```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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Los Angeles, CA  90066

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Copyright (c) 1998-2010 Muthen & Muthen
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