Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:13 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a LCA with
  binary latent class indicators using
  automatic starting values with random starts
  DATA:	FILE IS ex7.3.dat;
  VARIABLE:	NAMES ARE u1-u4 x1-x10;
  	USEVARIABLES = u1-u4;
  	CLASSES = c (2);
  	CATEGORICAL = u1-u4;
  	AUXILIARY = x1-x10 (e);
  ANALYSIS:	TYPE = MIXTURE;
  OUTPUT:	TECH1 TECH8 TECH10;



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 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

Observed auxiliary variables
   X1          X2          X3          X4          X5          X6
   X7          X8          X9          X10

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
Random Starts Specifications
  Number of initial stage random starts                         20
  Number of final stage optimizations                            4
  Number of initial stage iterations                            10
  Initial stage convergence criterion                    0.100D+01
  Random starts scale                                    0.500D+01
  Random seed for generating random starts                       0
Link                                                         LOGIT

Input data file(s)
  ex7.3.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.678          339.000
      Category 2    0.322          161.000
    U2
      Category 1    0.686          343.000
      Category 2    0.314          157.000
    U3
      Category 1    0.322          161.000
      Category 2    0.678          339.000
    U4
      Category 1    0.334          167.000
      Category 2    0.666          333.000


RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES

Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:

            -965.244  253358           2
            -965.244  93468            3
            -965.244  939021           8
            -965.244  76974            16



THE BEST LOGLIKELIHOOD VALUE HAS BEEN REPLICATED.  RERUN WITH AT LEAST TWICE THE
RANDOM STARTS TO CHECK THAT THE BEST LOGLIKELIHOOD IS STILL OBTAINED AND REPLICATED.


THE MODEL ESTIMATION TERMINATED NORMALLY

     WARNING:  AUXILIARY (E) CAN GIVE BIASED RESULTS AND IS SUPERSEDED BY THE BCH AND DU3STEP OPTIONS.
     USE AUXILIARY (E) ONLY FOR METHODS RESEARCH PURPOSES.



MODEL FIT INFORMATION

Number of Free Parameters                        9

Loglikelihood

          H0 Value                        -965.244
          H0 Scaling Correction Factor      1.0131
            for MLR

Information Criteria

          Akaike (AIC)                    1948.488
          Bayesian (BIC)                  1986.420
          Sample-Size Adjusted BIC        1957.853
            (n* = (n + 2) / 24)

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

          Pearson Chi-Square

          Value                              6.287
          Degrees of Freedom                     6
          P-Value                           0.3918

          Likelihood Ratio Chi-Square

          Value                              5.605
          Degrees of Freedom                     6
          P-Value                           0.4688



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

    Latent
   Classes

       1        136.38064          0.27276
       2        363.61936          0.72724


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

    Latent
   Classes

       1        136.38064          0.27276
       2        363.61936          0.72724


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

Class Counts and Proportions

    Latent
   Classes

       1              127          0.25400
       2              373          0.74600


CLASSIFICATION QUALITY

     Entropy                         0.904


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

           1        2

    1   0.986    0.014
    2   0.030    0.970


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

           1        2

    1   0.918    0.082
    2   0.005    0.995


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

              1        2

    1      2.422    0.000
    2     -5.339    0.000


MODEL RESULTS

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

Latent Class 1

 Thresholds
    U1$1              -2.063      0.373     -5.536      0.000
    U2$1              -1.724      0.300     -5.755      0.000
    U3$1               2.331      0.390      5.985      0.000
    U4$1               2.078      0.320      6.490      0.000

Latent Class 2

 Thresholds
    U1$1               2.091      0.182     11.502      0.000
    U2$1               2.056      0.180     11.401      0.000
    U3$1              -2.187      0.203    -10.760      0.000
    U4$1              -1.937      0.183    -10.613      0.000

Categorical Latent Variables

 Means
    C#1               -0.981      0.116     -8.468      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.600E-01
       (ratio of smallest to largest eigenvalue)


RESULTS IN PROBABILITY SCALE

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

Latent Class 1

 U1
    Category 1         0.113      0.037      3.024      0.002
    Category 2         0.887      0.037     23.800      0.000
 U2
    Category 1         0.151      0.038      3.934      0.000
    Category 2         0.849      0.038     22.056      0.000
 U3
    Category 1         0.911      0.031     28.987      0.000
    Category 2         0.089      0.031      2.817      0.005
 U4
    Category 1         0.889      0.032     28.072      0.000
    Category 2         0.111      0.032      3.514      0.000

Latent Class 2

 U1
    Category 1         0.890      0.018     50.016      0.000
    Category 2         0.110      0.018      6.181      0.000
 U2
    Category 1         0.887      0.018     48.873      0.000
    Category 2         0.113      0.018      6.256      0.000
 U3
    Category 1         0.101      0.018      5.472      0.000
    Category 2         0.899      0.018     48.748      0.000
 U4
    Category 1         0.126      0.020      6.267      0.000
    Category 2         0.874      0.020     43.498      0.000


LATENT CLASS INDICATOR ODDS RATIOS FOR THE LATENT CLASSES

                                                95% C.I.
                    Estimate       S.E.  Lower 2.5% Upper 2.5%

Latent Class 1 Compared to Latent Class 2

 U1
    Category > 1      63.673     25.877     28.708    141.221
 U2
    Category > 1      43.796     14.941     22.441     85.473
 U3
    Category > 1       0.011      0.005      0.005      0.025
 U4
    Category > 1       0.018      0.007      0.009      0.037


EQUALITY TESTS OF MEANS ACROSS CLASSES USING POSTERIOR PROBABILITY-BASED
MULTIPLE IMPUTATIONS WITH 1 DEGREE(S) OF FREEDOM FOR THE OVERALL TEST

X1
                          Mean       S.E.

  Class 1                1.660      0.146
  Class 2               -1.984      0.067

                    Chi-Square     P-Value

  Overall test         504.821      0.000

X2
                          Mean       S.E.

  Class 1                1.613      0.153
  Class 2               -1.975      0.063

                    Chi-Square     P-Value

  Overall test         451.062      0.000

X3
                          Mean       S.E.

  Class 1                0.855      0.099
  Class 2               -0.961      0.057

                    Chi-Square     P-Value

  Overall test         246.680      0.000

X4
                          Mean       S.E.

  Class 1                0.653      0.099
  Class 2               -0.946      0.055

                    Chi-Square     P-Value

  Overall test         194.248      0.000

X5
                          Mean       S.E.

  Class 1                0.085      0.094
  Class 2               -0.037      0.054

                    Chi-Square     P-Value

  Overall test           1.241      0.265

X6
                          Mean       S.E.

  Class 1               -0.029      0.088
  Class 2               -0.030      0.051

                    Chi-Square     P-Value

  Overall test           0.000      0.994

X7
                          Mean       S.E.

  Class 1               -0.681      0.110
  Class 2                0.921      0.054

                    Chi-Square     P-Value

  Overall test         165.266      0.000

X8
                          Mean       S.E.

  Class 1               -0.793      0.103
  Class 2                0.904      0.058

                    Chi-Square     P-Value

  Overall test         194.849      0.000

X9
                          Mean       S.E.

  Class 1               -1.511      0.152
  Class 2                1.864      0.062

                    Chi-Square     P-Value

  Overall test         408.496      0.000

X10
                          Mean       S.E.

  Class 1               -1.743      0.154
  Class 2                1.957      0.063

                    Chi-Square     P-Value

  Overall test         484.687      0.000



TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


     PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART


           LAMBDA(U)
              C#1           C#2
              ________      ________
 U1                 1             2
 U2                 3             4
 U3                 5             6
 U4                 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


           LAMBDA(U)
              C#1           C#2
              ________      ________
 U1             0.255        -1.745
 U2             0.219        -1.781
 U3             1.745        -0.255
 U4             1.690        -0.310


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


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


TECHNICAL 10 OUTPUT


     MODEL FIT INFORMATION FOR THE LATENT CLASS INDICATOR MODEL PART


     RESPONSE PATTERNS

     No.  Pattern    No.  Pattern    No.  Pattern    No.  Pattern
       1  1101         2  1000         3  0011         4  1100
       5  0111         6  0010         7  0001         8  1011
       9  1010        10  0101        11  1110        12  0100
      13  0000        14  1111        15  0110        16  1001



     RESPONSE PATTERN FREQUENCIES AND CHI-SQUARE CONTRIBUTIONS

    Response          Frequency     Standardized  Chi-square Contribution
     Pattern    Observed  Estimated   Residual    Pearson   Loglikelihood  Deleted
                                     (z-score)
         1        11.00      10.81       0.06       0.00         0.38
         2        14.00      15.29      -0.33       0.11        -2.46
         3       230.00     225.48       0.41       0.09         9.13
         4        85.00      83.24       0.21       0.04         3.56
         5        27.00      28.99      -0.38       0.14        -3.84
         6        28.00      32.67      -0.84       0.67        -8.63
         7        23.00      25.54      -0.52       0.25        -4.83
         8        28.00      28.04      -0.01       0.00        -0.09
         9         6.00       5.46       0.23       0.05         1.14
        10         5.00       4.56       0.21       0.04         0.91
        11         8.00       8.60      -0.21       0.04        -1.15
        12         9.00      11.04      -0.62       0.38        -3.67
        13        10.00       5.53       1.91       3.61        11.84
        14         5.00       4.58       0.20       0.04         0.88
        15         7.00       5.19       0.80       0.63         4.20
        16         4.00       4.99      -0.44       0.19        -1.76

     THE TOTAL PEARSON CHI-SQUARE CONTRIBUTION FROM EMPTY CELLS IS         0.00


     UNIVARIATE MODEL FIT INFORMATION

                               Estimated Probabilities
                                                  Standardized
     Variable              H1           H0          Residual
                                                   (z-score)
     U1
       Category 1        0.678        0.678           0.000
       Category 2        0.322        0.322           0.000
       Univariate Pearson Chi-Square                  0.000
       Univariate Log-Likelihood Chi-Square           0.000
       Number of Significant Standardized Residuals   0
     U2
       Category 1        0.686        0.686           0.000
       Category 2        0.314        0.314           0.000
       Univariate Pearson Chi-Square                  0.000
       Univariate Log-Likelihood Chi-Square           0.000
       Number of Significant Standardized Residuals   0
     U3
       Category 1        0.322        0.322           0.000
       Category 2        0.678        0.678           0.000
       Univariate Pearson Chi-Square                  0.000
       Univariate Log-Likelihood Chi-Square           0.000
       Number of Significant Standardized Residuals   0
     U4
       Category 1        0.334        0.334           0.000
       Category 2        0.666        0.666           0.000
       Univariate Pearson Chi-Square                  0.000
       Univariate Log-Likelihood Chi-Square           0.000
       Number of Significant Standardized Residuals   0

       Overall Univariate Pearson Chi-Square                         0.000
       Overall Univariate Log-Likelihood Chi-Square                  0.000
       Overall Number of Significant Standardized Residuals          0


     BIVARIATE MODEL FIT INFORMATION

                                              Estimated Probabilities
                                                                 Standardized
     Variable       Variable              H1           H0          Residual
                                                                  (z-score)
     U1             U2
       Category 1     Category 1        0.582        0.578           0.161
       Category 1     Category 2        0.096        0.100          -0.265
       Category 2     Category 1        0.104        0.108          -0.256
       Category 2     Category 2        0.218        0.214           0.193
       Bivariate Pearson Chi-Square                                  0.162
       Bivariate Log-Likelihood Chi-Square                           0.163
       Number of Significant Standardized Residuals                  0
     U1             U3
       Category 1     Category 1        0.094        0.093           0.050
       Category 1     Category 2        0.584        0.585          -0.029
       Category 2     Category 1        0.228        0.229          -0.034
       Category 2     Category 2        0.094        0.093           0.050
       Bivariate Pearson Chi-Square                                  0.006
       Bivariate Log-Likelihood Chi-Square                           0.006
       Number of Significant Standardized Residuals                  0
     U1             U4
       Category 1     Category 1        0.108        0.109          -0.061
       Category 1     Category 2        0.570        0.569           0.038
       Category 2     Category 1        0.226        0.225           0.045
       Category 2     Category 2        0.096        0.097          -0.064
       Bivariate Pearson Chi-Square                                  0.009
       Bivariate Log-Likelihood Chi-Square                           0.009
       Number of Significant Standardized Residuals                  0
     U2             U3
       Category 1     Category 1        0.102        0.103          -0.052
       Category 1     Category 2        0.584        0.583           0.032
       Category 2     Category 1        0.220        0.219           0.038
       Category 2     Category 2        0.094        0.095          -0.053
       Bivariate Pearson Chi-Square                                  0.007
       Bivariate Log-Likelihood Chi-Square                           0.007
       Number of Significant Standardized Residuals                  0
     U2             U4
       Category 1     Category 1        0.116        0.118          -0.131
       Category 1     Category 2        0.570        0.568           0.085
       Category 2     Category 1        0.218        0.216           0.103
       Category 2     Category 2        0.096        0.098          -0.142
       Bivariate Pearson Chi-Square                                  0.045
       Bivariate Log-Likelihood Chi-Square                           0.045
       Number of Significant Standardized Residuals                  0
     U3             U4
       Category 1     Category 1        0.236        0.230           0.309
       Category 1     Category 2        0.086        0.092          -0.450
       Category 2     Category 1        0.098        0.104          -0.426
       Category 2     Category 2        0.580        0.574           0.263
       Bivariate Pearson Chi-Square                                  0.450
       Bivariate Log-Likelihood Chi-Square                           0.456
       Number of Significant Standardized Residuals                  0

       Overall Bivariate Pearson Chi-Square                          0.678
       Overall Bivariate Log-Likelihood Chi-Square                   0.686
       Overall Number of Significant Standardized Residuals          0


     UNIVARIATE DISTRIBUTION FIT FOR CLASS 1

     Variable          Observed      Estimated      Residual (Obs.-Est.)    Stand. Residual
     U1
       Category 1        0.113          0.113                  0.000                0.000
       Category 2        0.887          0.887                  0.000                0.000
     U2
       Category 1        0.151          0.151                  0.000                0.000
       Category 2        0.849          0.849                  0.000                0.000
     U3
       Category 1        0.911          0.911                  0.000                0.000
       Category 2        0.089          0.089                  0.000                0.000
     U4
       Category 1        0.889          0.889                  0.000                0.000
       Category 2        0.111          0.111                  0.000                0.000


     BIVARIATE DISTRIBUTIONS FIT FOR CLASS 1

     Variable       Variable          Observed     Estimated    Residual (Obs.-Est.)  Stand. Residual
     U1             U2
       Category 1     Category 1        0.028       0.017             0.011            0.974
       Category 1     Category 2        0.085       0.096            -0.011           -0.429
       Category 2     Category 1        0.124       0.134            -0.011           -0.370
       Category 2     Category 2        0.764       0.753             0.011            0.293
     U1             U3
       Category 1     Category 1        0.100       0.103            -0.002           -0.092
       Category 1     Category 2        0.012       0.010             0.002            0.280
       Category 2     Category 1        0.811       0.809             0.002            0.071
       Category 2     Category 2        0.076       0.079            -0.002           -0.103
     U1             U4
       Category 1     Category 1        0.100       0.100            -0.001           -0.027
       Category 1     Category 2        0.013       0.013             0.001            0.073
       Category 2     Category 1        0.789       0.789             0.001            0.020
       Category 2     Category 2        0.098       0.099            -0.001           -0.027
     U2             U3
       Category 1     Category 1        0.137       0.138            -0.001           -0.029
       Category 1     Category 2        0.014       0.013             0.001            0.088
       Category 2     Category 1        0.774       0.773             0.001            0.024
       Category 2     Category 2        0.074       0.075            -0.001           -0.038
     U2             U4
       Category 1     Category 1        0.137       0.135             0.003            0.098
       Category 1     Category 2        0.014       0.017            -0.003           -0.260
       Category 2     Category 1        0.751       0.754            -0.003           -0.078
       Category 2     Category 2        0.097       0.094             0.003            0.114
     U3             U4
       Category 1     Category 1        0.811       0.810             0.001            0.018
       Category 1     Category 2        0.101       0.101            -0.001           -0.024
       Category 2     Category 1        0.078       0.079            -0.001           -0.027
       Category 2     Category 2        0.010       0.010             0.001            0.073


     UNIVARIATE DISTRIBUTION FIT FOR CLASS 2

     Variable          Observed      Estimated      Residual (Obs.-Est.)    Stand. Residual
     U1
       Category 1        0.890          0.890                  0.000                0.000
       Category 2        0.110          0.110                  0.000                0.000
     U2
       Category 1        0.887          0.887                  0.000                0.000
       Category 2        0.113          0.113                  0.000                0.000
     U3
       Category 1        0.101          0.101                  0.000                0.000
       Category 2        0.899          0.899                  0.000                0.000
     U4
       Category 1        0.126          0.126                  0.000                0.000
       Category 2        0.874          0.874                  0.000                0.000


     BIVARIATE DISTRIBUTIONS FIT FOR CLASS 2

     Variable       Variable          Observed     Estimated    Residual (Obs.-Est.)  Stand. Residual
     U1             U2
       Category 1     Category 1        0.790       0.789             0.001            0.039
       Category 1     Category 2        0.100       0.101            -0.001           -0.052
       Category 2     Category 1        0.097       0.098            -0.001           -0.053
       Category 2     Category 2        0.013       0.012             0.001            0.142
     U1             U3
       Category 1     Category 1        0.092       0.090             0.002            0.119
       Category 1     Category 2        0.798       0.800            -0.002           -0.085
       Category 2     Category 1        0.009       0.011            -0.002           -0.324
       Category 2     Category 2        0.101       0.099             0.002            0.114
     U1             U4
       Category 1     Category 1        0.111       0.112            -0.001           -0.054
       Category 1     Category 2        0.779       0.778             0.001            0.041
       Category 2     Category 1        0.015       0.014             0.001            0.147
       Category 2     Category 2        0.095       0.096            -0.001           -0.058
     U2             U3
       Category 1     Category 1        0.089       0.089            -0.001           -0.043
       Category 1     Category 2        0.798       0.797             0.001            0.030
       Category 2     Category 1        0.012       0.011             0.001            0.114
       Category 2     Category 2        0.101       0.102            -0.001           -0.040
     U2             U4
       Category 1     Category 1        0.108       0.112            -0.004           -0.222
       Category 1     Category 2        0.779       0.775             0.004            0.168
       Category 2     Category 1        0.018       0.014             0.004            0.590
       Category 2     Category 2        0.096       0.099            -0.004           -0.234
     U3             U4
       Category 1     Category 1        0.020       0.013             0.008            1.321
       Category 1     Category 2        0.080       0.088            -0.008           -0.522
       Category 2     Category 1        0.105       0.113            -0.008           -0.467
       Category 2     Category 2        0.794       0.786             0.008            0.361


TECHNICAL 8 OUTPUT


  INITIAL STAGE ITERATIONS


  TECHNICAL 8 OUTPUT FOR UNPERTURBED STARTING VALUE SET


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.13869879D+04    0.0000000    0.0000000  EM
              2 -0.12702693D+04  116.7185367    0.0841525  EM
              3 -0.12589112D+04   11.3581502    0.0089415  EM
              4 -0.12478774D+04   11.0337489    0.0087645  EM
              5 -0.11983398D+04   49.5376061    0.0396975  EM
              6 -0.10772317D+04  121.1080636    0.1010632  EM
              7 -0.10051822D+04   72.0495455    0.0668840  EM
              8 -0.98532143D+03   19.8607722    0.0197584  EM
              9 -0.97512648D+03   10.1949488    0.0103468  EM
             10 -0.97007663D+03    5.0498505    0.0051787  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.15116121D+04    0.0000000    0.0000000  EM
              2 -0.11480793D+04  363.5328009    0.2404934  EM
              3 -0.10461566D+04  101.9227111    0.0887767  EM
              4 -0.10145372D+04   31.6194102    0.0302244  EM
              5 -0.99710032D+03   17.4368618    0.0171870  EM
              6 -0.98230351D+03   14.7968176    0.0148398  EM
              7 -0.97355276D+03    8.7507460    0.0089084  EM
              8 -0.96932847D+03    4.2242926    0.0043390  EM
              9 -0.96727928D+03    2.0491854    0.0021140  EM
             10 -0.96625386D+03    1.0254204    0.0010601  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.15000208D+04    0.0000000    0.0000000  EM
              2 -0.97385583D+03  526.1649184    0.3507718  EM
              3 -0.96721955D+03    6.6362839    0.0068144  EM
              4 -0.96593581D+03    1.2837366    0.0013272  EM
              5 -0.96551949D+03    0.4163233    0.0004310  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.15446417D+04    0.0000000    0.0000000  EM
              2 -0.10562425D+04  488.3992421    0.3161893  EM
              3 -0.96991442D+03   86.3280665    0.0817313  EM
              4 -0.96549509D+03    4.4193308    0.0045564  EM
              5 -0.96528859D+03    0.2065026    0.0002139  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 4


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.13675461D+04    0.0000000    0.0000000  EM
              2 -0.12613574D+04  106.1887504    0.0776491  EM
              3 -0.12464494D+04   14.9080102    0.0118190  EM
              4 -0.11789977D+04   67.4516817    0.0541151  EM
              5 -0.10213105D+04  157.6872253    0.1337468  EM
              6 -0.96950196D+03   51.8084932    0.0507275  EM
              7 -0.96669533D+03    2.8066284    0.0028949  EM
              8 -0.96594213D+03    0.7532030    0.0007792  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 5


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.19471580D+04    0.0000000    0.0000000  EM
              2 -0.12804435D+04  666.7144669    0.3424039  EM
              3 -0.12644716D+04   15.9719368    0.0124738  EM
              4 -0.12584280D+04    6.0435562    0.0047795  EM
              5 -0.12467505D+04   11.6775060    0.0092794  EM
              6 -0.11636209D+04   83.1295947    0.0666770  EM
              7 -0.10038791D+04  159.7418389    0.1372800  EM
              8 -0.97199363D+03   31.8854758    0.0317623  EM
              9 -0.96723580D+03    4.7578244    0.0048949  EM
             10 -0.96596815D+03    1.2676543    0.0013106  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 6


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.22235298D+04    0.0000000    0.0000000  EM
              2 -0.11875514D+04 1035.9783955    0.4659161  EM
              3 -0.10399659D+04  147.5854958    0.1242771  EM
              4 -0.98585714D+03   54.1087592    0.0520294  EM
              5 -0.97461678D+03   11.2403661    0.0114016  EM
              6 -0.96979329D+03    4.8234909    0.0049491  EM
              7 -0.96750381D+03    2.2894796    0.0023608  EM
              8 -0.96636652D+03    1.1372858    0.0011755  EM
              9 -0.96579457D+03    0.5719482    0.0005919  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 7


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.16319304D+04    0.0000000    0.0000000  EM
              2 -0.10255918D+04  606.3386568    0.3715469  EM
              3 -0.10188865D+04    6.7053289    0.0065380  EM
              4 -0.10102510D+04    8.6354763    0.0084754  EM
              5 -0.99498339D+03   15.2675833    0.0151127  EM
              6 -0.97906686D+03   15.9165393    0.0159968  EM
              7 -0.97122814D+03    7.8387109    0.0080063  EM
              8 -0.96809300D+03    3.1351488    0.0032280  EM
              9 -0.96664685D+03    1.4461480    0.0014938  EM
             10 -0.96593282D+03    0.7140328    0.0007387  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.16040280D+04    0.0000000    0.0000000  EM
              2 -0.12321579D+04  371.8700258    0.2318351  EM
              3 -0.10592858D+04  172.8721781    0.1403003  EM
              4 -0.97851276D+03   80.7730107    0.0762523  EM
              5 -0.97047796D+03    8.0348000    0.0082112  EM
              6 -0.96687787D+03    3.6000867    0.0037096  EM
              7 -0.96579270D+03    1.0851748    0.0011223  EM
              8 -0.96545790D+03    0.3348001    0.0003467  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 9


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.22793079D+04    0.0000000    0.0000000  EM
              2 -0.11069887D+04 1172.3192038    0.5143312  EM
              3 -0.10583793D+04   48.6093468    0.0439113  EM
              4 -0.10413742D+04   17.0051299    0.0160671  EM
              5 -0.10299223D+04   11.4519536    0.0109970  EM
              6 -0.10161584D+04   13.7639034    0.0133640  EM
              7 -0.10005327D+04   15.6256929    0.0153772  EM
              8 -0.98551375D+03   15.0189203    0.0150109  EM
              9 -0.97515262D+03   10.3611266    0.0105134  EM
             10 -0.97002150D+03    5.1311241    0.0052619  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 10


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.31179791D+04    0.0000000    0.0000000  EM
              2 -0.12444524D+04 1873.5266839    0.6008785  EM
              3 -0.11699978D+04   74.4546229    0.0598292  EM
              4 -0.10979763D+04   72.0214727    0.0615569  EM
              5 -0.10574964D+04   40.4798461    0.0368677  EM
              6 -0.10422538D+04   15.2426327    0.0144139  EM
              7 -0.10289875D+04   13.2662797    0.0127285  EM
              8 -0.10120582D+04   16.9292825    0.0164524  EM
              9 -0.99365065D+03   18.4075940    0.0181883  EM
             10 -0.97977343D+03   13.8772158    0.0139659  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 11


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.18054063D+04    0.0000000    0.0000000  EM
              2 -0.10249527D+04  780.4535851    0.4322870  EM
              3 -0.98161080D+03   43.3418991    0.0422867  EM
              4 -0.97097898D+03   10.6318208    0.0108310  EM
              5 -0.96772712D+03    3.2518590    0.0033491  EM
              6 -0.96642920D+03    1.2979202    0.0013412  EM
              7 -0.96581851D+03    0.6106819    0.0006319  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 12


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.18897512D+04    0.0000000    0.0000000  EM
              2 -0.12351379D+04  654.6133029    0.3464018  EM
              3 -0.11172058D+04  117.9321629    0.0954810  EM
              4 -0.10069352D+04  110.2705471    0.0987021  EM
              5 -0.98155888D+03   25.3763339    0.0252016  EM
              6 -0.97304404D+03    8.5148430    0.0086748  EM
              7 -0.96907828D+03    3.9657591    0.0040756  EM
              8 -0.96715327D+03    1.9250017    0.0019864  EM
              9 -0.96618991D+03    0.9633622    0.0009961  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 13


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.13427210D+04    0.0000000    0.0000000  EM
              2 -0.98958236D+03  353.1386200    0.2630022  EM
              3 -0.97308015D+03   16.5022106    0.0166759  EM
              4 -0.96865755D+03    4.4225968    0.0045449  EM
              5 -0.96689174D+03    1.7658115    0.0018229  EM
              6 -0.96605103D+03    0.8407141    0.0008695  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 14


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.28159305D+04    0.0000000    0.0000000  EM
              2 -0.12603418D+04 1555.5886958    0.5524244  EM
              3 -0.12072986D+04   53.0432761    0.0420864  EM
              4 -0.11468888D+04   60.4098112    0.0500372  EM
              5 -0.10908355D+04   56.0532467    0.0488742  EM
              6 -0.10616778D+04   29.1577338    0.0267297  EM
              7 -0.10505687D+04   11.1090788    0.0104637  EM
              8 -0.10391866D+04   11.3821361    0.0108343  EM
              9 -0.10232461D+04   15.9404753    0.0153394  EM
             10 -0.10044636D+04   18.7824995    0.0183558  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 15


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.16054417D+04    0.0000000    0.0000000  EM
              2 -0.12634854D+04  341.9563118    0.2129983  EM
              3 -0.12208126D+04   42.6728112    0.0337739  EM
              4 -0.11078778D+04  112.9347926    0.0925079  EM
              5 -0.10082026D+04   99.6752613    0.0899695  EM
              6 -0.98366031D+03   24.5422571    0.0243426  EM
              7 -0.97409946D+03    9.5608524    0.0097197  EM
              8 -0.96956995D+03    4.5295144    0.0046500  EM
              9 -0.96739359D+03    2.1763610    0.0022447  EM
             10 -0.96631033D+03    1.0832593    0.0011198  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 16


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.13869042D+04    0.0000000    0.0000000  EM
              2 -0.10835166D+04  303.3876494    0.2187517  EM
              3 -0.98367326D+03   99.8432979    0.0921475  EM
              4 -0.97028845D+03   13.3848041    0.0136070  EM
              5 -0.96685733D+03    3.4311200    0.0035362  EM
              6 -0.96584854D+03    1.0087921    0.0010434  EM
              7 -0.96548979D+03    0.3587519    0.0003714  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 17


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.29268154D+04    0.0000000    0.0000000  EM
              2 -0.10620013D+04 1864.8140480    0.6371478  EM
              3 -0.10082281D+04   53.7732103    0.0506338  EM
              4 -0.99157992D+03   16.6481976    0.0165123  EM
              5 -0.97825706D+03   13.3228593    0.0134360  EM
              6 -0.97139918D+03    6.8578806    0.0070103  EM
              7 -0.96827623D+03    3.1229490    0.0032149  EM
              8 -0.96675415D+03    1.5220842    0.0015720  EM
              9 -0.96598941D+03    0.7647408    0.0007910  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 18


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.25092236D+04    0.0000000    0.0000000  EM
              2 -0.10372505D+04 1471.9731893    0.5866249  EM
              3 -0.99304514D+03   44.2053167    0.0426178  EM
              4 -0.97684831D+03   16.1968297    0.0163103  EM
              5 -0.97035820D+03    6.4901087    0.0066439  EM
              6 -0.96770291D+03    2.6552841    0.0027364  EM
              7 -0.96645399D+03    1.2489192    0.0012906  EM
              8 -0.96583617D+03    0.6178279    0.0006393  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 19


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.29591680D+04    0.0000000    0.0000000  EM
              2 -0.12835674D+04 1675.6005719    0.5662404  EM
              3 -0.12593470D+04   24.2203553    0.0188696  EM
              4 -0.12389982D+04   20.3488665    0.0161583  EM
              5 -0.12063418D+04   32.6564078    0.0263571  EM
              6 -0.11587874D+04   47.5543186    0.0394203  EM
              7 -0.11054792D+04   53.3082606    0.0460035  EM
              8 -0.10711046D+04   34.3745789    0.0310947  EM
              9 -0.10595257D+04   11.5789253    0.0108103  EM
             10 -0.10529623D+04    6.5634056    0.0061947  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 20


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.15746821D+04    0.0000000    0.0000000  EM
              2 -0.12126864D+04  361.9957095    0.2298849  EM
              3 -0.10471607D+04  165.5257274    0.1364951  EM
              4 -0.96978319D+03   77.3774808    0.0738927  EM
              5 -0.96600353D+03    3.7796633    0.0038974  EM
              6 -0.96556698D+03    0.4365451    0.0004519  EM


  FINAL STAGE ITERATIONS


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 3


              5 -0.96528859D+03    0.2065026    0.0002139  EM
              6 -0.96525915D+03    0.0294404    0.0000305  EM
              7 -0.96525050D+03    0.0086493    0.0000090  EM
              8 -0.96524696D+03    0.0035394    0.0000037  EM
              9 -0.96524539D+03    0.0015734    0.0000016  EM
             10 -0.96524467D+03    0.0007113    0.0000007  EM
             11 -0.96524435D+03    0.0003224    0.0000003  EM
             12 -0.96524421D+03    0.0001461    0.0000002  EM
             13 -0.96524414D+03    0.0000662    0.0000001  EM
             14 -0.96524411D+03    0.0000299    0.0000000  EM
             15 -0.96524410D+03    0.0000135    0.0000000  EM
             16 -0.96524409D+03    0.0000061    0.0000000  EM
             17 -0.96524409D+03    0.0000028    0.0000000  EM
             18 -0.96524409D+03    0.0000013    0.0000000  EM
             19 -0.96524409D+03    0.0000006    0.0000000  EM
             20 -0.96524408D+03    0.0000003    0.0000000  EM
             21 -0.96524408D+03    0.0000001    0.0000000  EM
             22 -0.96524408D+03    0.0000001    0.0000000  EM
             23 -0.96524408D+03    0.0000000    0.0000000  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 8


              8 -0.96545790D+03    0.3348001    0.0003467  EM
              9 -0.96533377D+03    0.1241303    0.0001286  EM
             10 -0.96528297D+03    0.0507996    0.0000526  EM
             11 -0.96526122D+03    0.0217444    0.0000225  EM
             12 -0.96525171D+03    0.0095144    0.0000099  EM
             13 -0.96524749D+03    0.0042133    0.0000044  EM
             14 -0.96524561D+03    0.0018791    0.0000019  EM
             15 -0.96524477D+03    0.0008418    0.0000009  EM
             16 -0.96524439D+03    0.0003782    0.0000004  EM
             17 -0.96524422D+03    0.0001703    0.0000002  EM
             18 -0.96524415D+03    0.0000767    0.0000001  EM
             19 -0.96524411D+03    0.0000346    0.0000000  EM
             20 -0.96524410D+03    0.0000156    0.0000000  EM
             21 -0.96524409D+03    0.0000071    0.0000000  EM
             22 -0.96524409D+03    0.0000032    0.0000000  EM
             23 -0.96524409D+03    0.0000014    0.0000000  EM
             24 -0.96524409D+03    0.0000007    0.0000000  EM
             25 -0.96524408D+03    0.0000003    0.0000000  EM
             26 -0.96524408D+03    0.0000001    0.0000000  EM
             27 -0.96524408D+03    0.0000001    0.0000000  EM
             28 -0.96524408D+03    0.0000000    0.0000000  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 16


              7 -0.96548979D+03    0.3587519    0.0003714  EM
              8 -0.96534827D+03    0.1415246    0.0001466  EM
              9 -0.96528932D+03    0.0589420    0.0000611  EM
             10 -0.96526401D+03    0.0253123    0.0000262  EM
             11 -0.96525294D+03    0.0110712    0.0000115  EM
             12 -0.96524804D+03    0.0048978    0.0000051  EM
             13 -0.96524586D+03    0.0021825    0.0000023  EM
             14 -0.96524488D+03    0.0009772    0.0000010  EM
             15 -0.96524444D+03    0.0004388    0.0000005  EM
             16 -0.96524425D+03    0.0001975    0.0000002  EM
             17 -0.96524416D+03    0.0000890    0.0000001  EM
             18 -0.96524412D+03    0.0000401    0.0000000  EM
             19 -0.96524410D+03    0.0000181    0.0000000  EM
             20 -0.96524409D+03    0.0000082    0.0000000  EM
             21 -0.96524409D+03    0.0000037    0.0000000  EM
             22 -0.96524409D+03    0.0000017    0.0000000  EM
             23 -0.96524409D+03    0.0000008    0.0000000  EM
             24 -0.96524408D+03    0.0000003    0.0000000  EM
             25 -0.96524408D+03    0.0000002    0.0000000  EM
             26 -0.96524408D+03    0.0000001    0.0000000  EM
             27 -0.96524408D+03    0.0000000    0.0000000  EM


  TECHNICAL 8 OUTPUT FOR STARTING VALUE SET 2


              5 -0.96551949D+03    0.4163233    0.0004310  EM
              6 -0.96535997D+03    0.1595151    0.0001652  EM
              7 -0.96529424D+03    0.0657366    0.0000681  EM
              8 -0.96526614D+03    0.0281004    0.0000291  EM
              9 -0.96525388D+03    0.0122619    0.0000127  EM
             10 -0.96524846D+03    0.0054174    0.0000056  EM
             11 -0.96524605D+03    0.0024121    0.0000025  EM
             12 -0.96524497D+03    0.0010794    0.0000011  EM
             13 -0.96524448D+03    0.0004846    0.0000005  EM
             14 -0.96524426D+03    0.0002180    0.0000002  EM
             15 -0.96524417D+03    0.0000982    0.0000001  EM
             16 -0.96524412D+03    0.0000443    0.0000000  EM
             17 -0.96524410D+03    0.0000200    0.0000000  EM
             18 -0.96524409D+03    0.0000090    0.0000000  EM
             19 -0.96524409D+03    0.0000041    0.0000000  EM
             20 -0.96524409D+03    0.0000018    0.0000000  EM
             21 -0.96524409D+03    0.0000008    0.0000000  EM
             22 -0.96524408D+03    0.0000004    0.0000000  EM
             23 -0.96524408D+03    0.0000002    0.0000000  EM
             24 -0.96524408D+03    0.0000001    0.0000000  EM
             25 -0.96524408D+03    0.0000000    0.0000000  EM
             26 -0.96524408D+03    0.0000000    0.0000000  EM


     Beginning Time:  23:13:22
        Ending Time:  23:13:22
       Elapsed Time:  00:00:00



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