Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:16 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level LCGA for a three-category outcome
  DATA:	FILE IS ex10.11.dat;
  VARIABLE:	NAMES ARE u1-u4 class clus;
  	USEVARIABLES = u1-u4;
  	CATEGORICAL = u1-u4;
  	CLASSES = c(2);
  	CLUSTER = clus;
  ANALYSIS:	TYPE = TWOLEVEL MIXTURE;
  MODEL:
  	%WITHIN%
  	%OVERALL%
  	i s | u1@0 u2@1 u3@2 u4@3;
  	i-s@0;
  	%c#1%
  	[i*1 s*1];
  	%c#2%
  	[i@0 s];
  	%BETWEEN%
  	%OVERALL%
  	c#1*1;
  	[u1$1-u4$1*1] (1);
  	[u1$2-u4$2*1.5] (2);



*** WARNING in MODEL command
  All continuous latent variable covariances involving I on the within level
  have been fixed to 0 because the variance of I is fixed at 0.
   1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



this is an example of a two-level LCGA for a three-category outcome

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

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

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Continuous latent variables
   I           S

Categorical latent variables
   C

Variables with special functions

  Cluster variable      CLUS

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                                 500
  Convergence criteria
    Loglikelihood change                                 0.100D-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
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-02
  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-02
  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
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            1
  Adaptive quadrature                                           ON
Random Starts Specifications
  Number of initial stage random starts                         20
  Number of final stage optimizations                            4
  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
Cholesky                                                        ON

Input data file(s)
  ex10.11.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                        110



UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.608      608.000
      Category 2    0.099       99.000
      Category 3    0.293      293.000
    U2
      Category 1    0.515      515.000
      Category 2    0.090       90.000
      Category 3    0.395      395.000
    U3
      Category 1    0.455      455.000
      Category 2    0.064       64.000
      Category 3    0.481      481.000
    U4
      Category 1    0.425      425.000
      Category 2    0.054       54.000
      Category 3    0.521      521.000


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:

           -3317.328  285380           1
           -3317.328  76974            16
           -3317.329  unperturbed      0
           -3441.891  903420           5



THE BEST LOGLIKELIHOOD VALUE HAS BEEN REPLICATED.  RERUN WITH AT LEAST TWICE THE
RANDOM STARTS TO CHECK THAT THE BEST LOGLIKELIHOOD IS STILL OBTAINED AND REPLICATED.


THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                        7

Loglikelihood

          H0 Value                       -3317.328
          H0 Scaling Correction Factor      0.9810
            for MLR

Information Criteria

          Akaike (AIC)                    6648.657
          Bayesian (BIC)                  6683.011
          Sample-Size Adjusted BIC        6660.779
            (n* = (n + 2) / 24)



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

    Latent
   Classes

       1        527.88727          0.52789
       2        472.11273          0.47211


CLASSIFICATION QUALITY

     Entropy                         0.723


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              529          0.52900
       2              471          0.47100


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

           1        2

    1   0.929    0.071
    2   0.078    0.922


MODEL RESULTS

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

Within Level

Latent Class 1

 I        |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 S        |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 Means
    I                 -0.722      0.120     -5.996      0.000
    S                 -0.133      0.054     -2.453      0.014

 Variances
    I                  0.000      0.000    999.000    999.000
    S                  0.000      0.000    999.000    999.000

Latent Class 2

 I        |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 S        |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 Means
    I                  0.000      0.000    999.000    999.000
    S                  1.037      0.072     14.418      0.000

 Variances
    I                  0.000      0.000    999.000    999.000
    S                  0.000      0.000    999.000    999.000

Between Level

Latent Class 1

 Thresholds
    U1$1               0.083      0.081      1.021      0.307
    U1$2               0.540      0.080      6.725      0.000
    U2$1               0.083      0.081      1.021      0.307
    U2$2               0.540      0.080      6.725      0.000
    U3$1               0.083      0.081      1.021      0.307
    U3$2               0.540      0.080      6.725      0.000
    U4$1               0.083      0.081      1.021      0.307
    U4$2               0.540      0.080      6.725      0.000

Latent Class 2

 Thresholds
    U1$1               0.083      0.081      1.021      0.307
    U1$2               0.540      0.080      6.725      0.000
    U2$1               0.083      0.081      1.021      0.307
    U2$2               0.540      0.080      6.725      0.000
    U3$1               0.083      0.081      1.021      0.307
    U3$2               0.540      0.080      6.725      0.000
    U4$1               0.083      0.081      1.021      0.307
    U4$2               0.540      0.080      6.725      0.000

Categorical Latent Variables

Within Level

 Means
    C#1                0.140      0.156      0.901      0.368

Between Level

 Variances
    C#1                1.027      0.303      3.384      0.001


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.805E-02
       (ratio of smallest to largest eigenvalue)


     Beginning Time:  22:16:56
        Ending Time:  22:17:05
       Elapsed Time:  00:00:09



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