Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:04 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;
  	algo = int;

  model population:

  	%overall%

  	f by u2-u3@0;
  	f@1; [f@0];
  	
  	%c#1%
  	[u1$1-u4$1*-1];
  	f by u2@1 u3*1;

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

  model:
  	
  	%overall%

  	f by u2-u3@0;
  	f@1; [f@0];
  	
  	%c#1%
  	[u1$1-u4$1*-1];
  	f by u2@1 u3*1;

  	%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                            1
Number of categorical latent variables                           1

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Continuous latent variables
   F

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                            1
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON





MODEL FIT INFORMATION

Number of Free Parameters                       10

Loglikelihood

    H0 Value

        Mean                             -2664.318
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2664.318      -2664.318
           0.980       0.000        -2664.318      -2664.318
           0.950       0.000        -2664.318      -2664.318
           0.900       0.000        -2664.318      -2664.318
           0.800       0.000        -2664.318      -2664.318
           0.700       0.000        -2664.318      -2664.318
           0.500       0.000        -2664.318      -2664.318
           0.300       0.000        -2664.318      -2664.318
           0.200       0.000        -2664.318      -2664.318
           0.100       0.000        -2664.318      -2664.318
           0.050       0.000        -2664.318      -2664.318
           0.020       0.000        -2664.318      -2664.318
           0.010       0.000        -2664.318      -2664.318

Information Criteria

    Akaike (AIC)

        Mean                              5348.635
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5348.635       5348.635
           0.980       0.000         5348.635       5348.635
           0.950       0.000         5348.635       5348.635
           0.900       0.000         5348.635       5348.635
           0.800       0.000         5348.635       5348.635
           0.700       0.000         5348.635       5348.635
           0.500       0.000         5348.635       5348.635
           0.300       0.000         5348.635       5348.635
           0.200       0.000         5348.635       5348.635
           0.100       0.000         5348.635       5348.635
           0.050       0.000         5348.635       5348.635
           0.020       0.000         5348.635       5348.635
           0.010       0.000         5348.635       5348.635

    Bayesian (BIC)

        Mean                              5397.713
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5397.713       5397.713
           0.980       0.000         5397.713       5397.713
           0.950       0.000         5397.713       5397.713
           0.900       0.000         5397.713       5397.713
           0.800       0.000         5397.713       5397.713
           0.700       0.000         5397.713       5397.713
           0.500       0.000         5397.713       5397.713
           0.300       0.000         5397.713       5397.713
           0.200       0.000         5397.713       5397.713
           0.100       0.000         5397.713       5397.713
           0.050       0.000         5397.713       5397.713
           0.020       0.000         5397.713       5397.713
           0.010       0.000         5397.713       5397.713

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

        Mean                              5365.952
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         5365.952       5365.952
           0.980       0.000         5365.952       5365.952
           0.950       0.000         5365.952       5365.952
           0.900       0.000         5365.952       5365.952
           0.800       0.000         5365.952       5365.952
           0.700       0.000         5365.952       5365.952
           0.500       0.000         5365.952       5365.952
           0.300       0.000         5365.952       5365.952
           0.200       0.000         5365.952       5365.952
           0.100       0.000         5365.952       5365.952
           0.050       0.000         5365.952       5365.952
           0.020       0.000         5365.952       5365.952
           0.010       0.000         5365.952       5365.952

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

    Pearson Chi-Square

        Mean                                 2.864
        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          2.864
           0.980       1.000            0.752          2.864
           0.950       1.000            1.145          2.864
           0.900       1.000            1.610          2.864
           0.800       1.000            2.343          2.864
           0.700       0.000            3.000          2.864
           0.500       0.000            4.351          2.864
           0.300       0.000            6.064          2.864
           0.200       0.000            7.289          2.864
           0.100       0.000            9.236          2.864
           0.050       0.000           11.070          2.864
           0.020       0.000           13.388          2.864
           0.010       0.000           15.086          2.864

    Likelihood Ratio Chi-Square

        Mean                                 2.837
        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          2.837
           0.980       1.000            0.752          2.837
           0.950       1.000            1.145          2.837
           0.900       1.000            1.610          2.837
           0.800       1.000            2.343          2.837
           0.700       0.000            3.000          2.837
           0.500       0.000            4.351          2.837
           0.300       0.000            6.064          2.837
           0.200       0.000            7.289          2.837
           0.100       0.000            9.236          2.837
           0.050       0.000           11.070          2.837
           0.020       0.000           13.388          2.837
           0.010       0.000           15.086          2.837



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

    Latent
   Classes

       1        478.79420          0.47879
       2        521.20580          0.52121


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

    Latent
   Classes

       1        478.79686          0.47880
       2        521.20314          0.52120


CLASSIFICATION QUALITY

     Entropy                         0.427


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              440          0.44000
       2              560          0.56000


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

           1        2

    1   0.840    0.160
    2   0.195    0.805


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

           1        2

    1   0.772    0.228
    2   0.135    0.865


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

              1        2

    1      1.221    0.000
    2     -1.859    0.000


MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
Latent Class 1

 F        BY
  U2                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U3                  1.000     1.8900     0.0000     1.2660     0.7922 1.000 0.000

 Means
  F                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Thresholds
  U1$1               -1.000    -0.9518     0.0000     0.1834     0.0023 1.000 1.000
  U2$1               -1.000    -1.1874     0.0000     0.2740     0.0351 1.000 1.000
  U3$1               -1.000    -1.2230     0.0000     0.5351     0.0497 1.000 1.000
  U4$1               -1.000    -0.9827     0.0000     0.2258     0.0003 1.000 1.000

 Variances
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Latent Class 2

 F        BY
  U2                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000
  U3                  0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Means
  F                   0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Thresholds
  U1$1                1.000     0.8002     0.0000     0.1846     0.0399 1.000 1.000
  U2$1                1.000     0.9071     0.0000     0.1799     0.0086 1.000 1.000
  U3$1                1.000     0.7921     0.0000     0.1562     0.0432 1.000 1.000
  U4$1                1.000     1.2114     0.0000     0.2408     0.0447 1.000 1.000

 Variances
  F                   1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000

Categorical Latent Variables

 Means
  C#1                 0.000    -0.0849     0.0000     0.2588     0.0072 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.343E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              F
              ________
 U1                 0
 U2                 0
 U3                 1
 U4                 0


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


           ALPHA
              F
              ________
 1                  0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1                  0             0             0             0


           LAMBDA
              F
              ________
 U1                 0
 U2                 0
 U3                 0
 U4                 0


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


           ALPHA
              F
              ________
 1                  0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


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


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


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


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


           GAMMA(C)
              F
              ________
 C#1                0
 C#2                0


     STARTING VALUES FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             0.000
 U2             1.000
 U3             1.000
 U4             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


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


     STARTING VALUES FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             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


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              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             -1.000        -1.000        -1.000        -1.000


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


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


           GAMMA(C)
              F
              ________
 C#1            0.000
 C#2            0.000


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             0.000
 U2             1.000
 U3             1.000
 U4             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


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              U1            U2            U3            U4
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             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


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


     POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART


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


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


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


           GAMMA(C)
              F
              ________
 C#1            0.000
 C#2            0.000


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.26697133D+04    0.0000000    0.0000000    497.714   502.286    EM
     2 -0.26654265D+04    4.2867587    0.0016057    497.706   502.294    EM
     3 -0.26650724D+04    0.3541407    0.0001329    497.127   502.873    EM
     4 -0.26648997D+04    0.1727292    0.0000648    496.486   503.514    EM
     5 -0.26648048D+04    0.0948432    0.0000356    495.848   504.152    EM
     6 -0.26647463D+04    0.0585387    0.0000220    495.223   504.777    EM
     7 -0.26643525D+04    0.3937843    0.0001478    483.204   516.796    FS
     8 -0.26643184D+04    0.0340882    0.0000128    479.683   520.317    FS
     9 -0.26643177D+04    0.0006718    0.0000003    478.797   521.203    FS


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:  14:04:57
        Ending Time:  14:04:57
       Elapsed Time:  00:00:00



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