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
  	!same as ex7.3 and ex7.4

  montecarlo:
  	names are u1-u4;
  	generate = u1-u4(1);
  	categorical = u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	nobs = 500;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.5.dat;

  analysis:
  	type = mixture;


  model population:

  	%overall%

  	[c#1*0];
  	
  	%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%
  	[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

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                                  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                        9

Loglikelihood

    H0 Value

        Mean                             -1325.213
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -1325.213      -1325.213
           0.980       0.000        -1325.213      -1325.213
           0.950       0.000        -1325.213      -1325.213
           0.900       0.000        -1325.213      -1325.213
           0.800       0.000        -1325.213      -1325.213
           0.700       0.000        -1325.213      -1325.213
           0.500       0.000        -1325.213      -1325.213
           0.300       0.000        -1325.213      -1325.213
           0.200       0.000        -1325.213      -1325.213
           0.100       0.000        -1325.213      -1325.213
           0.050       0.000        -1325.213      -1325.213
           0.020       0.000        -1325.213      -1325.213
           0.010       0.000        -1325.213      -1325.213

Information Criteria

    Akaike (AIC)

        Mean                              2668.425
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2668.425       2668.425
           0.980       0.000         2668.425       2668.425
           0.950       0.000         2668.425       2668.425
           0.900       0.000         2668.425       2668.425
           0.800       0.000         2668.425       2668.425
           0.700       0.000         2668.425       2668.425
           0.500       0.000         2668.425       2668.425
           0.300       0.000         2668.425       2668.425
           0.200       0.000         2668.425       2668.425
           0.100       0.000         2668.425       2668.425
           0.050       0.000         2668.425       2668.425
           0.020       0.000         2668.425       2668.425
           0.010       0.000         2668.425       2668.425

    Bayesian (BIC)

        Mean                              2706.357
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2706.357       2706.357
           0.980       0.000         2706.357       2706.357
           0.950       0.000         2706.357       2706.357
           0.900       0.000         2706.357       2706.357
           0.800       0.000         2706.357       2706.357
           0.700       0.000         2706.357       2706.357
           0.500       0.000         2706.357       2706.357
           0.300       0.000         2706.357       2706.357
           0.200       0.000         2706.357       2706.357
           0.100       0.000         2706.357       2706.357
           0.050       0.000         2706.357       2706.357
           0.020       0.000         2706.357       2706.357
           0.010       0.000         2706.357       2706.357

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

        Mean                              2677.790
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         2677.790       2677.790
           0.980       0.000         2677.790       2677.790
           0.950       0.000         2677.790       2677.790
           0.900       0.000         2677.790       2677.790
           0.800       0.000         2677.790       2677.790
           0.700       0.000         2677.790       2677.790
           0.500       0.000         2677.790       2677.790
           0.300       0.000         2677.790       2677.790
           0.200       0.000         2677.790       2677.790
           0.100       0.000         2677.790       2677.790
           0.050       0.000         2677.790       2677.790
           0.020       0.000         2677.790       2677.790
           0.010       0.000         2677.790       2677.790

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

    Pearson Chi-Square

        Mean                                12.611
        Std Dev                              0.000
        Degrees of freedom                       6
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.872         12.611
           0.980       1.000            1.134         12.611
           0.950       1.000            1.635         12.611
           0.900       1.000            2.204         12.611
           0.800       1.000            3.070         12.611
           0.700       1.000            3.828         12.611
           0.500       1.000            5.348         12.611
           0.300       1.000            7.231         12.611
           0.200       1.000            8.558         12.611
           0.100       1.000           10.645         12.611
           0.050       1.000           12.592         12.611
           0.020       0.000           15.033         12.611
           0.010       0.000           16.812         12.611

    Likelihood Ratio Chi-Square

        Mean                                12.742
        Std Dev                              0.000
        Degrees of freedom                       6
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000            0.872         12.742
           0.980       1.000            1.134         12.742
           0.950       1.000            1.635         12.742
           0.900       1.000            2.204         12.742
           0.800       1.000            3.070         12.742
           0.700       1.000            3.828         12.742
           0.500       1.000            5.348         12.742
           0.300       1.000            7.231         12.742
           0.200       1.000            8.558         12.742
           0.100       1.000           10.645         12.742
           0.050       1.000           12.592         12.742
           0.020       0.000           15.033         12.742
           0.010       0.000           16.812         12.742



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

    Latent
   Classes

       1        255.11204          0.51022
       2        244.88796          0.48978


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

    Latent
   Classes

       1        255.11204          0.51022
       2        244.88796          0.48978


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

Class Counts and Proportions

    Latent
   Classes

       1              272          0.54400
       2              228          0.45600


CLASSIFICATION QUALITY

     Entropy                         0.504


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

           1        2

    1   0.832    0.168
    2   0.126    0.874


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

           1        2

    1   0.888    0.112
    2   0.186    0.814


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

              1        2

    1      2.066    0.000
    2     -1.475    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     1.2208     0.0000     0.2428     0.0487 1.000 1.000
  U2$1                1.000     1.0856     0.0000     0.2730     0.0073 1.000 1.000
  U3$1               -1.000    -0.9059     0.0000     0.1897     0.0089 1.000 1.000
  U4$1               -1.000    -0.5107     0.0000     0.2238     0.2394 0.000 1.000

Latent Class 2

 Thresholds
  U1$1               -1.000    -1.2865     0.0000     0.3444     0.0821 1.000 1.000
  U2$1               -1.000    -1.1190     0.0000     0.2394     0.0142 1.000 1.000
  U3$1                1.000     0.9905     0.0000     0.2597     0.0001 1.000 1.000
  U4$1                1.000     1.0483     0.0000     0.1793     0.0023 1.000 1.000

Categorical Latent Variables

 Means
  C#1                 0.000     0.0409     0.0000     0.2536     0.0017 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.421E-01
       (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             2             3             4


           TAU(U) FOR LATENT CLASS 2
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                    5             6             7             8


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                    9             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
              ________      ________      ________      ________
                1.000         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


     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
              ________      ________      ________      ________
                1.000         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 -0.13308427D+04    0.0000000    0.0000000  EM
              2 -0.13261044D+04    4.7383081    0.0035604  EM
              3 -0.13255717D+04    0.5326802    0.0004017  EM
              4 -0.13253885D+04    0.1831222    0.0001381  EM
              5 -0.13253222D+04    0.0663120    0.0000500  EM
              6 -0.13252942D+04    0.0280563    0.0000212  EM
              7 -0.13252792D+04    0.0149917    0.0000113  EM
              8 -0.13252692D+04    0.0099642    0.0000075  EM
              9 -0.13252616D+04    0.0076148    0.0000057  EM
             10 -0.13252554D+04    0.0062499    0.0000047  EM
             11 -0.13252501D+04    0.0053068    0.0000040  EM
             12 -0.13252455D+04    0.0045809    0.0000035  EM
             13 -0.13252415D+04    0.0039878    0.0000030  EM
             14 -0.13252380D+04    0.0034873    0.0000026  EM
             15 -0.13252349D+04    0.0030574    0.0000023  EM
             16 -0.13252323D+04    0.0026844    0.0000020  EM
             17 -0.13252299D+04    0.0023588    0.0000018  EM
             18 -0.13252278D+04    0.0020738    0.0000016  EM
             19 -0.13252260D+04    0.0018236    0.0000014  EM
             20 -0.13252244D+04    0.0016038    0.0000012  EM
             21 -0.13252230D+04    0.0014106    0.0000011  EM
             22 -0.13252217D+04    0.0012407    0.0000009  EM
             23 -0.13252207D+04    0.0010912    0.0000008  EM
             24 -0.13252197D+04    0.0009598    0.0000007  EM
             25 -0.13252188D+04    0.0008441    0.0000006  EM
             26 -0.13252181D+04    0.0007424    0.0000006  EM
             27 -0.13252175D+04    0.0006529    0.0000005  EM
             28 -0.13252169D+04    0.0005741    0.0000004  EM
             29 -0.13252164D+04    0.0005049    0.0000004  EM
             30 -0.13252159D+04    0.0004439    0.0000003  EM
             31 -0.13252155D+04    0.0003904    0.0000003  EM
             32 -0.13252152D+04    0.0003432    0.0000003  EM
             33 -0.13252149D+04    0.0003018    0.0000002  EM
             34 -0.13252146D+04    0.0002653    0.0000002  EM
             35 -0.13252144D+04    0.0002333    0.0000002  EM
             36 -0.13252142D+04    0.0002051    0.0000002  EM
             37 -0.13252140D+04    0.0001803    0.0000001  EM
             38 -0.13252128D+04    0.0011615    0.0000009  FS
             39 -0.13252127D+04    0.0001294    0.0000001  FS
             40 -0.13252127D+04    0.0000172    0.0000000  FS
             41 -0.13252127D+04    0.0000024    0.0000000  FS
             42 -0.13252127D+04    0.0000003    0.0000000  FS
             43 -0.13252127D+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
    C

  Save file
    ex7.5.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:24:38
        Ending Time:  22:24:39
       Elapsed Time:  00:00:01



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