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

INPUT INSTRUCTIONS

  title:
  	this is an example of a LCA with unordered
  	categorical latent class indicators using
  	automatic starting values with random
  	starts
  	! using the population threshold values
  	! in ex 7.6 as intercept values
  	! so that in effect ordinal outcomes
  	! are treated as unordered in the analysis.
  	! note that intercept values need not be
  	! ordered with nominal outcomes.

  montecarlo:
  	names are u1-u4;
  	generate = u1-u4(n 2);
  	nominal = u1-u4;
  	genclasses = c(2);
  	classes = c(2);
  	nobs = 5000;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.7.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 unordered
categorical latent class indicators using
automatic starting values with 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

  Unordered categorical (nominal)
   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





MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

    H0 Value

        Mean                            -21408.482
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000       -21408.482     -21408.482
           0.980       0.000       -21408.482     -21408.482
           0.950       0.000       -21408.482     -21408.482
           0.900       0.000       -21408.482     -21408.482
           0.800       0.000       -21408.482     -21408.482
           0.700       0.000       -21408.482     -21408.482
           0.500       0.000       -21408.482     -21408.482
           0.300       0.000       -21408.482     -21408.482
           0.200       0.000       -21408.482     -21408.482
           0.100       0.000       -21408.482     -21408.482
           0.050       0.000       -21408.482     -21408.482
           0.020       0.000       -21408.482     -21408.482
           0.010       0.000       -21408.482     -21408.482

Information Criteria

    Akaike (AIC)

        Mean                             42850.964
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        42850.964      42850.964
           0.980       0.000        42850.964      42850.964
           0.950       0.000        42850.964      42850.964
           0.900       0.000        42850.964      42850.964
           0.800       0.000        42850.964      42850.964
           0.700       0.000        42850.964      42850.964
           0.500       0.000        42850.964      42850.964
           0.300       0.000        42850.964      42850.964
           0.200       0.000        42850.964      42850.964
           0.100       0.000        42850.964      42850.964
           0.050       0.000        42850.964      42850.964
           0.020       0.000        42850.964      42850.964
           0.010       0.000        42850.964      42850.964

    Bayesian (BIC)

        Mean                             42961.756
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        42961.756      42961.756
           0.980       0.000        42961.756      42961.756
           0.950       0.000        42961.756      42961.756
           0.900       0.000        42961.756      42961.756
           0.800       0.000        42961.756      42961.756
           0.700       0.000        42961.756      42961.756
           0.500       0.000        42961.756      42961.756
           0.300       0.000        42961.756      42961.756
           0.200       0.000        42961.756      42961.756
           0.100       0.000        42961.756      42961.756
           0.050       0.000        42961.756      42961.756
           0.020       0.000        42961.756      42961.756
           0.010       0.000        42961.756      42961.756

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

        Mean                             42907.736
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        42907.736      42907.736
           0.980       0.000        42907.736      42907.736
           0.950       0.000        42907.736      42907.736
           0.900       0.000        42907.736      42907.736
           0.800       0.000        42907.736      42907.736
           0.700       0.000        42907.736      42907.736
           0.500       0.000        42907.736      42907.736
           0.300       0.000        42907.736      42907.736
           0.200       0.000        42907.736      42907.736
           0.100       0.000        42907.736      42907.736
           0.050       0.000        42907.736      42907.736
           0.020       0.000        42907.736      42907.736
           0.010       0.000        42907.736      42907.736



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

    Latent
   Classes

       1       1286.98163          0.25740
       2       3713.01837          0.74260


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

    Latent
   Classes

       1       1286.98163          0.25740
       2       3713.01837          0.74260


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

Class Counts and Proportions

    Latent
   Classes

       1              683          0.13660
       2             4317          0.86340


CLASSIFICATION QUALITY

     Entropy                         0.343


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

           1        2

    1   0.584    0.416
    2   0.206    0.794


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

           1        2

    1   0.310    0.690
    2   0.076    0.924


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

              1        2

    1     -0.800    0.000
    2     -2.491    0.000


MODEL RESULTS

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

Latent Class 1

 Means
  U1#1                0.500     0.9666     0.0000     0.9629     0.2178 1.000 0.000
  U1#2                1.000     1.4079     0.0000     0.8821     0.1664 1.000 0.000
  U2#1                0.500     2.3526     0.0000     3.9184     3.4320 1.000 0.000
  U2#2                1.000     2.8377     0.0000     3.8780     3.3772 1.000 0.000
  U3#1               -0.500    -0.7716     0.0000     0.4872     0.0738 1.000 0.000
  U3#2                0.000    -0.0428     0.0000     0.2357     0.0018 1.000 0.000
  U4#1               -0.500    -0.6820     0.0000     0.4242     0.0331 1.000 0.000
  U4#2                0.000    -0.1610     0.0000     0.4161     0.0259 1.000 0.000

Latent Class 2

 Means
  U1#1               -0.500    -0.3794     0.0000     0.1624     0.0145 1.000 1.000
  U1#2                0.000     0.1451     0.0000     0.1672     0.0210 1.000 0.000
  U2#1               -0.500    -0.4979     0.0000     0.2871     0.0000 1.000 0.000
  U2#2                0.000     0.0706     0.0000     0.2755     0.0050 1.000 0.000
  U3#1                0.500     0.1446     0.0000     0.1680     0.1263 0.000 0.000
  U3#2                1.000     0.6192     0.0000     0.1687     0.1450 0.000 1.000
  U4#1                0.500     0.1955     0.0000     0.1560     0.0927 1.000 0.000
  U4#2                1.000     0.6398     0.0000     0.1441     0.1297 0.000 1.000

Categorical Latent Variables

 Means
  C#1                 0.000    -1.0595     0.0000     1.1926     1.1226 1.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.443E-04
       (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 REGRESSION MODEL PART


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


     PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
                    2             3             4             5             6


           NU(P) FOR LATENT CLASS 1
              U3#2          U4#1          U4#2
              ________      ________      ________
                    7             8             9


           NU(P) FOR LATENT CLASS 2
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
                   10            11            12            13            14


           NU(P) FOR LATENT CLASS 2
              U3#2          U4#1          U4#2
              ________      ________      ________
                   15            16            17


     STARTING VALUES FOR LATENT CLASS 1


     STARTING VALUES FOR LATENT CLASS 2


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


     STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
                0.500         1.000         0.500         1.000        -0.500


           NU(P) FOR LATENT CLASS 1
              U3#2          U4#1          U4#2
              ________      ________      ________
                0.000        -0.500         0.000


           NU(P) FOR LATENT CLASS 2
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
               -0.500         0.000        -0.500         0.000         0.500


           NU(P) FOR LATENT CLASS 2
              U3#2          U4#1          U4#2
              ________      ________      ________
                1.000         0.500         1.000


     POPULATION VALUES FOR LATENT CLASS 1


     POPULATION VALUES FOR LATENT CLASS 2


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


     POPULATION VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART


           NU(P) FOR LATENT CLASS 1
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
                0.500         1.000         0.500         1.000        -0.500


           NU(P) FOR LATENT CLASS 1
              U3#2          U4#1          U4#2
              ________      ________      ________
                0.000        -0.500         0.000


           NU(P) FOR LATENT CLASS 2
              U1#1          U1#2          U2#1          U2#2          U3#1
              ________      ________      ________      ________      ________
               -0.500         0.000        -0.500         0.000         0.500


           NU(P) FOR LATENT CLASS 2
              U3#2          U4#1          U4#2
              ________      ________      ________
                1.000         0.500         1.000


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.21416857D+05    0.0000000    0.0000000  EM
              2 -0.21412508D+05    4.3488559    0.0002031  EM
              3 -0.21411996D+05    0.5113224    0.0000239  EM
              4 -0.21411591D+05    0.4053413    0.0000189  EM
              5 -0.21411264D+05    0.3274560    0.0000153  EM
              6 -0.21410995D+05    0.2688449    0.0000126  EM
              7 -0.21410771D+05    0.2238267    0.0000105  EM
              8 -0.21410582D+05    0.1886182    0.0000088  EM
              9 -0.21410422D+05    0.1606294    0.0000075  EM
             10 -0.21410284D+05    0.1380470    0.0000064  EM
             11 -0.21410164D+05    0.1195775    0.0000056  EM
             12 -0.21410060D+05    0.1042836    0.0000049  EM
             13 -0.21409968D+05    0.0914767    0.0000043  EM
             14 -0.21409888D+05    0.0806446    0.0000038  EM
             15 -0.21409816D+05    0.0714012    0.0000033  EM
             16 -0.21409753D+05    0.0634523    0.0000030  EM
             17 -0.21409696D+05    0.0565707    0.0000026  EM
             18 -0.21409646D+05    0.0505787    0.0000024  EM
             19 -0.21409600D+05    0.0453355    0.0000021  EM
             20 -0.21409560D+05    0.0407283    0.0000019  EM
             21 -0.21409523D+05    0.0366652    0.0000017  EM
             22 -0.21409490D+05    0.0330710    0.0000015  EM
             23 -0.21409460D+05    0.0298830    0.0000014  EM
             24 -0.21409433D+05    0.0270488    0.0000013  EM
             25 -0.21409408D+05    0.0245238    0.0000011  EM
             26 -0.21409386D+05    0.0222701    0.0000010  EM
             27 -0.21409366D+05    0.0202552    0.0000009  EM
             28 -0.21409347D+05    0.0184511    0.0000009  EM
             29 -0.21409331D+05    0.0168332    0.0000008  EM
             30 -0.21409315D+05    0.0153804    0.0000007  EM
             31 -0.21409301D+05    0.0140742    0.0000007  EM
             32 -0.21409288D+05    0.0128982    0.0000006  EM
             33 -0.21409276D+05    0.0118382    0.0000006  EM
             34 -0.21409266D+05    0.0108815    0.0000005  EM
             35 -0.21409256D+05    0.0100172    0.0000005  EM
             36 -0.21409246D+05    0.0092354    0.0000004  EM
             37 -0.21409238D+05    0.0085274    0.0000004  EM
             38 -0.21409230D+05    0.0078855    0.0000004  EM
             39 -0.21409223D+05    0.0073030    0.0000003  EM
             40 -0.21409216D+05    0.0067737    0.0000003  EM
             41 -0.21409210D+05    0.0062922    0.0000003  EM
             42 -0.21409204D+05    0.0058539    0.0000003  EM
             43 -0.21409198D+05    0.0054544    0.0000003  EM
             44 -0.21409193D+05    0.0050898    0.0000002  EM
             45 -0.21409188D+05    0.0047569    0.0000002  EM
             46 -0.21409184D+05    0.0044526    0.0000002  EM
             47 -0.21409180D+05    0.0041741    0.0000002  EM
             48 -0.21409176D+05    0.0039191    0.0000002  EM
             49 -0.21409172D+05    0.0036853    0.0000002  EM
             50 -0.21409169D+05    0.0034708    0.0000002  EM
             51 -0.21409165D+05    0.0032738    0.0000002  EM
             52 -0.21409162D+05    0.0030928    0.0000001  EM
             53 -0.21409159D+05    0.0029263    0.0000001  EM
             54 -0.21409157D+05    0.0027730    0.0000001  EM
             55 -0.21409154D+05    0.0026318    0.0000001  EM
             56 -0.21408482D+05    0.6719633    0.0000314  QN
             57 -0.21408482D+05    0.0000000    0.0000000  EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    C

  Save file
    ex7.7.dat

  Save file format           Free
  Save file record length    10000


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



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