Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 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
              ________
               -0.072


           Covariances
              X
              ________
 X              1.014


           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 CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES

    Latent
   Classes

       1        249.27676          0.49855
       2        250.72324          0.50145


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

Class Counts and Proportions

    Latent
   Classes

       1              248          0.49600
       2              252          0.50400


CLASSIFICATION QUALITY

     Entropy                         0.586


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


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

           1        2

    1   0.877    0.123
    2   0.117    0.883


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

              1        2

    1      1.964    0.000
    2     -2.019    0.000


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
              ________
                    0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
                    0


           BETA
              X
              ________
 X                  0


           PSI
              X
              ________
 X                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              X
              ________
                    0


           LAMBDA
              X
              ________
 X                  0


           THETA
              X
              ________
 X                  0


           ALPHA
              X
              ________
                    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             2             3             4


           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


           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
              ________
                    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
              ________
                    0


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


     STARTING VALUES FOR LATENT CLASS 1


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              0.500


     STARTING VALUES FOR LATENT CLASS 2


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                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
              ________      ________      ________      ________
                1.000         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


           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
              ________
                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
              ________
                0.000


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


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                0.000


           BETA
              X
              ________
 X              0.000


           PSI
              X
              ________
 X              1.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              X
              ________
                0.000


           LAMBDA
              X
              ________
 X              1.000


           THETA
              X
              ________
 X              0.000


           ALPHA
              X
              ________
                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
              ________      ________      ________      ________
                1.000         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


           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
              ________
                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
              ________
                0.000


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


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.12598594D+04    0.0000000    0.0000000  EM
              2 -0.12566708D+04    3.1886149    0.0025309  EM
              3 -0.12559336D+04    0.7372358    0.0005867  EM
              4 -0.12556664D+04    0.2671668    0.0002127  EM
              5 -0.12555545D+04    0.1118609    0.0000891  EM
              6 -0.12555009D+04    0.0536395    0.0000427  EM
              7 -0.12554714D+04    0.0294607    0.0000235  EM
              8 -0.12554531D+04    0.0183427    0.0000146  EM
              9 -0.12554405D+04    0.0126080    0.0000100  EM
             10 -0.12554312D+04    0.0092662    0.0000074  EM
             11 -0.12554241D+04    0.0070917    0.0000056  EM
             12 -0.12554186D+04    0.0055529    0.0000044  EM
             13 -0.12554142D+04    0.0044024    0.0000035  EM
             14 -0.12554107D+04    0.0035138    0.0000028  EM
             15 -0.12554079D+04    0.0028146    0.0000022  EM
             16 -0.12554056D+04    0.0022590    0.0000018  EM
             17 -0.12554038D+04    0.0018151    0.0000014  EM
             18 -0.12554023D+04    0.0014594    0.0000012  EM
             19 -0.12554011D+04    0.0011739    0.0000009  EM
             20 -0.12554002D+04    0.0009445    0.0000008  EM
             21 -0.12553994D+04    0.0007601    0.0000006  EM
             22 -0.12553988D+04    0.0006118    0.0000005  EM
             23 -0.12553983D+04    0.0004925    0.0000004  EM
             24 -0.12553979D+04    0.0003965    0.0000003  EM
             25 -0.12553976D+04    0.0003193    0.0000003  EM
             26 -0.12553974D+04    0.0002571    0.0000002  EM
             27 -0.12553972D+04    0.0002071    0.0000002  EM
             28 -0.12553970D+04    0.0001668    0.0000001  EM
             29 -0.12553969D+04    0.0001343    0.0000001  EM
             30 -0.12553967D+04    0.0001082    0.0000001  EM
             31 -0.12553967D+04    0.0000872    0.0000001  EM
             32 -0.12553966D+04    0.0000702    0.0000001  EM
             33 -0.12553965D+04    0.0000566    0.0000000  EM
             34 -0.12553965D+04    0.0000456    0.0000000  EM
             35 -0.12553965D+04    0.0000367    0.0000000  EM
             36 -0.12553964D+04    0.0000296    0.0000000  EM
             37 -0.12553964D+04    0.0000238    0.0000000  EM
             38 -0.12553963D+04    0.0000961    0.0000001  FS
             39 -0.12553963D+04    0.0000027    0.0000000  FS
             40 -0.12553963D+04    0.0000001    0.0000000  FS
             41 -0.12553963D+04    0.0000000    0.0000000  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:  22:24:28
        Ending Time:  22:24:28
       Elapsed Time:  00:00:00



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