Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  10:24 PM

INPUT INSTRUCTIONS

  title:
  	this is an example of a LCA with three-
  	category latent class indicators using
  	user-specified starting values without
  	random starts

  montecarlo:
  	names are u1-u4;
  	generate = u1-u4(2);
  	categorical = u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	nobs = 5000;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.6.dat;

  analysis:
  	type = mixture;

  model population:

  	%overall%

  	[c#1*0];
  	
  	%c#1%
  	[u1$1*.5 u2$1*.5 u3$1*-.5 u4$1*-.5];
  	[u1$2*1 u2$2*1 u3$2*0 u4$2*0];

  	%c#2%
  	[u1$1*-.5 u2$1*-.5 u3$1*.5 u4$1*.5];
  	[u1$2*0 u2$2*0 u3$2*1 u4$2*1];

  model:

  	%overall%

  	[c#1*0];
  	
  	%c#1%
  	[u1$1*.5 u2$1*.5 u3$1*-.5 u4$1*-.5];
  	[u1$2*1 u2$2*1 u3$2*0 u4$2*0];

  	%c#2%
  	[u1$1*-.5 u2$1*-.5 u3$1*.5 u4$1*.5];
  	[u1$2*0 u2$2*0 u3$2*1 u4$2*1];


  output:
  	tech8 tech9;
  	
  	
  	

  	
  	



INPUT READING TERMINATED NORMALLY




this is an example of a LCA with three-
category latent class indicators using
user-specified starting values without
random starts

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        5000

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                       17

Loglikelihood

    H0 Value

        Mean                            -19214.480
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000       -19214.480     -19214.480
           0.980       0.000       -19214.480     -19214.480
           0.950       0.000       -19214.480     -19214.480
           0.900       0.000       -19214.480     -19214.480
           0.800       0.000       -19214.480     -19214.480
           0.700       0.000       -19214.480     -19214.480
           0.500       0.000       -19214.480     -19214.480
           0.300       0.000       -19214.480     -19214.480
           0.200       0.000       -19214.480     -19214.480
           0.100       0.000       -19214.480     -19214.480
           0.050       0.000       -19214.480     -19214.480
           0.020       0.000       -19214.480     -19214.480
           0.010       0.000       -19214.480     -19214.480

Information Criteria

    Akaike (AIC)

        Mean                             38462.961
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        38462.961      38462.961
           0.980       0.000        38462.961      38462.961
           0.950       0.000        38462.961      38462.961
           0.900       0.000        38462.961      38462.961
           0.800       0.000        38462.961      38462.961
           0.700       0.000        38462.961      38462.961
           0.500       0.000        38462.961      38462.961
           0.300       0.000        38462.961      38462.961
           0.200       0.000        38462.961      38462.961
           0.100       0.000        38462.961      38462.961
           0.050       0.000        38462.961      38462.961
           0.020       0.000        38462.961      38462.961
           0.010       0.000        38462.961      38462.961

    Bayesian (BIC)

        Mean                             38573.753
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        38573.753      38573.753
           0.980       0.000        38573.753      38573.753
           0.950       0.000        38573.753      38573.753
           0.900       0.000        38573.753      38573.753
           0.800       0.000        38573.753      38573.753
           0.700       0.000        38573.753      38573.753
           0.500       0.000        38573.753      38573.753
           0.300       0.000        38573.753      38573.753
           0.200       0.000        38573.753      38573.753
           0.100       0.000        38573.753      38573.753
           0.050       0.000        38573.753      38573.753
           0.020       0.000        38573.753      38573.753
           0.010       0.000        38573.753      38573.753

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

        Mean                             38519.733
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        38519.733      38519.733
           0.980       0.000        38519.733      38519.733
           0.950       0.000        38519.733      38519.733
           0.900       0.000        38519.733      38519.733
           0.800       0.000        38519.733      38519.733
           0.700       0.000        38519.733      38519.733
           0.500       0.000        38519.733      38519.733
           0.300       0.000        38519.733      38519.733
           0.200       0.000        38519.733      38519.733
           0.100       0.000        38519.733      38519.733
           0.050       0.000        38519.733      38519.733
           0.020       0.000        38519.733      38519.733
           0.010       0.000        38519.733      38519.733

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

    Pearson Chi-Square

        Mean                                65.388
        Std Dev                              0.000
        Degrees of freedom                      63
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           39.855         65.388
           0.980       1.000           42.143         65.388
           0.950       1.000           45.741         65.388
           0.900       1.000           49.111         65.388
           0.800       1.000           53.412         65.388
           0.700       1.000           56.666         65.388
           0.500       1.000           62.335         65.388
           0.300       0.000           68.369         65.388
           0.200       0.000           72.201         65.388
           0.100       0.000           77.745         65.388
           0.050       0.000           82.529         65.388
           0.020       0.000           88.137         65.388
           0.010       0.000           92.010         65.388

    Likelihood Ratio Chi-Square

        Mean                                62.447
        Std Dev                              0.000
        Degrees of freedom                      63
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       1.000           39.855         62.447
           0.980       1.000           42.143         62.447
           0.950       1.000           45.741         62.447
           0.900       1.000           49.111         62.447
           0.800       1.000           53.412         62.447
           0.700       1.000           56.666         62.447
           0.500       1.000           62.335         62.447
           0.300       0.000           68.369         62.447
           0.200       0.000           72.201         62.447
           0.100       0.000           77.745         62.447
           0.050       0.000           82.529         62.447
           0.020       0.000           88.137         62.447
           0.010       0.000           92.010         62.447



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

    Latent
   Classes

       1       2072.13560          0.41443
       2       2927.86440          0.58557


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

    Latent
   Classes

       1       2072.13560          0.41443
       2       2927.86440          0.58557


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

Class Counts and Proportions

    Latent
   Classes

       1             1889          0.37780
       2             3111          0.62220


CLASSIFICATION QUALITY

     Entropy                         0.205


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

           1        2

    1   0.680    0.320
    2   0.253    0.747


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

           1        2

    1   0.620    0.380
    2   0.206    0.794


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

              1        2

    1      0.489    0.000
    2     -1.346    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                0.500     0.6155     0.0000     0.1922     0.0133 1.000 1.000
  U1$2                1.000     1.1468     0.0000     0.2238     0.0215 1.000 1.000
  U2$1                0.500     0.6035     0.0000     0.1786     0.0107 1.000 1.000
  U2$2                1.000     1.1436     0.0000     0.2142     0.0206 1.000 1.000
  U3$1               -0.500    -0.7133     0.0000     0.1820     0.0455 1.000 1.000
  U3$2                0.000    -0.1972     0.0000     0.1535     0.0389 1.000 0.000
  U4$1               -0.500    -0.5559     0.0000     0.1735     0.0031 1.000 1.000
  U4$2                0.000    -0.0520     0.0000     0.1592     0.0027 1.000 0.000

Latent Class 2

 Thresholds
  U1$1               -0.500    -0.5227     0.0000     0.1412     0.0005 1.000 1.000
  U1$2                0.000    -0.0021     0.0000     0.1282     0.0000 1.000 0.000
  U2$1               -0.500    -0.3639     0.0000     0.1136     0.0185 1.000 1.000
  U2$2                0.000     0.1021     0.0000     0.1092     0.0104 1.000 0.000
  U3$1                0.500     0.4252     0.0000     0.1472     0.0056 1.000 1.000
  U3$2                1.000     0.8937     0.0000     0.1625     0.0113 1.000 1.000
  U4$1                0.500     0.3827     0.0000     0.1093     0.0138 1.000 1.000
  U4$2                1.000     0.8724     0.0000     0.1162     0.0163 1.000 1.000

Categorical Latent Variables

 Means
  C#1                 0.000    -0.3457     0.0000     0.4738     0.1195 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.788E-03
       (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          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
                    1             2             3             4             5


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


           TAU(U) FOR LATENT CLASS 2
              U1$1          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
                    9            10            11            12            13


           TAU(U) FOR LATENT CLASS 2
              U3$2          U4$1          U4$2
              ________      ________      ________
                   14            15            16


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
                   17             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          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
                0.500         1.000         0.500         1.000        -0.500


           TAU(U) FOR LATENT CLASS 1
              U3$2          U4$1          U4$2
              ________      ________      ________
                0.000        -0.500         0.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
               -0.500         0.000        -0.500         0.000         0.500


           TAU(U) FOR LATENT CLASS 2
              U3$2          U4$1          U4$2
              ________      ________      ________
                1.000         0.500         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          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
                0.500         1.000         0.500         1.000        -0.500


           TAU(U) FOR LATENT CLASS 1
              U3$2          U4$1          U4$2
              ________      ________      ________
                0.000        -0.500         0.000


           TAU(U) FOR LATENT CLASS 2
              U1$1          U1$2          U2$1          U2$2          U3$1
              ________      ________      ________      ________      ________
               -0.500         0.000        -0.500         0.000         0.500


           TAU(U) FOR LATENT CLASS 2
              U3$2          U4$1          U4$2
              ________      ________      ________
                1.000         0.500         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 -0.19220264D+05    0.0000000    0.0000000  EM
              2 -0.19215521D+05    4.7428188    0.0002468  EM
              3 -0.19215311D+05    0.2101882    0.0000109  EM
              4 -0.19215164D+05    0.1468223    0.0000076  EM
              5 -0.19215060D+05    0.1041606    0.0000054  EM
              6 -0.19214985D+05    0.0749645    0.0000039  EM
              7 -0.19214930D+05    0.0546586    0.0000028  EM
              8 -0.19214890D+05    0.0403263    0.0000021  EM
              9 -0.19214860D+05    0.0300803    0.0000016  EM
             10 -0.19214837D+05    0.0226767    0.0000012  EM
             11 -0.19214820D+05    0.0172794    0.0000009  EM
             12 -0.19214807D+05    0.0133160    0.0000007  EM
             13 -0.19214796D+05    0.0103883    0.0000005  EM
             14 -0.19214788D+05    0.0082147    0.0000004  EM
             15 -0.19214781D+05    0.0065943    0.0000003  EM
             16 -0.19214776D+05    0.0053817    0.0000003  EM
             17 -0.19214772D+05    0.0044714    0.0000002  EM
             18 -0.19214768D+05    0.0037858    0.0000002  EM
             19 -0.19214764D+05    0.0032679    0.0000002  EM
             20 -0.19214762D+05    0.0028755    0.0000001  EM
             21 -0.19214759D+05    0.0025771    0.0000001  EM
             22 -0.19214757D+05    0.0023495    0.0000001  EM
             23 -0.19214755D+05    0.0021750    0.0000001  EM
             24 -0.19214752D+05    0.0020406    0.0000001  EM
             25 -0.19214751D+05    0.0019365    0.0000001  EM
             26 -0.19214749D+05    0.0018553    0.0000001  EM
             27 -0.19214747D+05    0.0017913    0.0000001  EM
             28 -0.19214745D+05    0.0017406    0.0000001  EM
             29 -0.19214743D+05    0.0016997    0.0000001  EM
             30 -0.19214742D+05    0.0016664    0.0000001  EM
             31 -0.19214740D+05    0.0016389    0.0000001  EM
             32 -0.19214739D+05    0.0016157    0.0000001  EM
             33 -0.19214737D+05    0.0015959    0.0000001  EM
             34 -0.19214735D+05    0.0015786    0.0000001  EM
             35 -0.19214525D+05    0.2104860    0.0000110  FS
             36 -0.19214481D+05    0.0441631    0.0000023  FS
             37 -0.19214480D+05    0.0003261    0.0000000  FS
             38 -0.19214480D+05    0.0000124    0.0000000  FS
             39 -0.19214480D+05    0.0000006    0.0000000  FS
             40 -0.19214480D+05    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
    ex7.6.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:24:39
        Ending Time:  22:24:41
       Elapsed Time:  00:00:02



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