Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE:
penn3
illustration of E step iterations getting stuck:
class-equal growth factor mean starting values
2-class no covariates invariant Psi invariant Theta
DATA: FILE IS lsay.dat;
FORMAT is 3f8 f8.4 8f8.2 3f8 2f8.2;
VARIABLE: NAMES ARE cohort id school weight math7 math8 math9 math10
att7 att8 att9 att10 gender mothed homeres;
USEOBS = (gender EQ 1 AND cohort EQ 2);
MISSING = ALL (999);
USEVAR = math7-math10 ;
classes = c(2);
ANALYSIS: TYPE = mixture;
miterations = 10;
MODEL:
%overall%
intercpt BY math7-math10 @1;
slope BY math8@1 math9@2.5 math10@3.5;
[math7-math10@0];
math7-math9*7 math10*13;
intercpt*64.5 slope*1.3;
slope with intercpt*3.1;
! intercpt ON homeres;
! slope ON homeres;
%c#1%
[intercpt*50 slope*2];
! intercpt ON homeres;
! slope ON homeres;
%c#2%
[intercpt*50 slope*2];
OUTPUT: tech8;
*** WARNING
Data set contains cases with missing on all variables.
These cases were not included in the analysis.
Number of cases with missing on all variables: 8
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
penn3
illustration of E step iterations getting stuck:
class-equal growth factor mean starting values
2-class no covariates invariant Psi invariant Theta
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1482
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
MATH7 MATH8 MATH9 MATH10
Continuous latent variables
INTERCPT SLOPE
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 10
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
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
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
Input data file(s)
lsay.dat
Input data format
(3F8 F8.4 8F8.2 3F8 2F8.2)
SUMMARY OF DATA
Number of missing data patterns 13
Number of y missing data patterns 13
Number of u missing data patterns 0
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT FOR Y
Covariance Coverage
MATH7 MATH8 MATH9 MATH10
________ ________ ________ ________
MATH7 0.990
MATH8 0.881 0.890
MATH9 0.790 0.758 0.799
MATH10 0.744 0.708 0.702 0.750
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:
2 perturbed starting value run(s) did not converge.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN INSUFFICIENT
NUMBER OF E STEPS. INCREASE THE NUMBER OF MITERATIONS. ESTIMATES
CANNOT BE TRUSTED.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A CHANGE IN THE
LOGLIKELIHOOD DURING THE LAST E STEP.
AN INSUFFICENT NUMBER OF E STEP ITERATIONS MAY HAVE BEEN USED. INCREASE
THE NUMBER OF MITERATIONS OR INCREASE THE MCONVERGENCE VALUE. ESTIMATES
CANNOT BE TRUSTED.
SLOW CONVERGENCE DUE TO PARAMETER 11.
THE LOGLIKELIHOOD DERIVATIVE FOR THIS PARAMETER IS -0.72658265D-02.
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 1090.52291 0.73585
2 391.47709 0.26415
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 1099.31829 0.74178
2 382.68171 0.25822
CLASSIFICATION QUALITY
Entropy 0.519
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 1182 0.79757
2 300 0.20243
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.873 0.127
2 0.225 0.775
MODEL RESULTS
Estimate
Latent Class 1
INTERCPT BY
MATH7 1.000
MATH8 1.000
MATH9 1.000
MATH10 1.000
SLOPE BY
MATH8 1.000
MATH9 2.500
MATH10 3.500
SLOPE WITH
INTERCPT 0.680
Means
INTERCPT 53.053
SLOPE 3.209
Intercepts
MATH7 0.000
MATH8 0.000
MATH9 0.000
MATH10 0.000
Variances
INTERCPT 68.717
SLOPE 0.036
Residual Variances
MATH7 13.596
MATH8 13.511
MATH9 16.581
MATH10 27.376
Latent Class 2
INTERCPT BY
MATH7 1.000
MATH8 1.000
MATH9 1.000
MATH10 1.000
SLOPE BY
MATH8 1.000
MATH9 2.500
MATH10 3.500
SLOPE WITH
INTERCPT 0.680
Means
INTERCPT 47.820
SLOPE 0.367
Intercepts
MATH7 0.000
MATH8 0.000
MATH9 0.000
MATH10 0.000
Variances
INTERCPT 68.717
SLOPE 0.036
Residual Variances
MATH7 13.596
MATH8 13.511
MATH9 16.581
MATH10 27.376
Categorical Latent Variables
Means
C#1 1.024
MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES
%OVERALL%
intercpt BY math7;
intercpt BY math8;
intercpt BY math9;
intercpt BY math10;
slope BY math8;
slope BY math9;
slope BY math10;
[ c#1*1.024 ];
%C#1%
intercpt BY math7@1;
intercpt BY math8@1;
intercpt BY math9@1;
intercpt BY math10@1;
slope BY math8@1;
slope BY math9@2.500;
slope BY math10@3.500;
slope WITH intercpt*0.680 (8);
[ math7@0 ];
[ math8@0 ];
[ math9@0 ];
[ math10@0 ];
[ intercpt*53.053 ];
[ slope*3.209 ];
math7*13.596 (1);
math8*13.511 (2);
math9*16.581 (3);
math10*27.376 (4);
intercpt*68.717 (7);
slope*0.036 (9);
%C#2%
intercpt BY math7@1;
intercpt BY math8@1;
intercpt BY math9@1;
intercpt BY math10@1;
slope BY math8@1;
slope BY math9@2.500;
slope BY math10@3.500;
slope WITH intercpt*0.680 (8);
[ math7@0 ];
[ math8@0 ];
[ math9@0 ];
[ math10@0 ];
[ intercpt*47.820 ];
[ slope*0.367 ];
math7*13.596 (1);
math8*13.511 (2);
math9*16.581 (3);
math10*27.376 (4);
intercpt*68.717 (7);
slope*0.036 (9);
TECHNICAL 8 OUTPUT
INITIAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.17340157D+05 0.0000000 0.0000000 741.000 741.000 EM
2 -0.16741551D+05 598.6063092 0.0345214 741.000 741.000 EM
3 -0.16741551D+05 0.0000000 0.0000000 741.000 741.000 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.19986322D+05 0.0000000 0.0000000 853.487 628.513 EM
2 -0.16776018D+05 3210.3036850 0.1606250 850.515 631.485 EM
3 -0.16761172D+05 14.8455072 0.0008849 837.375 644.625 EM
4 -0.16754301D+05 6.8718180 0.0004100 825.415 656.585 EM
5 -0.16750031D+05 4.2692256 0.0002548 814.508 667.492 EM
6 -0.16747091D+05 2.9405632 0.0001756 804.408 677.592 EM
7 -0.16744914D+05 2.1773547 0.0001300 794.943 687.057 EM
8 -0.16743203D+05 1.7101850 0.0001021 785.985 696.015 EM
9 -0.16741788D+05 1.4150480 0.0000845 777.435 704.565 EM
10 -0.16740560D+05 1.2283830 0.0000734 769.211 712.789 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.20788160D+05 0.0000000 0.0000000 54.624 1427.376 EM
2 -0.16735312D+05 4052.8476451 0.1949594 55.020 1426.980 EM
3 -0.16729821D+05 5.4916561 0.0003281 61.142 1420.858 EM
4 -0.16727527D+05 2.2941620 0.0001371 68.508 1413.492 EM
5 -0.16725838D+05 1.6884946 0.0001009 76.378 1405.622 EM
6 -0.16724340D+05 1.4977724 0.0000895 84.601 1397.399 EM
7 -0.16722898D+05 1.4426508 0.0000863 93.158 1388.842 EM
8 -0.16721449D+05 1.4486479 0.0000866 102.063 1379.937 EM
9 -0.16719965D+05 1.4845889 0.0000888 111.333 1370.667 EM
10 -0.16718430D+05 1.5341179 0.0000918 120.971 1361.029 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.17993677D+05 0.0000000 0.0000000 44.218 1437.782 EM
2 -0.16745471D+05 1248.2066381 0.0693692 41.564 1440.436 EM
3 -0.16736681D+05 8.7898610 0.0005249 45.338 1436.662 EM
4 -0.16733336D+05 3.3446548 0.0001998 51.125 1430.875 EM
5 -0.16730774D+05 2.5620172 0.0001531 58.043 1423.957 EM
6 -0.16728547D+05 2.2273607 0.0001331 65.645 1416.355 EM
7 -0.16726620D+05 1.9267523 0.0001152 73.660 1408.340 EM
8 -0.16724934D+05 1.6862281 0.0001008 81.971 1400.029 EM
9 -0.16723388D+05 1.5460742 0.0000924 90.560 1391.440 EM
10 -0.16721894D+05 1.4940245 0.0000893 99.453 1382.547 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.24323139D+05 0.0000000 0.0000000 1195.554 286.446 EM
2 -0.16788117D+05 7535.0221319 0.3097882 1183.654 298.346 EM
3 -0.16762665D+05 25.4513611 0.0015160 1175.512 306.488 EM
4 -0.16754162D+05 8.5034585 0.0005073 1169.454 312.546 EM
5 -0.16750152D+05 4.0097234 0.0002393 1164.675 317.325 EM
6 -0.16747896D+05 2.2558179 0.0001347 1160.762 321.238 EM
7 -0.16746481D+05 1.4149540 0.0000845 1157.473 324.527 EM
8 -0.16745525D+05 0.9560670 0.0000571 1154.652 327.348 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.17462870D+05 0.0000000 0.0000000 979.743 502.257 EM
2 -0.16747306D+05 715.5642849 0.0409763 1005.480 476.520 EM
3 -0.16741206D+05 6.0996648 0.0003642 1019.124 462.876 EM
4 -0.16736863D+05 4.3430485 0.0002594 1031.934 450.066 EM
5 -0.16732722D+05 4.1410473 0.0002474 1044.562 437.438 EM
6 -0.16728386D+05 4.3359727 0.0002591 1056.965 425.035 EM
7 -0.16723612D+05 4.7740369 0.0002854 1068.967 413.033 EM
8 -0.16718318D+05 5.2940728 0.0003166 1080.279 401.721 EM
9 -0.16712653D+05 5.6651585 0.0003389 1090.523 391.477 EM
10 -0.16707044D+05 5.6086409 0.0003356 1099.318 382.682 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.29263609D+05 0.0000000 0.0000000 696.208 785.792 EM
2 -0.16751145D+05 ************ 0.4275776 721.472 760.528 EM
3 -0.16747197D+05 3.9479667 0.0002357 739.791 742.209 EM
4 -0.16744714D+05 2.4821808 0.0001482 756.676 725.324 EM
5 -0.16742862D+05 1.8520608 0.0001106 772.737 709.263 EM
6 -0.16741352D+05 1.5106347 0.0000902 788.270 693.730 EM
7 -0.16740009D+05 1.3431728 0.0000802 803.506 678.494 EM
8 -0.16738714D+05 1.2950753 0.0000774 818.633 663.367 EM
9 -0.16737372D+05 1.3413693 0.0000801 833.812 648.188 EM
10 -0.16735899D+05 1.4733716 0.0000880 849.180 632.820 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.30124137D+05 0.0000000 0.0000000 1404.149 77.851 EM
2 -0.16725317D+05 ************ 0.4447868 1392.996 89.004 EM
3 -0.16722822D+05 2.4951016 0.0001492 1385.211 96.789 EM
4 -0.16721245D+05 1.5765544 0.0000943 1376.996 105.004 EM
5 -0.16719728D+05 1.5168363 0.0000907 1368.186 113.814 EM
6 -0.16718185D+05 1.5430211 0.0000923 1358.846 123.154 EM
7 -0.16716595D+05 1.5901852 0.0000951 1349.046 132.954 EM
8 -0.16714957D+05 1.6383882 0.0000980 1338.853 143.147 EM
9 -0.16713280D+05 1.6772362 0.0001003 1328.344 153.656 EM
10 -0.16711580D+05 1.6992626 0.0001017 1317.607 164.393 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.21797470D+05 0.0000000 0.0000000 1212.010 269.990 EM
2 -0.16766220D+05 5031.2499506 0.2308181 1203.743 278.257 EM
3 -0.16748256D+05 17.9643066 0.0010715 1202.609 279.391 EM
4 -0.16743091D+05 5.1644398 0.0003084 1201.986 280.014 EM
5 -0.16740898D+05 2.1937774 0.0001310 1201.529 280.471 EM
6 -0.16739788D+05 1.1096437 0.0000663 1201.184 280.816 EM
7 -0.16739164D+05 0.6238962 0.0000373 1200.923 281.077 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.31735936D+05 0.0000000 0.0000000 1380.626 101.374 EM
2 -0.16727825D+05 ************ 0.4729059 1371.477 110.523 EM
3 -0.16723675D+05 4.1502283 0.0002481 1364.413 117.587 EM
4 -0.16720363D+05 3.3124483 0.0001981 1356.496 125.504 EM
5 -0.16717701D+05 2.6614705 0.0001592 1347.737 134.263 EM
6 -0.16715529D+05 2.1723290 0.0001299 1338.292 143.708 EM
7 -0.16713617D+05 1.9117031 0.0001144 1328.312 153.688 EM
8 -0.16711820D+05 1.7975197 0.0001075 1317.939 164.061 EM
9 -0.16710078D+05 1.7415323 0.0001042 1307.318 174.682 EM
10 -0.16708385D+05 1.6927283 0.0001013 1296.595 185.405 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10
ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE CLASS COUNTS ALGORITHM
1 -0.25974225D+05 0.0000000 0.0000000 984.181 497.819 EM
2 -0.16786376D+05 9187.8487989 0.3537295 943.050 538.950 EM
3 -0.16755925D+05 30.4505402 0.0018140 911.780 570.220 EM
4 -0.16745868D+05 10.0577528 0.0006003 885.661 596.339 EM
5 -0.16740895D+05 4.9722335 0.0002969 862.725 619.275 EM
6 -0.16737806D+05 3.0893385 0.0001845 841.973 640.027 EM
7 -0.16735563D+05 2.2427537 0.0001340 822.842 659.158 EM
8 -0.16733748D+05 1.8158272 0.0001085 804.994 677.006 EM
9 -0.16732166D+05 1.5816946 0.0000945 788.230 693.770 EM
10 -0.16730725D+05 1.4406644 0.0000861 772.431 709.569 EM
FINAL STAGE ITERATIONS
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5
10 -0.16707044D+05 5.6086409 0.0003356 1099.318 382.682 EM
TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9
10 -0.16708385D+05 1.6927283 0.0001013 1296.595 185.405 EM
Beginning Time: 22:58:15
Ending Time: 22:58:16
Elapsed Time: 00:00:01
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