```Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010  10:58 PM

INPUT INSTRUCTIONS

TITLE: mix2

An example of LCA with insufficient number of iterations

DATA: FILE IS bart.dat;

VARIABLE: NAMES ARE u1-u4;
USEV ARE  u1-u4;
CATEGORICAL = u1 - u4;
CLASSES = c(2);

ANALYSIS: TYPE=MIXTURE;
MITERATIONS = 2;

!        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 2 to illustrate nonconvergence

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

mix2

An example of LCA with insufficient number of iterations

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                                   2
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

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:

Unperturbed starting value run did not converge.

1 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 9.
THE LOGLIKELIHOOD DERIVATIVE FOR THIS PARAMETER IS -0.89765970D-02.

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

Latent
Classes

1         67.57111          0.47585
2         74.42889          0.52415

FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES

Latent
Classes

1         66.29643          0.46688
2         75.70357          0.53312

CLASSIFICATION QUALITY

Entropy                         0.715

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   0.933    0.067
2   0.073    0.927

MODEL RESULTS

Estimate

Latent Class 1

Thresholds
U1\$1               1.249
U2\$1               1.912
U3\$1               3.060
U4\$1               2.136

Latent Class 2

Thresholds
U1\$1              -1.420
U2\$1              -1.451
U3\$1               0.175
U4\$1              -1.031

Categorical Latent Variables

Means
C#1               -0.097

MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES

%OVERALL%

[ c#1*-0.097 ];

%C#1%

[ u1\$1*1.249 ];
[ u2\$1*1.912 ];
[ u3\$1*3.060 ];
[ u4\$1*2.136 ];

%C#2%

[ u1\$1*-1.420 ];
[ u2\$1*-1.451 ];
[ u3\$1*0.175 ];
[ u4\$1*-1.031 ];

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

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

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

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

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

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

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

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

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

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

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

FINAL STAGE ITERATIONS

TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET

2 -0.33273204D+03   20.6858009    0.0585307     66.296    75.704    EM

TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6

2 -0.33398857D+03  459.0866854    0.5788690     67.718    74.282    EM

Beginning Time:  22:58:12
Ending Time:  22:58:12
Elapsed Time:  00:00:00

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Los Angeles, CA  90066

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Fax: (310) 391-8971
Web: www.StatModel.com
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Copyright (c) 1998-2010 Muthen & Muthen
```