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




INPUT READING TERMINATED NORMALLY



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
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:


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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