Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 PM

INPUT INSTRUCTIONS

  title:
  	this is an example of LCA with partial
  	conditional independence

  	! this is the Qu-Tan-Kutner (1996) Biometrics
  	! model

  montecarlo:
  	names are u1-u4;
  	generate = u1-u4(1);
  	categorical = u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	nobs = 1000;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.16.dat;

  analysis:
  	type = mixture;
      parameterization = rescovariances;

  model population:

  	%overall%

  	%c#1%
  	[u1$1-u4$1*-1];
      u2 WITH u3*0.3;

  	%c#2%
  	[u1$1-u4$1*1];
  	

  model:
  	
  	%overall%

  	%c#1%
  	[u1$1-u4$1*-1];
      u2 WITH u3;

  	%c#2%
  	[u1$1-u4$1*1];
  	

  output:
  	tech8 tech9;
  	
  	
  	

  	
  	



INPUT READING TERMINATED NORMALLY




this is an example of LCA with partial
conditional independence

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                              3454367

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                                 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                            0
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON





MODEL FIT INFORMATION

Number of Free Parameters                       10

Loglikelihood

    H0 Value

        Mean                             -2598.123
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2598.123      -2598.123
           0.980       0.000        -2598.123      -2598.123
           0.950       0.000        -2598.123      -2598.123
           0.900       0.000        -2598.123      -2598.123
           0.800       0.000        -2598.123      -2598.123
           0.700       0.000        -2598.123      -2598.123
           0.500       0.000        -2598.123      -2598.123
           0.300       0.000        -2598.123      -2598.123
           0.200       0.000        -2598.123      -2598.123
           0.100       0.000        -2598.123      -2598.123
           0.050       0.000        -2598.123      -2598.123
           0.020       0.000        -2598.123      -2598.123
           0.010       0.000        -2598.123      -2598.123

Information Criteria

    Akaike (AIC)

        Mean                              5216.247
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5216.247       5216.247
           0.980       0.000         5216.247       5216.247
           0.950       0.000         5216.247       5216.247
           0.900       0.000         5216.247       5216.247
           0.800       0.000         5216.247       5216.247
           0.700       0.000         5216.247       5216.247
           0.500       0.000         5216.247       5216.247
           0.300       0.000         5216.247       5216.247
           0.200       0.000         5216.247       5216.247
           0.100       0.000         5216.247       5216.247
           0.050       0.000         5216.247       5216.247
           0.020       0.000         5216.247       5216.247
           0.010       0.000         5216.247       5216.247

    Bayesian (BIC)

        Mean                              5265.325
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5265.325       5265.325
           0.980       0.000         5265.325       5265.325
           0.950       0.000         5265.325       5265.325
           0.900       0.000         5265.325       5265.325
           0.800       0.000         5265.325       5265.325
           0.700       0.000         5265.325       5265.325
           0.500       0.000         5265.325       5265.325
           0.300       0.000         5265.325       5265.325
           0.200       0.000         5265.325       5265.325
           0.100       0.000         5265.325       5265.325
           0.050       0.000         5265.325       5265.325
           0.020       0.000         5265.325       5265.325
           0.010       0.000         5265.325       5265.325

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              5233.564
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5233.564       5233.564
           0.980       0.000         5233.564       5233.564
           0.950       0.000         5233.564       5233.564
           0.900       0.000         5233.564       5233.564
           0.800       0.000         5233.564       5233.564
           0.700       0.000         5233.564       5233.564
           0.500       0.000         5233.564       5233.564
           0.300       0.000         5233.564       5233.564
           0.200       0.000         5233.564       5233.564
           0.100       0.000         5233.564       5233.564
           0.050       0.000         5233.564       5233.564
           0.020       0.000         5233.564       5233.564
           0.010       0.000         5233.564       5233.564

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

    Pearson Chi-Square

        Mean                                11.084
        Std Dev                              0.000
        Degrees of freedom                       5
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.554         11.084
           0.980       1.000            0.752         11.084
           0.950       1.000            1.145         11.084
           0.900       1.000            1.610         11.084
           0.800       1.000            2.343         11.084
           0.700       1.000            3.000         11.084
           0.500       1.000            4.351         11.084
           0.300       1.000            6.064         11.084
           0.200       1.000            7.289         11.084
           0.100       1.000            9.236         11.084
           0.050       1.000           11.070         11.084
           0.020       0.000           13.388         11.084
           0.010       0.000           15.086         11.084

    Likelihood Ratio Chi-Square

        Mean                                10.882
        Std Dev                              0.000
        Degrees of freedom                       5
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.554         10.882
           0.980       1.000            0.752         10.882
           0.950       1.000            1.145         10.882
           0.900       1.000            1.610         10.882
           0.800       1.000            2.343         10.882
           0.700       1.000            3.000         10.882
           0.500       1.000            4.351         10.882
           0.300       1.000            6.064         10.882
           0.200       1.000            7.289         10.882
           0.100       1.000            9.236         10.882
           0.050       0.000           11.070         10.882
           0.020       0.000           13.388         10.882
           0.010       0.000           15.086         10.882



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

    Latent
   Classes

       1        467.70875          0.46771
       2        532.29125          0.53229


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

    Latent
   Classes

       1        467.70874          0.46771
       2        532.29126          0.53229


FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              471          0.47100
       2              529          0.52900


CLASSIFICATION QUALITY

     Entropy                         0.561


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

           1        2

    1   0.866    0.134
    2   0.113    0.887


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

           1        2

    1   0.872    0.128
    2   0.118    0.882


Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)

              1        2

    1      1.922    0.000
    2     -2.009    0.000


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff

Latent Class 1

 U2       WITH
  U3                  0.000     0.5067     0.0000     0.8508     0.2568 1.000 0.000

 Thresholds
  U1$1               -1.000    -1.0602     0.0000     0.1572     0.0036 1.000 1.000
  U2$1               -1.000    -0.9014     0.0000     1.6980     0.0097 1.000 0.000
  U3$1               -1.000    -0.8974     0.0000     1.7042     0.0105 1.000 0.000
  U4$1               -1.000    -1.0163     0.0000     0.1330     0.0003 1.000 1.000

Latent Class 2

 Thresholds
  U1$1                1.000     0.8462     0.0000     0.1376     0.0237 1.000 1.000
  U2$1                1.000     0.8349     0.0000     0.1519     0.0273 1.000 1.000
  U3$1                1.000     0.9351     0.0000     0.1418     0.0042 1.000 1.000
  U4$1                1.000     0.7751     0.0000     0.1462     0.0506 1.000 1.000

Categorical Latent Variables

 Means
  C#1                 0.000    -0.1293     0.0000     0.1530     0.0167 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.230E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             1             0
 U4                 0             0             0             0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                    0             0             0             0


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    2             3             4             5


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    6             7             8             9


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                   10             0


     STARTING VALUES FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000


     STARTING VALUES FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000


     STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
               -1.000        -1.000        -1.000        -1.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                1.000         1.000         1.000         1.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.300         0.000
 U4             0.000         0.000         0.000         0.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
                0.000         0.000         0.000         0.000


           THETA
              U1            U2            U3            U4
              ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.000         0.000
 U4             0.000         0.000         0.000         0.000


     POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART


           TAU(U) FOR LATENT CLASS 1
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
               -1.000        -1.000        -1.000        -1.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                1.000         1.000         1.000         1.000


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.26230473D+04    0.0000000    0.0000000  EM
              2 -0.26003271D+04   22.7201985    0.0086618  EM
              3 -0.25995987D+04    0.7283835    0.0002801  EM
              4 -0.25992899D+04    0.3087793    0.0001188  EM
              5 -0.25991092D+04    0.1807334    0.0000695  EM
              6 -0.25989819D+04    0.1272928    0.0000490  EM
              7 -0.25982628D+04    0.7191166    0.0002767  FS
              8 -0.25981375D+04    0.1253028    0.0000482  EM
              9 -0.25981238D+04    0.0137065    0.0000053  EM
             10 -0.25981235D+04    0.0002893    0.0000001  EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    C

  Save file
    ex7.16.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:24:29
        Ending Time:  22:24:29
       Elapsed Time:  00:00:00



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