Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:04 PM

INPUT INSTRUCTIONS

  TITLE:	
  	this is an example of a LCA with binary
  	latent class indicators and parameter
  	constraints

  	! this model is that of pp. 70-72 in
  	! McCutcheon (2002) in the Hagenaars & McCutcheon (2002)
  	! book Applied Latent Class Analysis (Cambridge Univ Press).

  montecarlo:
  	names are u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	generate = u1-u4(1);
  	categorical = u1-u4;
  	nobs = 1000;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.13.dat;

  ANALYSIS:
  	TYPE = MIXTURE;

  MODEL POPULATION:
  	%OVERALL%
  	[c#1*-1];
  	%c#1%
  	[u1$1*-1];
  	[u2$1*-1];
  	[u3$1*-1];
  	[u4$1*-1];
  	%c#2%
  	[u1$1@-15];
  	[u2$1*1];
  	[u3$1*1];
  	[u4$1*1];

  MODEL:
  	%OVERALL%
  	[c#1*-1];
  	%c#1%
  	[u1$1*-1];
  	[u2$1*-1] (1);
  	[u3$1*-1] (1);
  	[u4$1*-1] (p1);
  	%c#2%
  	[u1$1@-15];
  	! this gives the McCutcheon p. 72 eqn (13)
  	! deterministic restriction P(u1=1 |c=2) = 1
  	[u2$1*1] (2);
  	[u3$1*1] (2);
  	! this gives the McCutcheon p. 70 eqn (11)
  	! parallell indicators hypothesis
  	[u4$1*1] (p2);

  MODEL CONSTRAINT:
  	p2 = - p1;
  	! this constraint gives the McCutcheon
  	! p. 71 eqn (12) equal error rate hypothesis

  OUTPUT:
  	TECH8 tech9;



INPUT READING TERMINATED NORMALLY




this is an example of a LCA with binary
latent class indicators and parameter
constraints

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-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
Link                                                         LOGIT





MODEL FIT INFORMATION

Number of Free Parameters                        5

Loglikelihood

    H0 Value

        Mean                             -2208.165
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2208.165      -2208.165
           0.980       0.000        -2208.165      -2208.165
           0.950       0.000        -2208.165      -2208.165
           0.900       0.000        -2208.165      -2208.165
           0.800       0.000        -2208.165      -2208.165
           0.700       0.000        -2208.165      -2208.165
           0.500       0.000        -2208.165      -2208.165
           0.300       0.000        -2208.165      -2208.165
           0.200       0.000        -2208.165      -2208.165
           0.100       0.000        -2208.165      -2208.165
           0.050       0.000        -2208.165      -2208.165
           0.020       0.000        -2208.165      -2208.165
           0.010       0.000        -2208.165      -2208.165

Information Criteria

    Akaike (AIC)

        Mean                              4426.329
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4426.329       4426.329
           0.980       0.000         4426.329       4426.329
           0.950       0.000         4426.329       4426.329
           0.900       0.000         4426.329       4426.329
           0.800       0.000         4426.329       4426.329
           0.700       0.000         4426.329       4426.329
           0.500       0.000         4426.329       4426.329
           0.300       0.000         4426.329       4426.329
           0.200       0.000         4426.329       4426.329
           0.100       0.000         4426.329       4426.329
           0.050       0.000         4426.329       4426.329
           0.020       0.000         4426.329       4426.329
           0.010       0.000         4426.329       4426.329

    Bayesian (BIC)

        Mean                              4450.868
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4450.868       4450.868
           0.980       0.000         4450.868       4450.868
           0.950       0.000         4450.868       4450.868
           0.900       0.000         4450.868       4450.868
           0.800       0.000         4450.868       4450.868
           0.700       0.000         4450.868       4450.868
           0.500       0.000         4450.868       4450.868
           0.300       0.000         4450.868       4450.868
           0.200       0.000         4450.868       4450.868
           0.100       0.000         4450.868       4450.868
           0.050       0.000         4450.868       4450.868
           0.020       0.000         4450.868       4450.868
           0.010       0.000         4450.868       4450.868

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

        Mean                              4434.988
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4434.988       4434.988
           0.980       0.000         4434.988       4434.988
           0.950       0.000         4434.988       4434.988
           0.900       0.000         4434.988       4434.988
           0.800       0.000         4434.988       4434.988
           0.700       0.000         4434.988       4434.988
           0.500       0.000         4434.988       4434.988
           0.300       0.000         4434.988       4434.988
           0.200       0.000         4434.988       4434.988
           0.100       0.000         4434.988       4434.988
           0.050       0.000         4434.988       4434.988
           0.020       0.000         4434.988       4434.988
           0.010       0.000         4434.988       4434.988

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

    Pearson Chi-Square

        Mean                                18.173
        Std Dev                              0.000
        Degrees of freedom                      10
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            2.558         18.173
           0.980       1.000            3.059         18.173
           0.950       1.000            3.940         18.173
           0.900       1.000            4.865         18.173
           0.800       1.000            6.179         18.173
           0.700       1.000            7.267         18.173
           0.500       1.000            9.342         18.173
           0.300       1.000           11.781         18.173
           0.200       1.000           13.442         18.173
           0.100       1.000           15.987         18.173
           0.050       0.000           18.307         18.173
           0.020       0.000           21.161         18.173
           0.010       0.000           23.209         18.173

    Likelihood Ratio Chi-Square

        Mean                                18.994
        Std Dev                              0.000
        Degrees of freedom                      10
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            2.558         18.994
           0.980       1.000            3.059         18.994
           0.950       1.000            3.940         18.994
           0.900       1.000            4.865         18.994
           0.800       1.000            6.179         18.994
           0.700       1.000            7.267         18.994
           0.500       1.000            9.342         18.994
           0.300       1.000           11.781         18.994
           0.200       1.000           13.442         18.994
           0.100       1.000           15.987         18.994
           0.050       1.000           18.307         18.994
           0.020       0.000           21.161         18.994
           0.010       0.000           23.209         18.994



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

    Latent
   Classes

       1        247.83625          0.24784
       2        752.16375          0.75216


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

    Latent
   Classes

       1        247.83532          0.24784
       2        752.16468          0.75216


CLASSIFICATION QUALITY

     Entropy                         0.636


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              176          0.17600
       2              824          0.82400


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

           1        2

    1   0.912    0.088
    2   0.106    0.894


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

           1        2

    1   0.648    0.352
    2   0.021    0.979


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

              1        2

    1      0.609    0.000
    2     -3.862    0.000


MODEL RESULTS

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

 Thresholds
  U1$1               -1.000    -0.5098     0.0000     0.1750     0.2403 0.000 1.000
  U2$1               -1.000    -1.1236     0.0000     0.1572     0.0153 1.000 1.000
  U3$1               -1.000    -1.1236     0.0000     0.1572     0.0153 1.000 1.000
  U4$1               -1.000    -1.0633     0.0000     0.0988     0.0040 1.000 1.000

Latent Class 2

 Thresholds
  U1$1              -15.000   -15.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2$1                1.000     0.9487     0.0000     0.0777     0.0026 1.000 1.000
  U3$1                1.000     0.9487     0.0000     0.0777     0.0026 1.000 1.000
  U4$1                1.000     1.0633     0.0000     0.0988     0.0040 1.000 1.000

Categorical Latent Variables

 Means
  C#1                -1.000    -1.1102     0.0000     0.1234     0.0121 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.377E-02
       (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 INDICATOR MODEL PART


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


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1                  0             4             4             5


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1                  6             0


     STARTING VALUES FOR LATENT CLASS 1


     STARTING VALUES FOR LATENT CLASS 2


     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            -15.000         1.000         1.000         1.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1             -1.000         0.000


     POPULATION VALUES FOR LATENT CLASS 1


     POPULATION VALUES FOR LATENT CLASS 2


     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            -15.000         1.000         1.000         1.000


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1             -1.000         0.000


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.22130073D+04    0.0000000    0.0000000    274.703   725.297    EM
     2 -0.22089547D+04    4.0525914    0.0018313    267.779   732.221    EM
     3 -0.22085912D+04    0.3635104    0.0001646    263.304   736.696    EM
     4 -0.22084197D+04    0.1714460    0.0000776    259.913   740.087    EM
     5 -0.22083218D+04    0.0979384    0.0000443    257.313   742.687    EM
     6 -0.22082625D+04    0.0592391    0.0000268    255.299   744.701    EM
     7 -0.22082259D+04    0.0366112    0.0000166    253.727   746.273    EM
     8 -0.22082031D+04    0.0228309    0.0000103    252.493   747.507    EM
     9 -0.22081888D+04    0.0142960    0.0000065    251.522   748.478    EM
    10 -0.22081798D+04    0.0089701    0.0000041    250.755   749.245    EM
    11 -0.22081742D+04    0.0056346    0.0000026    250.149   749.851    EM
    12 -0.22081707D+04    0.0035419    0.0000016    249.669   750.331    EM
    13 -0.22081684D+04    0.0022274    0.0000010    249.289   750.711    EM
    14 -0.22081670D+04    0.0014013    0.0000006    248.988   751.012    EM
    15 -0.22081661D+04    0.0008818    0.0000004    248.749   751.251    EM
    16 -0.22081656D+04    0.0005550    0.0000003    248.559   751.441    EM
    17 -0.22081652D+04    0.0003494    0.0000002    248.409   751.591    EM
    18 -0.22081650D+04    0.0002200    0.0000001    248.290   751.710    EM
    19 -0.22081649D+04    0.0001385    0.0000001    248.195   751.805    EM
    20 -0.22081648D+04    0.0000872    0.0000000    248.120   751.880    EM
    21 -0.22081647D+04    0.0000549    0.0000000    248.061   751.939    EM
    22 -0.22081647D+04    0.0000346    0.0000000    248.014   751.986    EM
    23 -0.22081647D+04    0.0000218    0.0000000    247.976   752.024    EM
    24 -0.22081647D+04    0.0000137    0.0000000    247.946   752.054    EM
    25 -0.22081647D+04    0.0000086    0.0000000    247.923   752.077    EM
    26 -0.22081647D+04    0.0000054    0.0000000    247.904   752.096    EM
    27 -0.22081646D+04    0.0000034    0.0000000    247.889   752.111    EM
    28 -0.22081646D+04    0.0000022    0.0000000    247.877   752.123    EM
    29 -0.22081646D+04    0.0000014    0.0000000    247.868   752.132    EM
    30 -0.22081646D+04    0.0000009    0.0000000    247.860   752.140    EM
    31 -0.22081646D+04    0.0000005    0.0000000    247.854   752.146    EM
    32 -0.22081646D+04    0.0000003    0.0000000    247.850   752.150    EM
    33 -0.22081646D+04    0.0000002    0.0000000    247.846   752.154    EM
    34 -0.22081646D+04    0.0000001    0.0000000    247.843   752.157    EM
    35 -0.22081646D+04    0.0000001    0.0000000    247.841   752.159    EM
    36 -0.22081646D+04    0.0000001    0.0000000    247.839   752.161    EM
    37 -0.22081646D+04    0.0000000    0.0000000    247.837   752.163    EM
    38 -0.22081646D+04    0.0000000    0.0000000    247.836   752.164    EM
    39 -0.22081646D+04    0.0000000    0.0000000    247.835   752.165    EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    C

  Save file
    ex7.13.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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