Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:50 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
  DATA:	FILE IS ex7.6.dat;
  VARIABLE:	NAMES ARE u1-u4 c;
  	USEVARIABLES ARE u1-u4;
  	CLASSES = c (2);
  	CATEGORICAL = u1-u4;
  ANALYSIS:	TYPE = MIXTURE;
  	STARTS = 0;
  MODEL:	
  	%OVERALL%
  	%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:	TECH1 TECH8;



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 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

Input data file(s)
  ex7.6.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.487     2435.000
      Category 2    0.120      600.000
      Category 3    0.393     1965.000
    U2
      Category 1    0.508     2540.000
      Category 2    0.114      570.000
      Category 3    0.378     1890.000
    U3
      Category 1    0.490     2452.000
      Category 2    0.112      560.000
      Category 3    0.398     1988.000
    U4
      Category 1    0.499     2496.000
      Category 2    0.116      578.000
      Category 3    0.385     1926.000



THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

          H0 Value                      -19214.480
          H0 Scaling Correction Factor      1.0208
            for MLR

Information Criteria

          Akaike (AIC)                   38462.961
          Bayesian (BIC)                 38573.753
          Sample-Size Adjusted BIC       38519.733
            (n* = (n + 2) / 24)

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

          Pearson Chi-Square

          Value                             65.388
          Degrees of Freedom                    63
          P-Value                           0.3938

          Likelihood Ratio Chi-Square

          Value                             62.447
          Degrees of Freedom                    63
          P-Value                           0.4960



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

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Latent Class 1

 Thresholds
    U1$1               0.615      0.192      3.203      0.001
    U1$2               1.147      0.224      5.123      0.000
    U2$1               0.604      0.179      3.379      0.001
    U2$2               1.144      0.214      5.339      0.000
    U3$1              -0.713      0.182     -3.918      0.000
    U3$2              -0.197      0.154     -1.284      0.199
    U4$1              -0.556      0.174     -3.203      0.001
    U4$2              -0.052      0.159     -0.327      0.744

Latent Class 2

 Thresholds
    U1$1              -0.523      0.141     -3.702      0.000
    U1$2              -0.002      0.128     -0.016      0.987
    U2$1              -0.364      0.114     -3.203      0.001
    U2$2               0.102      0.109      0.935      0.350
    U3$1               0.425      0.147      2.888      0.004
    U3$2               0.894      0.163      5.499      0.000
    U4$1               0.383      0.109      3.503      0.000
    U4$2               0.872      0.116      7.510      0.000

Categorical Latent Variables

 Means
    C#1               -0.346      0.474     -0.730      0.466


RESULTS IN PROBABILITY SCALE

Latent Class 1

 U1
    Category 1         0.649      0.044     14.834      0.000
    Category 2         0.110      0.015      7.417      0.000
    Category 3         0.241      0.041      5.887      0.000
 U2
    Category 1         0.646      0.041     15.835      0.000
    Category 2         0.112      0.014      8.031      0.000
    Category 3         0.242      0.039      6.156      0.000
 U3
    Category 1         0.329      0.040      8.185      0.000
    Category 2         0.122      0.014      8.729      0.000
    Category 3         0.549      0.038     14.446      0.000
 U4
    Category 1         0.365      0.040      9.068      0.000
    Category 2         0.123      0.014      8.912      0.000
    Category 3         0.513      0.040     12.896      0.000

Latent Class 2

 U1
    Category 1         0.372      0.033     11.281      0.000
    Category 2         0.127      0.011     11.576      0.000
    Category 3         0.501      0.032     15.617      0.000
 U2
    Category 1         0.410      0.027     14.918      0.000
    Category 2         0.115      0.010     11.137      0.000
    Category 3         0.474      0.027     17.428      0.000
 U3
    Category 1         0.605      0.035     17.184      0.000
    Category 2         0.105      0.010     10.330      0.000
    Category 3         0.290      0.033      8.671      0.000
 U4
    Category 1         0.595      0.026     22.571      0.000
    Category 2         0.111      0.010     10.727      0.000
    Category 3         0.295      0.024     12.207      0.000


LATENT CLASS ODDS RATIO RESULTS

Latent Class 1 Compared to Latent Class 2

 U1
    Category > 1       0.320      0.055      5.848      0.000
    Category > 2       0.317      0.063      5.002      0.000
 U2
    Category > 1       0.380      0.062      6.094      0.000
    Category > 2       0.353      0.067      5.274      0.000
 U3
    Category > 1       3.122      0.520      6.004      0.000
    Category > 2       2.977      0.479      6.210      0.000
 U4
    Category > 1       2.556      0.404      6.320      0.000
    Category > 2       2.520      0.379      6.658      0.000


QUALITY OF NUMERICAL RESULTS

     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                  1             2             3             4             5


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


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


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


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2
              ________      ________
 1                 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
              ________      ________      ________      ________      ________
 1              0.500         1.000         0.500         1.000        -0.500


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


           TAU(U) 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


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


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


TECHNICAL 8 OUTPUT


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.19220264D+05    0.0000000    0.0000000   2507.984  2492.016    EM
     2 -0.19215521D+05    4.7428188    0.0002468   2506.584  2493.416    EM
     3 -0.19215311D+05    0.2101882    0.0000109   2505.184  2494.816    EM
     4 -0.19215164D+05    0.1468223    0.0000076   2503.787  2496.213    EM
     5 -0.19215060D+05    0.1041606    0.0000054   2502.394  2497.606    EM
     6 -0.19214985D+05    0.0749645    0.0000039   2501.008  2498.992    EM
     7 -0.19214930D+05    0.0546586    0.0000028   2499.628  2500.372    EM
     8 -0.19214890D+05    0.0403263    0.0000021   2498.256  2501.744    EM
     9 -0.19214860D+05    0.0300803    0.0000016   2496.892  2503.108    EM
    10 -0.19214837D+05    0.0226767    0.0000012   2495.536  2504.464    EM
    11 -0.19214820D+05    0.0172794    0.0000009   2494.187  2505.813    EM
    12 -0.19214807D+05    0.0133160    0.0000007   2492.847  2507.153    EM
    13 -0.19214796D+05    0.0103883    0.0000005   2491.514  2508.486    EM
    14 -0.19214788D+05    0.0082147    0.0000004   2490.188  2509.812    EM
    15 -0.19214781D+05    0.0065943    0.0000003   2488.870  2511.130    EM
    16 -0.19214776D+05    0.0053817    0.0000003   2487.559  2512.441    EM
    17 -0.19214772D+05    0.0044714    0.0000002   2486.254  2513.746    EM
    18 -0.19214768D+05    0.0037858    0.0000002   2484.956  2515.044    EM
    19 -0.19214764D+05    0.0032679    0.0000002   2483.663  2516.337    EM
    20 -0.19214762D+05    0.0028755    0.0000001   2482.377  2517.623    EM
    21 -0.19214759D+05    0.0025771    0.0000001   2481.096  2518.904    EM
    22 -0.19214757D+05    0.0023495    0.0000001   2479.821  2520.179    EM
    23 -0.19214755D+05    0.0021750    0.0000001   2478.551  2521.449    EM
    24 -0.19214752D+05    0.0020406    0.0000001   2477.286  2522.714    EM
    25 -0.19214751D+05    0.0019365    0.0000001   2476.026  2523.974    EM
    26 -0.19214749D+05    0.0018553    0.0000001   2474.771  2525.229    EM
    27 -0.19214747D+05    0.0017913    0.0000001   2473.520  2526.480    EM
    28 -0.19214745D+05    0.0017406    0.0000001   2472.275  2527.725    EM
    29 -0.19214743D+05    0.0016997    0.0000001   2471.033  2528.967    EM
    30 -0.19214742D+05    0.0016664    0.0000001   2469.796  2530.204    EM
    31 -0.19214740D+05    0.0016389    0.0000001   2468.564  2531.436    EM
    32 -0.19214739D+05    0.0016157    0.0000001   2467.335  2532.665    EM
    33 -0.19214737D+05    0.0015959    0.0000001   2466.111  2533.889    EM
    34 -0.19214735D+05    0.0015786    0.0000001   2464.890  2535.110    EM
    35 -0.19214525D+05    0.2104860    0.0000110   2112.963  2887.037    FS
    36 -0.19214481D+05    0.0441631    0.0000023   2082.494  2917.506    FS
    37 -0.19214480D+05    0.0003261    0.0000000   2073.984  2926.016    FS
    38 -0.19214480D+05    0.0000124    0.0000000   2072.576  2927.424    FS
    39 -0.19214480D+05    0.0000006    0.0000000   2072.192  2927.808    FS
    40 -0.19214480D+05    0.0000000    0.0000000   2072.136  2927.864    FS


     Beginning Time:  17:50:03
        Ending Time:  17:50:03
       Elapsed Time:  00:00:00



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