Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:03 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       1286.98173          0.25740
       2       3713.01827          0.74260


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

    Latent
   Classes

       1       1286.98163          0.25740
       2       3713.01837          0.74260


CLASSIFICATION QUALITY

     Entropy                         0.343


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1              683          0.13660
       2             4317          0.86340


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


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                  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
              ________      ________      ________      ________      ________
 1                  2             3             4             5             6


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


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


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


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


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


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


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


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


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


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.21416857D+05    0.0000000    0.0000000   2500.543  2499.457    EM
     2 -0.21412508D+05    4.3488559    0.0002031   2500.598  2499.402    EM
     3 -0.21411996D+05    0.5113224    0.0000239   2500.592  2499.408    EM
     4 -0.21411591D+05    0.4053413    0.0000189   2500.535  2499.465    EM
     5 -0.21411264D+05    0.3274560    0.0000153   2500.430  2499.570    EM
     6 -0.21410995D+05    0.2688449    0.0000126   2500.282  2499.718    EM
     7 -0.21410771D+05    0.2238267    0.0000105   2500.093  2499.907    EM
     8 -0.21410582D+05    0.1886182    0.0000088   2499.867  2500.133    EM
     9 -0.21410422D+05    0.1606294    0.0000075   2499.605  2500.395    EM
    10 -0.21410284D+05    0.1380470    0.0000064   2499.310  2500.690    EM
    11 -0.21410164D+05    0.1195775    0.0000056   2498.983  2501.017    EM
    12 -0.21410060D+05    0.1042836    0.0000049   2498.626  2501.374    EM
    13 -0.21409968D+05    0.0914767    0.0000043   2498.241  2501.759    EM
    14 -0.21409888D+05    0.0806446    0.0000038   2497.829  2502.171    EM
    15 -0.21409816D+05    0.0714012    0.0000033   2497.393  2502.607    EM
    16 -0.21409753D+05    0.0634523    0.0000030   2496.932  2503.068    EM
    17 -0.21409696D+05    0.0565707    0.0000026   2496.449  2503.551    EM
    18 -0.21409646D+05    0.0505787    0.0000024   2495.944  2504.056    EM
    19 -0.21409600D+05    0.0453355    0.0000021   2495.420  2504.580    EM
    20 -0.21409560D+05    0.0407283    0.0000019   2494.876  2505.124    EM
    21 -0.21409523D+05    0.0366652    0.0000017   2494.315  2505.685    EM
    22 -0.21409490D+05    0.0330710    0.0000015   2493.736  2506.264    EM
    23 -0.21409460D+05    0.0298830    0.0000014   2493.142  2506.858    EM
    24 -0.21409433D+05    0.0270488    0.0000013   2492.532  2507.468    EM
    25 -0.21409408D+05    0.0245238    0.0000011   2491.908  2508.092    EM
    26 -0.21409386D+05    0.0222701    0.0000010   2491.270  2508.730    EM
    27 -0.21409366D+05    0.0202552    0.0000009   2490.620  2509.380    EM
    28 -0.21409347D+05    0.0184511    0.0000009   2489.957  2510.043    EM
    29 -0.21409331D+05    0.0168332    0.0000008   2489.282  2510.718    EM
    30 -0.21409315D+05    0.0153804    0.0000007   2488.597  2511.403    EM
    31 -0.21409301D+05    0.0140742    0.0000007   2487.901  2512.099    EM
    32 -0.21409288D+05    0.0128982    0.0000006   2487.196  2512.804    EM
    33 -0.21409276D+05    0.0118382    0.0000006   2486.481  2513.519    EM
    34 -0.21409266D+05    0.0108815    0.0000005   2485.758  2514.242    EM
    35 -0.21409256D+05    0.0100172    0.0000005   2485.026  2514.974    EM
    36 -0.21409246D+05    0.0092354    0.0000004   2484.287  2515.713    EM
    37 -0.21409238D+05    0.0085274    0.0000004   2483.540  2516.460    EM
    38 -0.21409230D+05    0.0078855    0.0000004   2482.786  2517.214    EM
    39 -0.21409223D+05    0.0073030    0.0000003   2482.026  2517.974    EM
    40 -0.21409216D+05    0.0067737    0.0000003   2481.259  2518.741    EM
    41 -0.21409210D+05    0.0062922    0.0000003   2480.486  2519.514    EM
    42 -0.21409204D+05    0.0058539    0.0000003   2479.708  2520.292    EM
    43 -0.21409198D+05    0.0054544    0.0000003   2478.924  2521.076    EM
    44 -0.21409193D+05    0.0050898    0.0000002   2478.135  2521.865    EM
    45 -0.21409188D+05    0.0047569    0.0000002   2477.341  2522.659    EM
    46 -0.21409184D+05    0.0044526    0.0000002   2476.543  2523.457    EM
    47 -0.21409180D+05    0.0041741    0.0000002   2475.741  2524.259    EM
    48 -0.21409176D+05    0.0039191    0.0000002   2474.934  2525.066    EM
    49 -0.21409172D+05    0.0036853    0.0000002   2474.123  2525.877    EM
    50 -0.21409169D+05    0.0034708    0.0000002   2473.309  2526.691    EM
    51 -0.21409165D+05    0.0032738    0.0000002   2472.491  2527.509    EM
    52 -0.21409162D+05    0.0030928    0.0000001   2471.670  2528.330    EM
    53 -0.21409159D+05    0.0029263    0.0000001   2470.846  2529.154    EM
    54 -0.21409157D+05    0.0027730    0.0000001   2470.019  2529.981    EM
    55 -0.21409154D+05    0.0026318    0.0000001   2469.189  2530.811    EM
    56 -0.21408482D+05    0.6719633    0.0000314   1286.982  3713.018    QN
    57 -0.21408482D+05    0.0000000    0.0000000   1286.982  3713.018    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:  22:03:27
        Ending Time:  22:03:27
       Elapsed Time:  00:00:00



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