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

INPUT INSTRUCTIONS

  TITLE: mix4
         stouffer & toby data.
          3 classes - non-identified model
          model h2 in Goodman (1974), p. 222

          Source: Goodman, L. (1974). Exploratory latent structure
          analysis using both identifiable and unidentifiable models.
          Biometrika, 61, 215-231.

  DATA: FILE IS stouf.dat;

  VARIABLE: NAMES ARE u1-u4 x1 x2;
            USEV ARE  u1-u4;
            CATEGORICAL ARE u1-u4;
            CLASSES = c(3);

  ANALYSIS: TYPE=MIXTURE;
    MITERATIONS = 9000;

  MODEL:
          %OVERALL%
  !  c#1 BY u1*2 u2*2 u3*2 u4*2;
  !  c#2 BY u1*1 u2*1 u3*1 u4*1;
  !  c#3 BY u1*0 u2*0 u3*0 u4*0;

    [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];

    %c#3%
    [u1$1*0 u2$1*0 u3$1*0 u4$1*0];

  !        this is the 3-class model labelled H2 on page 222
  !        with these starting values the iterations move towards
  !        goodman's H2'' estimates

  !        for comments on parameter specifications and starting
  !        values, see the file mix1.inp

  OUTPUT:
          TECH1;




INPUT READING TERMINATED NORMALLY



mix4
stouffer & toby data.
3 classes - non-identified model
model h2 in Goodman (1974), p. 222

Source: Goodman, L. (1974). Exploratory latent structure
analysis using both identifiable and unidentifiable models.
Biometrika, 61, 215-231.

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         216

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                                9000
  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)
  stouf.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.208       45.000
      Category 2    0.792      171.000
    U2
      Category 1    0.500      108.000
      Category 2    0.500      108.000
    U3
      Category 1    0.486      105.000
      Category 2    0.514      111.000
    U4
      Category 1    0.690      149.000
      Category 2    0.310       67.000


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:

            -503.301  195873           6
            -503.301  608496           4



     WARNING:  WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE
     NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION
     TO AVOID LOCAL MAXIMA.

     THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE
     TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE
     FIRST-ORDER DERIVATIVE PRODUCT MATRIX.  THIS MAY BE DUE TO THE STARTING
     VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION.  THE
     CONDITION NUMBER IS      -0.125D-15.  PROBLEM INVOLVING PARAMETER 14.


THE MODEL ESTIMATION TERMINATED NORMALLY



TESTS OF MODEL FIT

Loglikelihood

          H0 Value                        -503.301
          H0 Scaling Correction Factor       0.946
            for MLR

Information Criteria

          Number of Free Parameters             14
          Akaike (AIC)                    1034.602
          Bayesian (BIC)                  1081.856
          Sample-Size Adjusted BIC        1037.492
            (n* = (n + 2) / 24)

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

          Pearson Chi-Square

          Value                              0.423
          Degrees of Freedom                     1
          P-Value                           0.5157

          Likelihood Ratio Chi-Square

          Value                              0.387
          Degrees of Freedom                     1
          P-Value                           0.5340



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

    Latent
   Classes

       1         47.08275          0.21798
       2         25.16870          0.11652
       3        143.74856          0.66550


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

    Latent
   Classes

       1         47.08273          0.21798
       2         25.16870          0.11652
       3        143.74856          0.66550


CLASSIFICATION QUALITY

     Entropy                         0.660


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1               42          0.19444
       2               20          0.09259
       3              154          0.71296


Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

           1        2        3

    1   0.916    0.000    0.084
    2   0.000    0.616    0.384
    3   0.056    0.083    0.861


MODEL RESULTS

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

Latent Class 1

 Thresholds
    U1$1              -5.421      8.336     -0.650      0.516
    U2$1              -3.436      3.137     -1.095      0.273
    U3$1              -3.764      4.846     -0.777      0.437
    U4$1              -1.870      1.627     -1.150      0.250

Latent Class 2

 Thresholds
    U1$1               0.796      3.593      0.222      0.825
    U2$1               4.682     19.329      0.242      0.809
    U3$1               1.135      1.303      0.871      0.384
    U4$1               2.770      3.179      0.871      0.384

Latent Class 3

 Thresholds
    U1$1              -1.444      0.445     -3.244      0.001
    U2$1               0.272      0.735      0.370      0.711
    U3$1               0.366      0.450      0.814      0.415
    U4$1               1.572      0.646      2.433      0.015

Categorical Latent Variables

 Means
    C#1               -1.116      0.545     -2.048      0.041
    C#2               -1.742      1.561     -1.116      0.264


RESULTS IN PROBABILITY SCALE

Latent Class 1

 U1
    Category 1         0.004      0.037      0.120      0.904
    Category 2         0.996      0.037     27.237      0.000
 U2
    Category 1         0.031      0.095      0.329      0.742
    Category 2         0.969      0.095     10.218      0.000
 U3
    Category 1         0.023      0.107      0.211      0.833
    Category 2         0.977      0.107      9.105      0.000
 U4
    Category 1         0.133      0.188      0.709      0.478
    Category 2         0.867      0.188      4.604      0.000

Latent Class 2

 U1
    Category 1         0.689      0.770      0.895      0.371
    Category 2         0.311      0.770      0.404      0.686
 U2
    Category 1         0.991      0.176      5.638      0.000
    Category 2         0.009      0.176      0.052      0.958
 U3
    Category 1         0.757      0.240      3.154      0.002
    Category 2         0.243      0.240      1.014      0.311
 U4
    Category 1         0.941      0.176      5.334      0.000
    Category 2         0.059      0.176      0.334      0.738

Latent Class 3

 U1
    Category 1         0.191      0.069      2.777      0.005
    Category 2         0.809      0.069     11.766      0.000
 U2
    Category 1         0.568      0.180      3.147      0.002
    Category 2         0.432      0.180      2.397      0.017
 U3
    Category 1         0.591      0.109      5.433      0.000
    Category 2         0.409      0.109      3.767      0.000
 U4
    Category 1         0.828      0.092      9.001      0.000
    Category 2         0.172      0.092      1.869      0.062


LATENT CLASS ODDS RATIO RESULTS

Latent Class 1 Compared to Latent Class 2

 U1
    Category > 1     501.233   3723.195      0.135      0.893
 U2
    Category > 1    3352.713  68183.250      0.049      0.961
 U3
    Category > 1     134.134    707.378      0.190      0.850
 U4
    Category > 1     103.592    387.069      0.268      0.789

Latent Class 1 Compared to Latent Class 3

 U1
    Category > 1      53.347    451.915      0.118      0.906
 U2
    Category > 1      40.758    126.897      0.321      0.748
 U3
    Category > 1      62.184    287.023      0.217      0.828
 U4
    Category > 1      31.258     44.269      0.706      0.480

Latent Class 2 Compared to Latent Class 3

 U1
    Category > 1       0.106      0.396      0.269      0.788
 U2
    Category > 1       0.012      0.243      0.050      0.960
 U3
    Category > 1       0.464      0.728      0.637      0.524
 U4
    Category > 1       0.302      1.080      0.279      0.780


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix             -0.125E-15
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


     PARAMETER SPECIFICATION FOR LATENT CLASS 3


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


           LAMBDA(U)
              C#1           C#2           C#3
              ________      ________      ________
 U1                 1             2             3
 U2                 4             5             6
 U3                 7             8             9
 U4                10            11            12


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2           C#3
              ________      ________      ________
 1                 13            14             0


     STARTING VALUES FOR LATENT CLASS 1


     STARTING VALUES FOR LATENT CLASS 2


     STARTING VALUES FOR LATENT CLASS 3


     STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART


           LAMBDA(U)
              C#1           C#2           C#3
              ________      ________      ________
 U1             2.000         1.000         0.000
 U2             2.000         1.000         0.000
 U3             2.000         1.000         0.000
 U4             2.000         1.000         0.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2           C#3
              ________      ________      ________
 1              0.000         0.000         0.000


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



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