042164 206.431 193.569 EM
7 -0.13126347D+04 5.1959872 0.0039428 206.274 193.726 EM
8 -0.13086938D+04 3.9409324 0.0030023 205.607 194.393 EM
9 -0.13063272D+04 2.3665689 0.0018083 204.699 195.301 EM
10 -0.13051044D+04 1.2227928 0.0009361 203.732 196.268 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.21331167D+04 0.0000000 0.0000000 228.164 171.836 EM
2 -0.13711248D+04 761.9918660 0.3572200 241.968 158.032 EM
3 -0.13621926D+04 8.9322271 0.0065145 243.115 156.885 EM
4 -0.13594365D+04 2.7560954 0.0020233 243.803 156.197 EM
5 -0.13581984D+04 1.2380784 0.0009107 244.257 155.743 EM
6 -0.13575308D+04 0.6675515 0.0004915 244.573 155.427 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.18959224D+04 0.0000000 0.0000000 214.004 185.996 EM
2 -0.13403624D+04 555.5599623 0.2930289 218.020 181.980 EM
3 -0.13192062D+04 21.1561829 0.0157839 216.135 183.865 EM
4 -0.13084767D+04 10.7295479 0.0081333 214.001 185.999 EM
5 -0.13049707D+04 3.5060082 0.0026795 212.043 187.957 EM
6 -0.13041243D+04 0.8463746 0.0006486 210.299 189.701 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.18175014D+04 0.0000000 0.0000000 197.925 202.075 EM
2 -0.13790036D+04 438.4977615 0.2412641 197.596 202.404 EM
3 -0.13563701D+04 22.6335578 0.0164130 197.697 202.303 EM
4 -0.13415207D+04 14.8493435 0.0109479 197.998 202.002 EM
5 -0.13245786D+04 16.9420773 0.0126290 198.213 201.787 EM
6 -0.13111923D+04 13.3862858 0.0101061 198.160 201.840 EM
7 -0.13055415D+04 5.6508923 0.0043097 197.963 202.037 EM
8 -0.13041324D+04 1.4090574 0.0010793 197.740 202.260 EM
9 -0.13038335D+04 0.2988581 0.0002292 197.546 202.454 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.15649528D+04 0.0000000 0.0000000 39.802 360.198 EM
2 -0.13677300D+04 197.2227116 0.1260247 40.564 359.436 EM
3 -0.13617895D+04 5.9404934 0.0043433 35.146 364.854 EM
4 -0.13594758D+04 2.3137961 0.0016991 31.155 368.845 EM
5 -0.13581232D+04 1.3525033 0.0009949 28.465 371.535 EM
6 -0.13570775D+04 1.0457019 0.0007700 26.798 373.202 EM
7 -0.13559504D+04 1.1271667 0.0008306 26.156 373.844 EM
8 -0.13543608D+04 1.5895576 0.0011723 26.829 373.171 EM
9 -0.13519208D+04 2.4399726 0.0018016 29.297 370.703 EM
10 -0.13485707D+04 3.3501240 0.0024780 33.747 366.253 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.27040111D+04 0.0000000 0.0000000 208.220 191.780 EM
2 -0.13204821D+04 1383.5290377 0.5116580 216.960 183.040 EM
3 -0.13102286D+04 10.2534400 0.0077649 214.043 185.957 EM
4 -0.13072014D+04 3.0272015 0.0023104 211.331 188.669 EM
5 -0.13058282D+04 1.3731849 0.0010505 209.022 190.978 EM
6 -0.13050607D+04 0.7675498 0.0005878 207.084 192.916 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.23602387D+04 0.0000000 0.0000000 181.250 218.750 EM
2 -0.13808043D+04 979.4343812 0.4149726 178.438 221.562 EM
3 -0.13638505D+04 16.9538146 0.0122782 177.273 222.727 EM
4 -0.13590032D+04 4.8473598 0.0035542 176.752 223.248 EM
5 -0.13554269D+04 3.5762515 0.0026315 176.721 223.279 EM
6 -0.13500172D+04 5.4096786 0.0039911 177.413 222.587 EM
7 -0.13403522D+04 9.6650077 0.0071592 179.228 220.772 EM
8 -0.13268289D+04 13.5233302 0.0100894 182.131 217.869 EM
9 -0.13150526D+04 11.7763107 0.0088755 185.348 214.652 EM
10 -0.13088684D+04 6.1841900 0.0047026 188.245 211.755 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.18161362D+04 0.0000000 0.0000000 259.309 140.691 EM
2 -0.13645194D+04 451.6167410 0.2486690 263.083 136.917 EM
3 -0.13399765D+04 24.5429277 0.0179865 260.084 139.916 EM
4 -0.13224254D+04 17.5510853 0.0130981 254.610 145.390 EM
5 -0.13115596D+04 10.8657910 0.0082166 249.457 150.543 EM
6 -0.13075621D+04 3.9975312 0.0030479 245.150 154.850 EM
7 -0.13063337D+04 1.2283742 0.0009394 241.355 158.645 EM
8 -0.13057760D+04 0.5577217 0.0004269 237.867 162.133 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.22596100D+04 0.0000000 0.0000000 222.900 177.100 EM
2 -0.13336437D+04 925.9663327 0.4097903 224.264 175.736 EM
3 -0.13139260D+04 19.7177425 0.0147849 224.378 175.622 EM
4 -0.13086401D+04 5.2858547 0.0040229 224.171 175.829 EM
5 -0.13067963D+04 1.8438071 0.0014089 223.625 176.375 EM
6 -0.13058312D+04 0.9650541 0.0007385 222.743 177.257 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.29622823D+04 0.0000000 0.0000000 190.549 209.451 EM
2 -0.13774618D+04 1584.8204574 0.5349998 188.607 211.393 EM
3 -0.13620630D+04 15.3988772 0.0111792 187.828 212.172 EM
4 -0.13581880D+04 3.8749867 0.0028449 187.623 212.377 EM
5 -0.13555755D+04 2.6124855 0.0019235 187.662 212.338 EM
6 -0.13517447D+04 3.8307627 0.0028259 187.825 212.175 EM
7 -0.13448545D+04 6.8902593 0.0050973 187.934 212.066 EM
8 -0.13343825D+04 10.4719745 0.0077867 187.735 212.265 EM
9 -0.13230683D+04 11.3141785 0.0084790 187.198 212.802 EM
10 -0.13146178D+04 8.4505476 0.0063871 186.615 213.385 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
9 -0.13038335D+04 0.2988581 0.0002292 197.546 202.454 EM
10 -0.13037423D+04 0.0911926 0.0000699 197.400 202.600 EM
11 -0.13036951D+04 0.0472345 0.0000362 197.302 202.698 EM
12 -0.13036640D+04 0.0310912 0.0000238 197.243 202.757 EM
13 -0.13036422D+04 0.0217819 0.0000167 197.217 202.783 EM
14 -0.13036267D+04 0.0155180 0.0000119 197.216 202.784 EM
15 -0.13036156D+04 0.0111375 0.0000085 197.233 202.767 EM
16 -0.13036075D+04 0.0080373 0.0000062 197.264 202.736 EM
17 -0.13036017D+04 0.0058295 0.0000045 197.304 202.696 EM
18 -0.13035975D+04 0.0042492 0.0000033 197.351 202.649 EM
19 -0.13035944D+04 0.0031127 0.0000024 197.401 202.599 EM
20 -0.13035921D+04 0.0022913 0.0000018 197.453 202.547 EM
21 -0.13035904D+04 0.0016950 0.0000013 197.506 202.494 EM
22 -0.13035891D+04 0.0012600 0.0000010 197.558 202.442 EM
23 -0.13035882D+04 0.0009410 0.0000007 197.609 202.391 EM
24 -0.13035875D+04 0.0007061 0.0000005 197.658 202.342 EM
25 -0.13035869D+04 0.0005322 0.0000004 197.704 202.296 EM
26 -0.13035865D+04 0.0004029 0.0000003 197.748 202.252 EM
27 -0.13035862D+04 0.0003063 0.0000002 197.789 202.211 EM
28 -0.13035860D+04 0.0002338 0.0000002 197.828 202.172 EM
29 -0.13035858D+04 0.0001791 0.0000001 197.863 202.137 EM
30 -0.13035857D+04 0.0001377 0.0000001 197.896 202.104 EM
31 -0.13035856D+04 0.0001062 0.0000001 197.927 202.073 EM
32 -0.13035855D+04 0.0000822 0.0000001 197.955 202.045 EM
33 -0.13035854D+04 0.0000638 0.0000000 197.981 202.019 EM
34 -0.13035854D+04 0.0000496 0.0000000 198.004 201.996 EM
35 -0.13035853D+04 0.0000387 0.0000000 198.026 201.974 EM
36 -0.13035853D+04 0.0000303 0.0000000 198.045 201.955 EM
37 -0.13035853D+04 0.0000237 0.0000000 198.063 201.937 EM
38 -0.13035853D+04 0.0000186 0.0000000 198.080 201.920 EM
39 -0.13035852D+04 0.0000565 0.0000000 198.209 201.791 FS
40 -0.13035852D+04 0.0000105 0.0000000 198.200 201.800 FS
41 -0.13035852D+04 0.0000021 0.0000000 198.223 201.777 FS
42 -0.13035852D+04 0.0000004 0.0000000 198.222 201.778 FS
43 -0.13035852D+04 0.0000001 0.0000000 198.226 201.774 FS
44 -0.13035852D+04 0.0000000 0.0000000 198.226 201.774 FS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
6 -0.13041243D+04 0.8463746 0.0006486 210.299 189.701 EM
7 -0.13038964D+04 0.2278697 0.0001747 208.761 191.239 EM
8 -0.13037993D+04 0.0971041 0.0000745 207.412 192.588 EM
9 -0.13037402D+04 0.0590869 0.0000453 206.235 193.765 EM
10 -0.13036992D+04 0.0410508 0.0000315 205.210 194.790 EM
11 -0.13036695D+04 0.0296552 0.0000227 204.319 195.681 EM
12 -0.13036478D+04 0.0216963 0.0000166 203.545 196.455 EM
13 -0.13036319D+04 0.0159606 0.0000122 202.872 197.128 EM
14 -0.13036201D+04 0.0117818 0.0000090 202.288 197.712 EM
15 -0.13036114D+04 0.0087227 0.0000067 201.780 198.220 EM
16 -0.13036049D+04 0.0064768 0.0000050 201.337 198.663 EM
17 -0.13036001D+04 0.0048237 0.0000037 200.952 199.048 EM
18 -0.13035965D+04 0.0036039 0.0000028 200.617 199.383 EM
19 -0.13035938D+04 0.0027015 0.0000021 200.324 199.676 EM
20 -0.13035917D+04 0.0020320 0.0000016 200.069 199.931 EM
21 -0.13035902D+04 0.0015336 0.0000012 199.846 200.154 EM
22 -0.13035890D+04 0.0011616 0.0000009 199.651 200.349 EM
23 -0.13035881D+04 0.0008828 0.0000007 199.480 200.520 EM
24 -0.13035875D+04 0.0006732 0.0000005 199.331 200.669 EM
25 -0.13035870D+04 0.0005151 0.0000004 199.200 200.800 EM
26 -0.13035866D+04 0.0003954 0.0000003 199.085 200.915 EM
27 -0.13035863D+04 0.0003045 0.0000002 198.984 201.016 EM
28 -0.13035860D+04 0.0002351 0.0000002 198.896 201.104 EM
29 -0.13035858D+04 0.0001821 0.0000001 198.818 201.182 EM
30 -0.13035857D+04 0.0001414 0.0000001 198.749 201.251 EM
31 -0.13035856D+04 0.0001101 0.0000001 198.689 201.311 EM
32 -0.13035855D+04 0.0000859 0.0000001 198.636 201.364 EM
33 -0.13035854D+04 0.0000671 0.0000001 198.589 201.411 EM
34 -0.13035854D+04 0.0000526 0.0000000 198.547 201.453 EM
35 -0.13035853D+04 0.0000413 0.0000000 198.511 201.489 EM
36 -0.13035853D+04 0.0000324 0.0000000 198.479 201.521 EM
37 -0.13035853D+04 0.0000255 0.0000000 198.450 201.550 EM
38 -0.13035853D+04 0.0000201 0.0000000 198.425 201.575 EM
39 -0.13035852D+04 0.0000635 0.0000000 198.222 201.778 FS
40 -0.13035852D+04 0.0000102 0.0000000 198.259 201.741 FS
41 -0.13035852D+04 0.0000020 0.0000000 198.227 201.773 FS
42 -0.13035852D+04 0.0000004 0.0000000 198.234 201.766 FS
43 -0.13035852D+04 0.0000001 0.0000000 198.227 201.773 FS
Beginning Time: 22:58:13
Ending Time: 22:58:13
Elapsed Time: 00:00:00
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