Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:03 PM

INPUT INSTRUCTIONS

  title:
  		this is an example of a LCA with binary
  	latent class indicators using automatic
  	starting values with random starts with a
  	covariate and a direct effect

  montecarlo:
  	names are u1-u4 x;
  	generate = u1-u4(1);
  	categorical = u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	nobs = 500;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.12.dat;

  analysis:
  	type = mixture;


  model population:

  	%overall%

  	[x@0]; x@1;

  	[c#1*0];

  	c#1 on x*1;

  	u4 on x*.5;
  	
  	%c#1%
  	[u1$1*1 u2$1*1 u3$1*-1 u4$1*-1];

  	%c#2%
  	[u1$1*-1 u2$1*-1 u3$1*1 u4$1*1];

  model:

  	%overall%

  	[c#1*0];

  	c#1 on x*1;

  	u4 on x*.5;
  	
  	%c#1%
  	[u1$1*1 u2$1*1 u3$1*-1 u4$1*-1];

  	%c#2%
  	[u1$1*-1 u2$1*-1 u3$1*1 u4$1*1];

  output:
  	tech8 tech9;
  	
  	
  	

  	
  	



INPUT READING TERMINATED NORMALLY




this is an example of a LCA with binary
latent class indicators using automatic
starting values with random starts with a
covariate and a direct effect

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                              3454367

Number of dependent variables                                    4
Number of independent variables                                  1
Number of continuous latent variables                            0
Number of categorical latent variables                           1

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Observed independent variables
   X

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


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              X
              ________
 1             -0.072


           Covariances
              X
              ________
 X              1.016


           Correlations
              X
              ________
 X              1.000




MODEL FIT INFORMATION

Number of Free Parameters                       11

Loglikelihood

    H0 Value

        Mean                             -1255.396
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -1255.396      -1255.396
           0.980       0.000        -1255.396      -1255.396
           0.950       0.000        -1255.396      -1255.396
           0.900       0.000        -1255.396      -1255.396
           0.800       0.000        -1255.396      -1255.396
           0.700       0.000        -1255.396      -1255.396
           0.500       0.000        -1255.396      -1255.396
           0.300       0.000        -1255.396      -1255.396
           0.200       0.000        -1255.396      -1255.396
           0.100       0.000        -1255.396      -1255.396
           0.050       0.000        -1255.396      -1255.396
           0.020       0.000        -1255.396      -1255.396
           0.010       0.000        -1255.396      -1255.396

Information Criteria

    Akaike (AIC)

        Mean                              2532.793
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2532.793       2532.793
           0.980       0.000         2532.793       2532.793
           0.950       0.000         2532.793       2532.793
           0.900       0.000         2532.793       2532.793
           0.800       0.000         2532.793       2532.793
           0.700       0.000         2532.793       2532.793
           0.500       0.000         2532.793       2532.793
           0.300       0.000         2532.793       2532.793
           0.200       0.000         2532.793       2532.793
           0.100       0.000         2532.793       2532.793
           0.050       0.000         2532.793       2532.793
           0.020       0.000         2532.793       2532.793
           0.010       0.000         2532.793       2532.793

    Bayesian (BIC)

        Mean                              2579.153
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2579.153       2579.153
           0.980       0.000         2579.153       2579.153
           0.950       0.000         2579.153       2579.153
           0.900       0.000         2579.153       2579.153
           0.800       0.000         2579.153       2579.153
           0.700       0.000         2579.153       2579.153
           0.500       0.000         2579.153       2579.153
           0.300       0.000         2579.153       2579.153
           0.200       0.000         2579.153       2579.153
           0.100       0.000         2579.153       2579.153
           0.050       0.000         2579.153       2579.153
           0.020       0.000         2579.153       2579.153
           0.010       0.000         2579.153       2579.153

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

        Mean                              2544.239
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2544.239       2544.239
           0.980       0.000         2544.239       2544.239
           0.950       0.000         2544.239       2544.239
           0.900       0.000         2544.239       2544.239
           0.800       0.000         2544.239       2544.239
           0.700       0.000         2544.239       2544.239
           0.500       0.000         2544.239       2544.239
           0.300       0.000         2544.239       2544.239
           0.200       0.000         2544.239       2544.239
           0.100       0.000         2544.239       2544.239
           0.050       0.000         2544.239       2544.239
           0.020       0.000         2544.239       2544.239
           0.010       0.000         2544.239       2544.239



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

    Latent
   Classes

       1        249.27676          0.49855
       2        250.72324          0.50145


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

    Latent
   Classes

       1        249.27676          0.49855
       2        250.72324          0.50145


CLASSIFICATION QUALITY

     Entropy                         0.586


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              248          0.49600
       2              252          0.50400


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

           1        2

    1   0.882    0.118
    2   0.122    0.878


MODEL RESULTS

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

 U4         ON
  X                0.500     0.5786     0.0000     0.1283     0.0062 1.000 1.000

 Thresholds
  U1$1             1.000     1.3370     0.0000     0.2455     0.1136 1.000 1.000
  U2$1             1.000     0.9287     0.0000     0.1974     0.0051 1.000 1.000
  U3$1            -1.000    -0.9464     0.0000     0.2048     0.0029 1.000 1.000
  U4$1            -1.000    -0.6627     0.0000     0.2118     0.1138 1.000 1.000

Latent Class 2

 U4         ON
  X                0.500     0.5786     0.0000     0.1283     0.0062 1.000 1.000

 Thresholds
  U1$1            -1.000    -1.4517     0.0000     0.2912     0.2040 1.000 1.000
  U2$1            -1.000    -1.1716     0.0000     0.2174     0.0294 1.000 1.000
  U3$1             1.000     1.0828     0.0000     0.2006     0.0069 1.000 1.000
  U4$1             1.000     0.9580     0.0000     0.2016     0.0018 1.000 1.000

Categorical Latent Variables

 C#1        ON
  X                1.000     1.0247     0.0000     0.1510     0.0006 1.000 1.000

 Intercepts
  C#1              0.000     0.0667     0.0000     0.2393     0.0045 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.762E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              X
              ________
 1                  0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
 1                  0


           BETA
              X
              ________
 X                  0


           PSI
              X
              ________
 X                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              X
              ________
 1                  0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
 1                  0


           BETA
              X
              ________
 X                  0


           PSI
              X
              ________
 X                  0


     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             3             4


           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)
              X
              ________
 C#1               11
 C#2                0


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART


           LAMBDA(F) FOR LATENT CLASS 1
              U4
              ________
 U1                 0
 U2                 0
 U3                 0
 U4                 0


           ALPHA(F) FOR LATENT CLASS 1
              U4
              ________
 1                  0


           GAMMA(F) FOR LATENT CLASS 1
              X
              ________
 U4                 5


           LAMBDA(F) FOR LATENT CLASS 2
              U4
              ________
 U1                 0
 U2                 0
 U3                 0
 U4                 0


           ALPHA(F) FOR LATENT CLASS 2
              U4
              ________
 1                  0


           GAMMA(F) FOR LATENT CLASS 2
              X
              ________
 U4                 5


     STARTING VALUES FOR LATENT CLASS 1


           NU
              X
              ________
 1              0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
 1              0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              0.500


     STARTING VALUES FOR LATENT CLASS 2


           NU
              X
              ________
 1              0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
 1              0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              0.500


     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)
              X
              ________
 C#1            1.000
 C#2            0.000


     STARTING VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART


           LAMBDA(F) FOR CLASS LATENT CLASS 1
              U4
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             1.000


           ALPHA(F) FOR LATENT CLASS 1
              U4
              ________
 1              0.000


           GAMMA(F) FOR LATENT CLASS 1
              X
              ________
 U4             0.500


           LAMBDA(F) FOR CLASS LATENT CLASS 2
              U4
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             1.000


           ALPHA(F) FOR LATENT CLASS 2
              U4
              ________
 1              0.000


           GAMMA(F) FOR LATENT CLASS 2
              X
              ________
 U4             0.500


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              X
              ________
 1              0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
 1              0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              X
              ________
 1              0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
 1              0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              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)
              X
              ________
 C#1            1.000
 C#2            0.000


     POPULATION VALUES FOR LATENT CLASS INDICATOR GROWTH MODEL PART


           LAMBDA(F) FOR LATENT CLASS 1
              U4
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             1.000


           ALPHA(F) FOR LATENT CLASS 1
              U4
              ________
 1              0.000


           GAMMA(F) FOR LATENT CLASS 1
              X
              ________
 U4             0.500


           LAMBDA(F) FOR LATENT CLASS 2
              U4
              ________
 U1             0.000
 U2             0.000
 U3             0.000
 U4             1.000


           ALPHA(F) FOR LATENT CLASS 2
              U4
              ________
 1              0.000


           GAMMA(F) FOR LATENT CLASS 2
              X
              ________
 U4             0.500


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.12598594D+04    0.0000000    0.0000000    236.864   263.136    EM
     2 -0.12566708D+04    3.1886149    0.0025309    237.897   262.103    EM
     3 -0.12559336D+04    0.7372358    0.0005867    238.861   261.139    EM
     4 -0.12556664D+04    0.2671668    0.0002127    239.803   260.197    EM
     5 -0.12555545D+04    0.1118609    0.0000891    240.698   259.302    EM
     6 -0.12555009D+04    0.0536395    0.0000427    241.532   258.468    EM
     7 -0.12554714D+04    0.0294607    0.0000235    242.298   257.702    EM
     8 -0.12554531D+04    0.0183427    0.0000146    242.997   257.003    EM
     9 -0.12554405D+04    0.0126080    0.0000100    243.631   256.369    EM
    10 -0.12554312D+04    0.0092662    0.0000074    244.204   255.796    EM
    11 -0.12554241D+04    0.0070917    0.0000056    244.721   255.279    EM
    12 -0.12554186D+04    0.0055529    0.0000044    245.187   254.813    EM
    13 -0.12554142D+04    0.0044024    0.0000035    245.605   254.395    EM
    14 -0.12554107D+04    0.0035138    0.0000028    245.981   254.019    EM
    15 -0.12554079D+04    0.0028146    0.0000022    246.319   253.681    EM
    16 -0.12554056D+04    0.0022590    0.0000018    246.622   253.378    EM
    17 -0.12554038D+04    0.0018151    0.0000014    246.895   253.105    EM
    18 -0.12554023D+04    0.0014594    0.0000012    247.139   252.861    EM
    19 -0.12554011D+04    0.0011739    0.0000009    247.358   252.642    EM
    20 -0.12554002D+04    0.0009445    0.0000008    247.555   252.445    EM
    21 -0.12553994D+04    0.0007601    0.0000006    247.731   252.269    EM
    22 -0.12553988D+04    0.0006118    0.0000005    247.890   252.110    EM
    23 -0.12553983D+04    0.0004925    0.0000004    248.032   251.968    EM
    24 -0.12553979D+04    0.0003965    0.0000003    248.160   251.840    EM
    25 -0.12553976D+04    0.0003193    0.0000003    248.274   251.726    EM
    26 -0.12553974D+04    0.0002571    0.0000002    248.377   251.623    EM
    27 -0.12553972D+04    0.0002071    0.0000002    248.469   251.531    EM
    28 -0.12553970D+04    0.0001668    0.0000001    248.552   251.448    EM
    29 -0.12553969D+04    0.0001343    0.0000001    248.626   251.374    EM
    30 -0.12553967D+04    0.0001082    0.0000001    248.693   251.307    EM
    31 -0.12553967D+04    0.0000872    0.0000001    248.752   251.248    EM
    32 -0.12553966D+04    0.0000702    0.0000001    248.806   251.194    EM
    33 -0.12553965D+04    0.0000566    0.0000000    248.854   251.146    EM
    34 -0.12553965D+04    0.0000456    0.0000000    248.898   251.102    EM
    35 -0.12553965D+04    0.0000367    0.0000000    248.936   251.064    EM
    36 -0.12553964D+04    0.0000296    0.0000000    248.971   251.029    EM
    37 -0.12553964D+04    0.0000238    0.0000000    249.003   250.997    EM
    38 -0.12553963D+04    0.0000961    0.0000001    249.246   250.754    FS
    39 -0.12553963D+04    0.0000027    0.0000000    249.269   250.731    FS
    40 -0.12553963D+04    0.0000001    0.0000000    249.276   250.724    FS
    41 -0.12553963D+04    0.0000000    0.0000000    249.277   250.723    FS


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    X
    C

  Save file
    ex7.12.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:03:04
        Ending Time:  22:03:04
       Elapsed Time:  00:00:00



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