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

INPUT INSTRUCTIONS

  TITLE: mix1

  DATA: FILE IS bart.dat;

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

  ANALYSIS: TYPE=MIXTURE;
            MITERATIONS = 100;

  !        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 60 because this example converges quickly even with rough
  !        starting values

  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



mix1

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                                 100
  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:

            -331.764  unperturbed      0
            -331.764  195873           6



THE MODEL ESTIMATION TERMINATED NORMALLY



TESTS OF MODEL FIT

Loglikelihood

          H0 Value                        -331.764
          H0 Scaling Correction Factor       1.018
            for MLR

Information Criteria

          Number of Free Parameters              9
          Akaike (AIC)                     681.527
          Bayesian (BIC)                   708.130
          Sample-Size Adjusted BIC         679.653
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes

          Pearson Chi-Square

          Value                              9.459
          Degrees of Freedom                     6
          P-Value                           0.1494

          Likelihood Ratio Chi-Square

          Value                              8.966
          Degrees of Freedom                     6
          P-Value                           0.1755



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

    Latent
   Classes

       1         58.70852          0.41344
       2         83.29148          0.58656


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

    Latent
   Classes

       1         58.70852          0.41344
       2         83.29148          0.58656


CLASSIFICATION QUALITY

     Entropy                         0.754


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   0.875    0.125
    2   0.024    0.976


MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Latent Class 1

 Thresholds
    U1$1               1.333      0.402      3.313      0.001
    U2$1               2.613      0.883      2.960      0.003
    U3$1               4.004      2.120      1.888      0.059
    U4$1               2.898      1.143      2.535      0.011

Latent Class 2

 Thresholds
    U1$1              -1.117      0.323     -3.455      0.001
    U2$1              -1.267      0.402     -3.155      0.002
    U3$1               0.275      0.238      1.158      0.247
    U4$1              -0.883      0.306     -2.886      0.004

Categorical Latent Variables

 Means
    C#1               -0.350      0.271     -1.290      0.197


RESULTS IN PROBABILITY SCALE

Latent Class 1

 U1
    Category 1         0.791      0.066     11.911      0.000
    Category 2         0.209      0.066      3.139      0.002
 U2
    Category 1         0.932      0.056     16.584      0.000
    Category 2         0.068      0.056      1.216      0.224
 U3
    Category 1         0.982      0.037     26.325      0.000
    Category 2         0.018      0.037      0.480      0.631
 U4
    Category 1         0.948      0.057     16.741      0.000
    Category 2         0.052      0.057      0.923      0.356

Latent Class 2

 U1
    Category 1         0.247      0.060      4.105      0.000
    Category 2         0.753      0.060     12.543      0.000
 U2
    Category 1         0.220      0.069      3.191      0.001
    Category 2         0.780      0.069     11.332      0.000
 U3
    Category 1         0.568      0.058      9.748      0.000
    Category 2         0.432      0.058      7.402      0.000
 U4
    Category 1         0.292      0.063      4.617      0.000
    Category 2         0.708      0.063     11.169      0.000


LATENT CLASS ODDS RATIO RESULTS

Latent Class 1 Compared to Latent Class 2

 U1
    Category > 1       0.086      0.043      2.025      0.043
 U2
    Category > 1       0.021      0.019      1.084      0.278
 U3
    Category > 1       0.024      0.051      0.468      0.639
 U4
    Category > 1       0.023      0.026      0.875      0.382


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.842E-02
       (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 -0.35341784D+03    0.0000000    0.0000000     67.571    74.429    EM
     2 -0.33273204D+03   20.6858009    0.0585307     66.296    75.704    EM
     3 -0.33232989D+03    0.4021470    0.0012086     65.255    76.745    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
     3 -0.34063962D+03    6.2336522    0.0179710     85.917    56.083    EM
     4 -0.33840420D+03    2.2354233    0.0065624     83.463    58.537    EM
     5 -0.33645180D+03    1.9523944    0.0057694     80.938    61.062    EM
     6 -0.33504185D+03    1.4099537    0.0041907     78.685    63.315    EM
     7 -0.33423040D+03    0.8114423    0.0024219     76.797    65.203    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
     3 -0.35165377D+03   17.8429484    0.0482899     52.522    89.478    EM
     4 -0.34077280D+03   10.8809669    0.0309423     55.474    86.526    EM
     5 -0.33731967D+03    3.4531338    0.0101332     57.798    84.202    EM
     6 -0.33570616D+03    1.6135105    0.0047833     59.878    82.122    EM
     7 -0.33481833D+03    0.8878320    0.0026447     61.695    80.305    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
     3 -0.37601374D+03    2.4182954    0.0063903     46.636    95.364    EM
     4 -0.37542767D+03    0.5860713    0.0015586     46.593    95.407    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
     3 -0.37598331D+03    1.4391617    0.0038131     43.868    98.132    EM
     4 -0.37555870D+03    0.4246111    0.0011293     43.774    98.226    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
     3 -0.33293099D+03    2.6828640    0.0079939     51.046    90.954    EM
     4 -0.33258677D+03    0.3442275    0.0010339     51.626    90.374    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
     3 -0.33273698D+03    1.2515866    0.0037474     66.925    75.075    EM
     4 -0.33243624D+03    0.3007386    0.0009038     66.093    75.907    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
     3 -0.35139501D+03    8.9116866    0.0247336    102.010    39.990    EM
     4 -0.34404878D+03    7.3462369    0.0209059     95.968    46.032    EM
     5 -0.33924135D+03    4.8074202    0.0139731     91.281    50.719    EM
     6 -0.33699025D+03    2.2511054    0.0066357     87.893    54.107    EM
     7 -0.33587049D+03    1.1197547    0.0033228     85.335    56.665    EM
     8 -0.33522041D+03    0.6500896    0.0019355     83.323    58.677    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
     3 -0.34021089D+03    2.4772094    0.0072288     91.611    50.389    EM
     4 -0.33840223D+03    1.8086548    0.0053163     88.867    53.133    EM
     5 -0.33677031D+03    1.6319190    0.0048224     86.145    55.855    EM
     6 -0.33563440D+03    1.1359109    0.0033730     83.786    58.214    EM
     7 -0.33495725D+03    0.6771488    0.0020175     81.836    60.164    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
     3 -0.34659260D+03    5.8413457    0.0165743     89.437    52.563    EM
     4 -0.34049161D+03    6.1009858    0.0176028     84.429    57.571    EM
     5 -0.33642426D+03    4.0673504    0.0119455     80.936    61.064    EM
     6 -0.33469993D+03    1.7243285    0.0051255     78.538    63.462    EM
     7 -0.33404244D+03    0.6574908    0.0019644     76.742    65.258    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
     3 -0.35935476D+03    3.4840776    0.0096023    120.617    21.383    EM
     4 -0.35742723D+03    1.9275333    0.0053639    117.671    24.329    EM
     5 -0.35482527D+03    2.6019530    0.0072797    113.446    28.554    EM
     6 -0.35057447D+03    4.2508072    0.0119800    107.466    34.534    EM
     7 -0.34500864D+03    5.5658275    0.0158763    100.907    41.093    EM
     8 -0.34044954D+03    4.5590949    0.0132144     95.655    46.345    EM
     9 -0.33805236D+03    2.3971878    0.0070412     91.960    50.040    EM
    10 -0.33683591D+03    1.2164475    0.0035984     89.280    52.720    EM


  FINAL STAGE ITERATIONS


  TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET


     3 -0.33232989D+03    0.4021470    0.0012086     65.255    76.745    EM
     4 -0.33216130D+03    0.1685907    0.0005073     64.365    77.635    EM
     5 -0.33206162D+03    0.0996882    0.0003001     63.596    78.404    EM
     6 -0.33199055D+03    0.0710615    0.0002140     62.931    79.069    EM
     7 -0.33193654D+03    0.0540137    0.0001627     62.355    79.645    EM
     8 -0.33189488D+03    0.0416624    0.0001255     61.855    80.145    EM
     9 -0.33186280D+03    0.0320784    0.0000967     61.423    80.577    EM
    10 -0.33183826D+03    0.0245411    0.0000739     61.050    80.950    EM
    11 -0.33181961D+03    0.0186462    0.0000562     60.728    81.272    EM
    12 -0.33180553D+03    0.0140837    0.0000424     60.449    81.551    EM
    13 -0.33179494D+03    0.0105887    0.0000319     60.210    81.790    EM
    14 -0.33178700D+03    0.0079344    0.0000239     60.003    81.997    EM
    15 -0.33178107D+03    0.0059317    0.0000179     59.825    82.175    EM
    16 -0.33177665D+03    0.0044279    0.0000133     59.672    82.328    EM
    17 -0.33177334D+03    0.0033023    0.0000100     59.540    82.460    EM
    18 -0.33177088D+03    0.0024618    0.0000074     59.426    82.574    EM
    19 -0.33176905D+03    0.0018349    0.0000055     59.328    82.672    EM
    20 -0.33176768D+03    0.0013678    0.0000041     59.243    82.757    EM
    21 -0.33176666D+03    0.0010197    0.0000031     59.171    82.829    EM
    22 -0.33176590D+03    0.0007604    0.0000023     59.108    82.892    EM
    23 -0.33176533D+03    0.0005673    0.0000017     59.053    82.947    EM
    24 -0.33176491D+03    0.0004233    0.0000013     59.007    82.993    EM
    25 -0.33176459D+03    0.0003160    0.0000010     58.966    83.034    EM
    26 -0.33176436D+03    0.0002359    0.0000007     58.931    83.069    EM
    27 -0.33176418D+03    0.0001762    0.0000005     58.901    83.099    EM
    28 -0.33176405D+03    0.0001317    0.0000004     58.875    83.125    EM
    29 -0.33176395D+03    0.0000984    0.0000003     58.852    83.148    EM
    30 -0.33176388D+03    0.0000735    0.0000002     58.833    83.167    EM
    31 -0.33176382D+03    0.0000550    0.0000002     58.816    83.184    EM
    32 -0.33176378D+03    0.0000411    0.0000001     58.802    83.198    EM
    33 -0.33176375D+03    0.0000307    0.0000001     58.789    83.211    EM
    34 -0.33176373D+03    0.0000230    0.0000001     58.778    83.222    EM
    35 -0.33176371D+03    0.0000172    0.0000001     58.769    83.231    EM
    36 -0.33176366D+03    0.0000477    0.0000001     58.719    83.281    FS
    37 -0.33176366D+03    0.0000031    0.0000000     58.713    83.287    FS
    38 -0.33176366D+03    0.0000003    0.0000000     58.709    83.291    FS
    39 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS
    40 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6


     4 -0.33243624D+03    0.3007386    0.0009038     66.093    75.907    EM
     5 -0.33229059D+03    0.1456529    0.0004381     65.280    76.720    EM
     6 -0.33218415D+03    0.1064426    0.0003203     64.513    77.487    EM
     7 -0.33209672D+03    0.0874278    0.0002632     63.807    78.193    EM
     8 -0.33202424D+03    0.0724758    0.0002182     63.165    78.835    EM
     9 -0.33196514D+03    0.0591075    0.0001780     62.591    79.409    EM
    10 -0.33191788D+03    0.0472563    0.0001424     62.081    79.919    EM
    11 -0.33188077D+03    0.0371104    0.0001118     61.631    80.369    EM
    12 -0.33185205D+03    0.0287177    0.0000865     61.238    80.762    EM
    13 -0.33183008D+03    0.0219701    0.0000662     60.895    81.105    EM
    14 -0.33181342D+03    0.0166642    0.0000502     60.597    81.403    EM
    15 -0.33180086D+03    0.0125612    0.0000379     60.339    81.661    EM
    16 -0.33179143D+03    0.0094270    0.0000284     60.116    81.884    EM
    17 -0.33178438D+03    0.0070539    0.0000213     59.924    82.076    EM
    18 -0.33177911D+03    0.0052681    0.0000159     59.757    82.243    EM
    19 -0.33177518D+03    0.0039298    0.0000118     59.614    82.386    EM
    20 -0.33177225D+03    0.0029296    0.0000088     59.490    82.510    EM
    21 -0.33177006D+03    0.0021834    0.0000066     59.383    82.617    EM
    22 -0.33176844D+03    0.0016272    0.0000049     59.291    82.709    EM
    23 -0.33176722D+03    0.0012129    0.0000037     59.212    82.788    EM
    24 -0.33176632D+03    0.0009043    0.0000027     59.143    82.857    EM
    25 -0.33176565D+03    0.0006744    0.0000020     59.084    82.916    EM
    26 -0.33176514D+03    0.0005032    0.0000015     59.033    82.967    EM
    27 -0.33176477D+03    0.0003755    0.0000011     58.989    83.011    EM
    28 -0.33176449D+03    0.0002803    0.0000008     58.951    83.049    EM
    29 -0.33176428D+03    0.0002093    0.0000006     58.918    83.082    EM
    30 -0.33176412D+03    0.0001564    0.0000005     58.890    83.110    EM
    31 -0.33176400D+03    0.0001168    0.0000004     58.865    83.135    EM
    32 -0.33176392D+03    0.0000873    0.0000003     58.844    83.156    EM
    33 -0.33176385D+03    0.0000653    0.0000002     58.826    83.174    EM
    34 -0.33176380D+03    0.0000488    0.0000001     58.810    83.190    EM
    35 -0.33176377D+03    0.0000365    0.0000001     58.796    83.204    EM
    36 -0.33176374D+03    0.0000273    0.0000001     58.784    83.216    EM
    37 -0.33176366D+03    0.0000756    0.0000002     58.721    83.279    FS
    38 -0.33176366D+03    0.0000050    0.0000000     58.714    83.286    FS
    39 -0.33176366D+03    0.0000005    0.0000000     58.710    83.290    FS
    40 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS
    41 -0.33176366D+03    0.0000000    0.0000000     58.709    83.291    FS


     Beginning Time:  22:58:10
        Ending Time:  22:58:10
       Elapsed Time:  00:00:00



MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA  90066

Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com

Copyright (c) 1998-2010 Muthen & Muthen

Back to table of examples