Measurement equations: continuous indicators

It is actually a simple linear regression.

author:

Michel Bierlaire, EPFL

date:

Thu Apr 13 16:42:02 2023

import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
from biogeme.models import piecewise_formula
import biogeme.loglikelihood as ll
from biogeme.expressions import Beta, Elem, bioMultSum
from biogeme.data.optima import (
    read_data,
    age_65_more,
    ScaledIncome,
    moreThanOneCar,
    moreThanOneBike,
    individualHouse,
    male,
    haveChildren,
    haveGA,
    highEducation,
    Envir01,
    Envir02,
    Envir03,
    Mobil11,
    Mobil14,
    Mobil16,
    Mobil17,
)

logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b01one_latent_regression.py')
Example b01one_latent_regression.py

Parameters to be estimated.

coef_intercept = Beta('coef_intercept', 0.0, None, None, 0)
coef_age_65_more = Beta('coef_age_65_more', 0.0, None, None, 0)
coef_haveGA = Beta('coef_haveGA', 0.0, None, None, 0)
coef_moreThanOneCar = Beta('coef_moreThanOneCar', 0.0, None, None, 0)
coef_moreThanOneBike = Beta('coef_moreThanOneBike', 0.0, None, None, 0)
coef_individualHouse = Beta('coef_individualHouse', 0.0, None, None, 0)
coef_male = Beta('coef_male', 0.0, None, None, 0)
coef_haveChildren = Beta('coef_haveChildren', 0.0, None, None, 0)
coef_highEducation = Beta('coef_highEducation', 0.0, None, None, 0)

thresholds = [None, 4, 6, 8, 10, None]
formula_income = piecewise_formula(variable=ScaledIncome, thresholds=thresholds)

Latent variable: structural equation.

CARLOVERS = (
    coef_intercept
    + coef_age_65_more * age_65_more
    + formula_income
    + coef_moreThanOneCar * moreThanOneCar
    + coef_moreThanOneBike * moreThanOneBike
    + coef_individualHouse * individualHouse
    + coef_male * male
    + coef_haveChildren * haveChildren
    + coef_haveGA * haveGA
    + coef_highEducation * highEducation
)

Measurement equations.

Intercepts.

INTER_Envir01 = Beta('INTER_Envir01', 0, None, None, 1)
INTER_Envir02 = Beta('INTER_Envir02', 0, None, None, 0)
INTER_Envir03 = Beta('INTER_Envir03', 0, None, None, 0)
INTER_Mobil11 = Beta('INTER_Mobil11', 0, None, None, 0)
INTER_Mobil14 = Beta('INTER_Mobil14', 0, None, None, 0)
INTER_Mobil16 = Beta('INTER_Mobil16', 0, None, None, 0)
INTER_Mobil17 = Beta('INTER_Mobil17', 0, None, None, 0)

Coefficients.

B_Envir01_F1 = Beta('B_Envir01_F1', -1, None, None, 1)
B_Envir02_F1 = Beta('B_Envir02_F1', -1, None, None, 0)
B_Envir03_F1 = Beta('B_Envir03_F1', 1, None, None, 0)
B_Mobil11_F1 = Beta('B_Mobil11_F1', 1, None, None, 0)
B_Mobil14_F1 = Beta('B_Mobil14_F1', 1, None, None, 0)
B_Mobil16_F1 = Beta('B_Mobil16_F1', 1, None, None, 0)
B_Mobil17_F1 = Beta('B_Mobil17_F1', 1, None, None, 0)

Linear models.

MODEL_Envir01 = INTER_Envir01 + B_Envir01_F1 * CARLOVERS
MODEL_Envir02 = INTER_Envir02 + B_Envir02_F1 * CARLOVERS
MODEL_Envir03 = INTER_Envir03 + B_Envir03_F1 * CARLOVERS
MODEL_Mobil11 = INTER_Mobil11 + B_Mobil11_F1 * CARLOVERS
MODEL_Mobil14 = INTER_Mobil14 + B_Mobil14_F1 * CARLOVERS
MODEL_Mobil16 = INTER_Mobil16 + B_Mobil16_F1 * CARLOVERS
MODEL_Mobil17 = INTER_Mobil17 + B_Mobil17_F1 * CARLOVERS

Scale parameters.

SIGMA_STAR_Envir01 = Beta('SIGMA_STAR_Envir01', 1, None, None, 0)
SIGMA_STAR_Envir02 = Beta('SIGMA_STAR_Envir02', 1, None, None, 0)
SIGMA_STAR_Envir03 = Beta('SIGMA_STAR_Envir03', 1, None, None, 0)
SIGMA_STAR_Mobil11 = Beta('SIGMA_STAR_Mobil11', 1, None, None, 0)
SIGMA_STAR_Mobil14 = Beta('SIGMA_STAR_Mobil14', 1, None, None, 0)
SIGMA_STAR_Mobil16 = Beta('SIGMA_STAR_Mobil16', 1, None, None, 0)
SIGMA_STAR_Mobil17 = Beta('SIGMA_STAR_Mobil17', 1, None, None, 0)

We build a dict with each contribution to the loglikelihood if (var > 0) and (var < 6). If not, 0 is returned.

F = {
    'Envir01': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir01, MODEL_Envir01, SIGMA_STAR_Envir01),
        },
        (Envir01 > 0) * (Envir01 < 6),
    ),
    'Envir02': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir02, MODEL_Envir02, SIGMA_STAR_Envir02),
        },
        (Envir02 > 0) * (Envir02 < 6),
    ),
    'Envir03': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Envir03, MODEL_Envir03, SIGMA_STAR_Envir03),
        },
        (Envir03 > 0) * (Envir03 < 6),
    ),
    'Mobil11': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil11, MODEL_Mobil11, SIGMA_STAR_Mobil11),
        },
        (Mobil11 > 0) * (Mobil11 < 6),
    ),
    'Mobil14': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil14, MODEL_Mobil14, SIGMA_STAR_Mobil14),
        },
        (Mobil14 > 0) * (Mobil14 < 6),
    ),
    'Mobil16': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil16, MODEL_Mobil16, SIGMA_STAR_Mobil16),
        },
        (Mobil16 > 0) * (Mobil16 < 6),
    ),
    'Mobil17': Elem(
        {
            0: 0,
            1: ll.loglikelihoodregression(Mobil17, MODEL_Mobil17, SIGMA_STAR_Mobil17),
        },
        (Mobil17 > 0) * (Mobil17 < 6),
    ),
}

The log likelihood is the sum of the elements of the above dict

loglike = bioMultSum(F)

Read the data

database = read_data()

Create the Biogeme object.

the_biogeme = bio.BIOGEME(database, loglike)
the_biogeme.modelName = 'b01one_latent_regression'
Default values of the Biogeme parameters are used.
File biogeme.toml has been created

Estimate the parameters

results = the_biogeme.estimate()
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
*** Initial values of the parameters are obtained from the file __b01one_latent_regression.iter
Cannot read file __b01one_latent_regression.iter. Statement is ignored.
As the model is not too complex, we activate the calculation of second derivatives. If you want to change it, change the name of the algorithm in the TOML file from "automatic" to "simple_bounds"
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter.     Function    Relgrad   Radius      Rho
    0      3.2e+04       0.13       10        1   ++
    1      3.2e+04       0.13        5       -7    -
    2      3.2e+04       0.13      2.5     -3.9    -
    3      3.2e+04       0.13      1.2 -4.8e+04    -
    4      3.2e+04       0.13     0.62   -0.018    -
    5      2.6e+04       0.15     0.62     0.82    +
    6      2.3e+04      0.025      6.2     0.95   ++
    7      2.3e+04      0.025      3.1 -6.9e+02    -
    8      2.3e+04      0.025      1.6      -80    -
    9      2.3e+04      0.025     0.78      -17    -
   10      2.3e+04      0.025     0.39     -1.9    -
   11      2.3e+04      0.025      0.2    0.011    -
   12      2.3e+04      0.075      0.2     0.61    +
   13      2.2e+04      0.015        2        1   ++
   14      2.2e+04      0.015     0.98      -49    -
   15      2.2e+04      0.015     0.49     -2.7    -
   16      2.2e+04      0.015     0.24    0.027    -
   17      2.2e+04      0.064     0.24     0.65    +
   18      2.2e+04      0.014     0.24     0.73    +
   19      2.2e+04      0.076     0.24     0.24    +
   20      2.1e+04      0.042     0.24     0.45    +
   21      2.1e+04      0.042     0.12    -0.62    -
   22      2.1e+04      0.042    0.061   0.0064    -
   23      2.1e+04      0.049    0.061     0.24    +
   24      2.1e+04     0.0098     0.61        1   ++
   25      2.1e+04     0.0098     0.31     -4.9    -
   26      2.1e+04     0.0098     0.15    -0.86    -
   27      2.1e+04      0.068     0.15     0.29    +
   28      2.1e+04      0.068    0.076    -0.15    -
   29      2.1e+04      0.031    0.076     0.31    +
   30      2.1e+04      0.031    0.038    -0.76    -
   31      2.1e+04      0.037    0.038     0.26    +
   32      2.1e+04     0.0068     0.38      1.1   ++
   33      2.1e+04     0.0068     0.19      -10    -
   34      2.1e+04     0.0068    0.095     -3.1    -
   35      2.1e+04     0.0068    0.048    -0.78    -
   36      2.1e+04      0.037    0.048     0.46    +
   37      2.1e+04      0.022    0.048     0.27    +
   38      2.1e+04      0.022    0.024     -0.1    -
   39      2.1e+04      0.023    0.024     0.46    +
   40      2.1e+04     0.0049     0.24      1.2   ++
   41      2.1e+04     0.0049     0.12     -5.3    -
   42      2.1e+04     0.0049     0.06     -1.3    -
   43      2.1e+04     0.0049     0.03    0.046    -
   44      2.1e+04      0.025     0.03     0.64    +
   45      2.1e+04      0.013     0.03     0.44    +
   46      2.1e+04      0.013    0.015    -0.14    -
   47      2.1e+04      0.017    0.015     0.35    +
   48      2.1e+04     0.0024     0.15      1.1   ++
   49      2.1e+04     0.0024    0.075     -2.4    -
   50      2.1e+04     0.0024    0.037    -0.23    -
   51      2.1e+04      0.029    0.037     0.49    +
   52      2.1e+04      0.029    0.019    0.073    -
   53      2.1e+04     0.0093    0.019     0.54    +
   54      2.1e+04     0.0056    0.019     0.84    +
   55      2.1e+04     0.0031     0.19      1.3   ++
   56      2.1e+04     0.0031    0.093    -0.93    -
   57      2.1e+04      0.035    0.093     0.53    +
   58      2.1e+04      0.035    0.047    -0.27    -
   59      2.1e+04      0.028    0.047     0.15    +
   60      2.1e+04      0.028    0.023    0.016    -
   61      2.1e+04      0.022    0.023     0.43    +
   62      2.1e+04      0.013    0.023     0.22    +
   63      2.1e+04      0.016    0.023     0.49    +
   64      2.1e+04     0.0065    0.023     0.69    +
   65      2.1e+04      0.023    0.023     0.15    +
   66      2.1e+04      0.011    0.023     0.41    +
   67      2.1e+04      0.011    0.012    0.075    -
   68      2.1e+04      0.011    0.012     0.61    +
   69      2.1e+04     0.0036     0.12      1.1   ++
   70      2.1e+04     0.0036    0.058     -0.9    -
   71      2.1e+04      0.039    0.058     0.39    +
   72      2.1e+04      0.039    0.029    -0.44    -
   73      2.1e+04      0.021    0.029     0.29    +
   74      2.1e+04      0.031    0.029     0.17    +
   75      2.1e+04       0.02    0.029     0.15    +
   76      2.1e+04      0.031    0.029     0.26    +
   77      2.1e+04      0.021    0.029     0.19    +
   78      2.1e+04      0.031    0.029     0.21    +
   79      2.1e+04      0.021    0.029     0.16    +
   80      2.1e+04      0.031    0.029     0.23    +
   81      2.1e+04      0.022    0.029     0.18    +
   82      2.1e+04      0.031    0.029     0.19    +
   83      2.1e+04      0.021    0.029     0.19    +
   84      2.1e+04      0.021    0.015    0.098    -
   85      2.1e+04      0.004     0.15     0.91   ++
   86      2.1e+04      0.029      1.5     0.94   ++
   87      2.1e+04      0.029     0.73      -10    -
   88      2.1e+04      0.029     0.36     -5.9    -
   89      2.1e+04      0.029     0.18     -3.2    -
   90      2.1e+04      0.029    0.091     -1.5    -
   91      2.1e+04      0.029    0.045    -0.49    -
   92      2.1e+04      0.029    0.023    0.089    -
   93      2.1e+04      0.017    0.023      0.4    +
   94      2.1e+04      0.013    0.023      0.7    +
   95      2.1e+04      0.014    0.023     0.38    +
   96      2.1e+04      0.023    0.023     0.18    +
   97      2.1e+04      0.013    0.023     0.31    +
   98      2.1e+04      0.024    0.023     0.28    +
   99      2.1e+04      0.016    0.023      0.3    +
  100      2.1e+04      0.023    0.023     0.22    +
  101      2.1e+04      0.015    0.023     0.31    +
  102      2.1e+04      0.024    0.023     0.17    +
  103      2.1e+04      0.016    0.023     0.34    +
  104      2.1e+04      0.022    0.023     0.22    +
  105      2.1e+04      0.015    0.023     0.33    +
  106      2.1e+04      0.022    0.023     0.23    +
  107      2.1e+04      0.015    0.023     0.29    +
  108      2.1e+04      0.022    0.023     0.25    +
  109      2.1e+04      0.015    0.023     0.28    +
  110      2.1e+04      0.022    0.023     0.27    +
  111      2.1e+04      0.016    0.023     0.24    +
  112      2.1e+04      0.022    0.023     0.25    +
  113      2.1e+04      0.016    0.023     0.32    +
  114      2.1e+04      0.022    0.023     0.23    +
  115      2.1e+04      0.016    0.023     0.28    +
  116      2.1e+04      0.022    0.023     0.23    +
  117      2.1e+04      0.016    0.023     0.29    +
  118      2.1e+04      0.022    0.023     0.24    +
  119      2.1e+04      0.016    0.023     0.26    +
  120      2.1e+04      0.022    0.023     0.25    +
  121      2.1e+04      0.016    0.023     0.26    +
  122      2.1e+04      0.022    0.023     0.26    +
  123      2.1e+04      0.016    0.023     0.25    +
  124      2.1e+04      0.022    0.023     0.26    +
  125      2.1e+04      0.016    0.023     0.26    +
  126      2.1e+04      0.022    0.023     0.25    +
  127      2.1e+04      0.017    0.023     0.25    +
  128      2.1e+04      0.022    0.023     0.25    +
  129      2.1e+04      0.017    0.023     0.26    +
  130      2.1e+04      0.022    0.023     0.24    +
  131      2.1e+04      0.017    0.023     0.26    +
  132      2.1e+04      0.022    0.023     0.23    +
  133      2.1e+04      0.017    0.023     0.27    +
  134      2.1e+04      0.022    0.023     0.22    +
  135      2.1e+04      0.017    0.023     0.28    +
  136      2.1e+04      0.022    0.023      0.2    +
  137      2.1e+04      0.017    0.023     0.29    +
  138      2.1e+04      0.022    0.023     0.18    +
  139      2.1e+04      0.017    0.023     0.31    +
  140      2.1e+04      0.022    0.023     0.16    +
  141      2.1e+04      0.017    0.023     0.33    +
  142      2.1e+04      0.022    0.023     0.13    +
  143      2.1e+04      0.017    0.023     0.33    +
  144      2.1e+04      0.022    0.023     0.14    +
  145      2.1e+04      0.017    0.023     0.34    +
  146      2.1e+04      0.022    0.023     0.13    +
  147      2.1e+04      0.017    0.023     0.34    +
  148      2.1e+04      0.022    0.023     0.12    +
  149      2.1e+04      0.017    0.023     0.35    +
  150      2.1e+04      0.022    0.023      0.1    +
  151      2.1e+04      0.017    0.023     0.36    +
  152      2.1e+04      0.019    0.023     0.16    +
  153        2e+04      0.017    0.023     0.34    +
  154        2e+04      0.022    0.023     0.12    +
  155        2e+04      0.011    0.023     0.55    +
  156        2e+04      0.023    0.023     0.17    +
  157        2e+04      0.016    0.023     0.34    +
  158        2e+04      0.011    0.023     0.54    +
  159        2e+04      0.013    0.023     0.35    +
  160        2e+04      0.014    0.023     0.47    +
  161        2e+04      0.014    0.011    0.062    -
  162        2e+04     0.0028    0.011     0.89    +
  163        2e+04     0.0035     0.11        1   ++
  164        2e+04      0.022     0.11     0.81    +
  165        2e+04      0.022    0.057       -1    -
  166        2e+04      0.022    0.028    -0.19    -
  167        2e+04      0.014    0.028     0.67    +
  168        2e+04      0.022    0.028     0.29    +
  169        2e+04     0.0075    0.028     0.74    +
  170        2e+04     0.0075    0.014    0.077    -
  171        2e+04     0.0047    0.014      0.8    +
  172        2e+04     0.0022     0.14     0.96   ++
  173        2e+04     0.0022    0.071    -0.33    -
  174        2e+04      0.034    0.071     0.34    +
  175        2e+04      0.034    0.036    -0.48    -
  176        2e+04      0.034    0.018     0.06    -
  177        2e+04      0.015    0.018     0.54    +
  178        2e+04      0.003     0.18      1.1   ++
  179        2e+04      0.042     0.18     0.35    +
  180        2e+04      0.042    0.089     -1.1    -
  181        2e+04      0.042    0.044    -0.21    -
  182        2e+04      0.039    0.044     0.24    +
  183        2e+04      0.019    0.044     0.58    +
  184        2e+04      0.019    0.022    -0.12    -
  185        2e+04      0.016    0.022     0.55    +
  186        2e+04     0.0089    0.022     0.85    +
  187        2e+04     0.0034     0.22     0.93   ++
  188        2e+04     0.0034     0.11     -2.7    -
  189        2e+04     0.0034    0.056     -1.2    -
  190        2e+04     0.0034    0.028    -0.33    -
  191        2e+04      0.018    0.028      0.2    +
  192        2e+04      0.019    0.028     0.24    +
  193        2e+04      0.025    0.028     0.16    +
  194        2e+04      0.022    0.028     0.22    +
  195        2e+04      0.026    0.028     0.17    +
  196        2e+04      0.026    0.014    0.056    -
  197        2e+04      0.013    0.014     0.47    +
  198        2e+04      0.004     0.14     0.92   ++
  199        2e+04      0.004    0.069       -3    -
  200        2e+04      0.004    0.035     -2.5    -
  201        2e+04      0.004    0.017    -0.26    -
  202        2e+04      0.014    0.017     0.43    +
  203        2e+04      0.011    0.017      0.5    +
  204        2e+04      0.013    0.017     0.47    +
  205        2e+04      0.017    0.017      0.2    +
  206        2e+04     0.0076    0.017     0.65    +
  207        2e+04      0.011    0.017      0.6    +
  208        2e+04      0.012    0.017     0.38    +
  209        2e+04      0.016    0.017      0.4    +
  210        2e+04      0.012    0.017     0.35    +
  211        2e+04      0.011    0.017     0.59    +
  212        2e+04      0.014    0.017     0.31    +
  213        2e+04     0.0074    0.017     0.67    +
  214        2e+04     0.0092    0.017     0.59    +
  215        2e+04     0.0079    0.017     0.65    +
  216        2e+04     0.0094    0.017      0.6    +
  217        2e+04      0.012    0.017     0.48    +
  218        2e+04      0.016    0.017     0.38    +
  219        2e+04      0.014    0.017     0.25    +
  220        2e+04      0.012    0.017      0.5    +
  221        2e+04      0.016    0.017     0.19    +
  222        2e+04      0.012    0.017     0.48    +
  223        2e+04      0.014    0.017     0.35    +
  224        2e+04      0.012    0.017     0.48    +
  225        2e+04      0.014    0.017     0.37    +
  226        2e+04      0.011    0.017     0.52    +
  227        2e+04     0.0093    0.017     0.65    +
  228        2e+04      0.011    0.017     0.45    +
  229        2e+04     0.0098    0.017     0.44    +
  230        2e+04       0.01    0.017     0.56    +
  231        2e+04     0.0088    0.017     0.52    +
  232        2e+04     0.0093    0.017     0.59    +
  233        2e+04       0.01    0.017     0.51    +
  234        2e+04      0.012    0.017     0.45    +
  235        2e+04     0.0092    0.017     0.57    +
  236        2e+04     0.0097    0.017     0.51    +
  237        2e+04       0.01    0.017     0.53    +
  238        2e+04      0.011    0.017     0.44    +
  239        2e+04      0.012    0.017     0.37    +
  240        2e+04      0.013    0.017     0.47    +
  241        2e+04      0.015    0.017     0.34    +
  242        2e+04      0.015    0.017     0.36    +
  243        2e+04     0.0092    0.017     0.53    +
  244        2e+04     0.0077    0.017     0.57    +
  245        2e+04       0.01    0.017     0.61    +
  246        2e+04      0.012    0.017     0.37    +
  247        2e+04      0.016    0.017      0.4    +
  248        2e+04      0.014    0.017      0.2    +
  249        2e+04     0.0068    0.017     0.73    +
  250        2e+04      0.014    0.017     0.31    +
  251        2e+04     0.0077    0.017     0.67    +
  252        2e+04     0.0069    0.017     0.62    +
  253        2e+04       0.01    0.017     0.61    +
  254        2e+04      0.009    0.017     0.49    +
  255        2e+04      0.013    0.017     0.49    +
  256        2e+04      0.012    0.017     0.41    +
  257        2e+04      0.013    0.017     0.41    +
  258        2e+04      0.013    0.017      0.4    +
  259        2e+04      0.015    0.017     0.31    +
  260        2e+04      0.017    0.017     0.33    +
  261        2e+04     0.0092    0.017     0.55    +
  262        2e+04      0.014    0.017     0.28    +
  263        2e+04      0.011    0.017     0.57    +
  264        2e+04      0.011    0.017     0.32    +
  265        2e+04     0.0095    0.017     0.63    +
  266        2e+04     0.0091    0.017     0.51    +
  267        2e+04     0.0094    0.017      0.6    +
  268        2e+04      0.011    0.017     0.46    +
  269        2e+04      0.012    0.017     0.42    +
  270        2e+04       0.01    0.017     0.55    +
  271        2e+04       0.01    0.017     0.47    +
  272        2e+04     0.0073    0.017     0.65    +
  273        2e+04     0.0073    0.017     0.72    +
  274        2e+04     0.0099    0.017     0.45    +
  275        2e+04      0.012    0.017     0.54    +
  276        2e+04      0.014    0.017     0.28    +
  277        2e+04     0.0075    0.017     0.63    +
  278        2e+04      0.011    0.017     0.48    +
  279        2e+04     0.0074    0.017     0.65    +
  280        2e+04     0.0098    0.017     0.57    +
  281        2e+04     0.0076    0.017     0.63    +
  282        2e+04      0.012    0.017     0.47    +
  283        2e+04       0.01    0.017     0.54    +
  284        2e+04      0.015    0.017     0.39    +
  285        2e+04      0.015    0.017      0.3    +
  286        2e+04     0.0091    0.017      0.6    +
  287        2e+04     0.0071    0.017     0.61    +
  288        2e+04       0.01    0.017     0.53    +
  289        2e+04     0.0092    0.017      0.6    +
  290        2e+04      0.015    0.017     0.29    +
  291        2e+04     0.0085    0.017     0.62    +
  292        2e+04       0.01    0.017     0.44    +
  293        2e+04     0.0052    0.017     0.77    +
  294        2e+04     0.0072    0.017     0.71    +
  295        2e+04     0.0087    0.017     0.64    +
  296        2e+04      0.011    0.017     0.42    +
  297        2e+04     0.0069    0.017     0.66    +
  298        2e+04     0.0087    0.017     0.57    +
  299        2e+04     0.0084    0.017     0.66    +
  300        2e+04      0.013    0.017     0.36    +
  301        2e+04     0.0075    0.017     0.63    +
  302        2e+04     0.0095    0.017     0.53    +
  303        2e+04     0.0062    0.017     0.71    +
  304        2e+04     0.0087    0.017     0.57    +
  305        2e+04     0.0083    0.017     0.66    +
  306        2e+04      0.012    0.017     0.39    +
  307        2e+04     0.0086    0.017     0.58    +
  308        2e+04      0.012    0.017     0.45    +
  309        2e+04     0.0075    0.017     0.63    +
  310        2e+04       0.01    0.017     0.53    +
  311        2e+04     0.0053    0.017     0.73    +
  312        2e+04     0.0074    0.017     0.67    +
  313        2e+04     0.0064    0.017     0.74    +
  314        2e+04      0.011    0.017     0.48    +
  315        2e+04     0.0057    0.017     0.72    +
  316        2e+04     0.0084    0.017     0.62    +
  317        2e+04     0.0038    0.017     0.81    +
  318        2e+04     0.0063    0.017     0.74    +
  319        2e+04     0.0046    0.017     0.81    +
  320        2e+04     0.0094    0.017     0.57    +
  321        2e+04      0.004    0.017      0.8    +
  322        2e+04     0.0068    0.017     0.71    +
  323        2e+04     0.0032    0.017     0.85    +
  324        2e+04     0.0067    0.017     0.73    +
  325        2e+04     0.0031    0.017     0.86    +
  326        2e+04      0.007    0.017     0.72    +
  327        2e+04     0.0027    0.017     0.87    +
  328        2e+04     0.0063    0.017     0.76    +
  329        2e+04     0.0027    0.017     0.87    +
  330        2e+04      0.007    0.017     0.73    +
  331        2e+04     0.0024    0.017     0.87    +
  332        2e+04     0.0062    0.017     0.77    +
  333        2e+04     0.0024    0.017     0.87    +
  334        2e+04     0.0068    0.017     0.75    +
  335        2e+04     0.0022    0.017     0.88    +
  336        2e+04     0.0063    0.017     0.78    +
  337        2e+04     0.0021    0.017     0.88    +
  338        2e+04     0.0066    0.017     0.77    +
  339        2e+04     0.0023    0.017     0.88    +
  340        2e+04     0.0064    0.017     0.78    +
  341        2e+04     0.0023    0.017     0.88    +
  342        2e+04     0.0064    0.017     0.78    +
  343        2e+04     0.0023    0.017     0.88    +
  344        2e+04     0.0063    0.017      0.8    +
  345        2e+04     0.0023    0.017     0.88    +
  346        2e+04     0.0062    0.017      0.8    +
  347        2e+04     0.0023    0.017     0.89    +
  348        2e+04     0.0061    0.017     0.81    +
  349        2e+04     0.0023    0.017     0.89    +
  350        2e+04     0.0059    0.017     0.83    +
  351        2e+04     0.0024    0.017      0.9    +
  352        2e+04     0.0057    0.017     0.84    +
  353        2e+04     0.0024     0.17      0.9   ++
  354        2e+04     0.0024    0.087    0.012    -
  355        2e+04      0.032    0.087     0.28    +
  356        2e+04      0.032    0.043    -0.77    -
  357        2e+04       0.02    0.043      0.5    +
  358        2e+04       0.02    0.022    -0.67    -
  359        2e+04     0.0086    0.022     0.65    +
  360        2e+04     0.0067    0.022     0.61    +
  361        2e+04      0.015    0.022     0.47    +
  362        2e+04      0.014    0.022     0.46    +
  363        2e+04      0.019    0.022     0.28    +
  364        2e+04      0.015    0.022     0.45    +
  365        2e+04      0.019    0.022     0.14    +
  366        2e+04      0.015    0.022     0.46    +
  367        2e+04      0.019    0.022     0.32    +
  368        2e+04      0.015    0.022     0.26    +
  369        2e+04      0.018    0.022      0.4    +
  370        2e+04      0.013    0.022      0.4    +
  371        2e+04      0.018    0.022     0.39    +
  372        2e+04      0.014    0.022     0.46    +
  373        2e+04      0.019    0.022     0.21    +
  374        2e+04      0.012    0.022     0.49    +
  375        2e+04       0.02    0.022     0.32    +
  376        2e+04      0.013    0.022     0.47    +
  377        2e+04       0.02    0.022     0.29    +
  378        2e+04      0.013    0.022     0.51    +
  379        2e+04      0.021    0.022     0.28    +
  380        2e+04      0.014    0.022     0.49    +
  381        2e+04      0.017    0.022     0.34    +
  382        2e+04      0.011    0.022     0.59    +
  383        2e+04      0.017    0.022     0.35    +
  384        2e+04     0.0064    0.022     0.75    +
  385        2e+04     0.0083    0.022     0.69    +
  386        2e+04     0.0055    0.022      0.7    +
  387        2e+04      0.014    0.022     0.54    +
  388        2e+04     0.0067    0.022     0.69    +
  389        2e+04      0.021    0.022      0.2    +
  390        2e+04     0.0067    0.022     0.79    +
  391        2e+04      0.011    0.022     0.56    +
  392        2e+04     0.0062    0.022     0.75    +
  393        2e+04      0.013    0.022     0.47    +
  394        2e+04     0.0067    0.022     0.76    +
  395        2e+04      0.013    0.022     0.46    +
  396        2e+04     0.0049    0.022     0.82    +
  397        2e+04      0.012    0.022     0.46    +
  398        2e+04     0.0033    0.022     0.89    +
  399        2e+04     0.0097    0.022     0.53    +
  400        2e+04     0.0031    0.022     0.88    +
  401        2e+04       0.01    0.022     0.63    +
  402        2e+04     0.0042    0.022     0.77    +
  403        2e+04      0.015    0.022     0.52    +
  404        2e+04      0.012    0.022      0.6    +
  405        2e+04      0.018    0.022     0.28    +
  406        2e+04     0.0062    0.022      0.8    +
  407        2e+04      0.012    0.022     0.34    +
  408        2e+04     0.0044    0.022     0.87    +
  409        2e+04      0.012    0.022     0.52    +
  410        2e+04     0.0048    0.022     0.76    +
  411        2e+04      0.014    0.022     0.59    +
  412        2e+04     0.0039    0.022     0.76    +
  413        2e+04      0.012    0.022     0.56    +
  414        2e+04     0.0041    0.022     0.86    +
  415        2e+04      0.011    0.022     0.65    +
  416        2e+04     0.0043    0.022     0.88    +
  417        2e+04     0.0059    0.022     0.77    +
  418        2e+04     0.0047     0.22     0.94   ++
  419        2e+04     0.0047     0.11   -0.091    -
  420        2e+04      0.027     0.11     0.21    +
  421        2e+04      0.027    0.054    -0.51    -
  422      1.9e+04      0.012    0.054     0.81    +
  423      1.9e+04      0.012    0.027    -0.45    -
  424      1.9e+04      0.021    0.027     0.27    +
  425      1.9e+04     0.0088    0.027      0.7    +
  426      1.9e+04      0.021    0.027      0.2    +
  427      1.9e+04     0.0074    0.027     0.74    +
  428      1.9e+04     0.0074    0.014    0.076    -
  429      1.9e+04      0.012    0.014     0.62    +
  430      1.9e+04     0.0056     0.14     0.95   ++
  431      1.9e+04     0.0056    0.068    0.044    -
  432      1.9e+04      0.017    0.068     0.27    +
  433      1.9e+04     0.0097    0.068     0.61    +
  434      1.9e+04     0.0097    0.034    -0.41    -
  435      1.9e+04      0.024    0.034      0.3    +
  436      1.9e+04     0.0069    0.034     0.87    +
  437      1.9e+04     0.0061     0.34     0.96   ++
  438      1.9e+04     0.0061     0.17    -0.36    -
  439      1.9e+04     0.0061    0.085    -0.17    -
  440      1.9e+04      0.037    0.085     0.18    +
  441      1.9e+04       0.04    0.085      0.2    +
  442      1.9e+04       0.04    0.042    -0.17    -
  443      1.9e+04      0.033    0.042      0.4    +
  444      1.9e+04      0.012    0.042     0.89    +
  445      1.9e+04      0.011    0.042     0.87    +
  446      1.9e+04      0.012    0.042      0.7    +
  447      1.9e+04     0.0066    0.042     0.86    +
  448      1.9e+04      0.014    0.042     0.58    +
  449      1.9e+04     0.0062    0.042     0.85    +
  450      1.9e+04      0.011    0.042     0.59    +
  451      1.9e+04     0.0064    0.042     0.79    +
  452      1.9e+04      0.013    0.042     0.52    +
  453      1.9e+04     0.0059    0.042     0.78    +
  454      1.9e+04       0.01    0.042     0.57    +
  455      1.9e+04     0.0052    0.042     0.75    +
  456      1.9e+04     0.0052    0.021    0.084    -
  457      1.9e+04     0.0068    0.021     0.68    +
  458      1.9e+04     0.0033    0.021     0.81    +
  459      1.9e+04     0.0074    0.021     0.54    +
  460      1.9e+04     0.0024    0.021     0.86    +
  461      1.9e+04     0.0059    0.021     0.51    +
  462      1.9e+04     0.0018    0.021     0.88    +
  463      1.9e+04     0.0048    0.021     0.54    +
  464      1.9e+04     0.0017     0.21     0.92   ++
  465      1.9e+04     0.0017     0.11     -4.2    -
  466      1.9e+04     0.0017    0.053     -3.5    -
  467      1.9e+04     0.0017    0.026    -0.86    -
  468      1.9e+04     0.0057    0.026      0.3    +
  469      1.9e+04     0.0034    0.026     0.63    +
  470      1.9e+04     0.0079    0.026     0.15    +
  471      1.9e+04     0.0047    0.026     0.36    +
  472      1.9e+04     0.0047    0.013    0.083    -
  473      1.9e+04      0.004    0.013     0.53    +
  474      1.9e+04     0.0018     0.13     0.96   ++
  475      1.9e+04     0.0018    0.066    -0.56    -
  476      1.9e+04     0.0018    0.033   -0.083    -
  477      1.9e+04     0.0053    0.033     0.34    +
  478      1.9e+04     0.0053    0.017    -0.67    -
  479      1.9e+04      0.003    0.017     0.48    +
  480      1.9e+04     0.0043    0.017     0.25    +
  481      1.9e+04     0.0035    0.017     0.36    +
  482      1.9e+04     0.0036    0.017      0.3    +
  483      1.9e+04     0.0034    0.017     0.35    +
  484      1.9e+04     0.0043    0.017     0.31    +
  485      1.9e+04     0.0036    0.017     0.23    +
  486      1.9e+04     0.0043    0.017     0.35    +
  487      1.9e+04     0.0035    0.017     0.12    +
  488      1.9e+04     0.0039    0.017     0.41    +
  489      1.9e+04     0.0039   0.0083   0.0072    -
  490      1.9e+04     0.0019   0.0083     0.68    +
  491      1.9e+04     0.0016   0.0083      0.6    +
  492      1.9e+04     0.0014    0.083     0.95   ++
  493      1.9e+04     0.0014    0.041    -0.12    -
  494      1.9e+04     0.0043    0.041     0.29    +
  495      1.9e+04     0.0043    0.021     -1.8    -
  496      1.9e+04     0.0043     0.01   0.0033    -
  497      1.9e+04     0.0022     0.01     0.59    +
  498      1.9e+04     0.0017     0.01     0.57    +
  499      1.9e+04     0.0021     0.01     0.44    +
  500      1.9e+04     0.0025     0.01     0.31    +
  501      1.9e+04     0.0024     0.01     0.29    +
  502      1.9e+04     0.0021     0.01     0.42    +
  503      1.9e+04     0.0023     0.01     0.29    +
  504      1.9e+04     0.0026     0.01     0.42    +
  505      1.9e+04     0.0022     0.01     0.21    +
  506      1.9e+04     0.0026     0.01     0.44    +
  507      1.9e+04      0.002     0.01     0.22    +
  508      1.9e+04     0.0024     0.01      0.4    +
  509      1.9e+04      0.002     0.01     0.24    +
  510      1.9e+04     0.0029     0.01     0.29    +
  511      1.9e+04     0.0024     0.01     0.11    +
  512      1.9e+04     0.0028     0.01     0.43    +
  513      1.9e+04     0.0017     0.01      0.2    +
  514      1.9e+04     0.0025     0.01     0.22    +
  515      1.9e+04     0.0025     0.01     0.13    +
  516      1.9e+04     0.0029     0.01     0.33    +
  517      1.9e+04     0.0029   0.0052    -0.12    -
  518      1.9e+04     0.0013   0.0052     0.64    +
  519      1.9e+04     0.0022   0.0052     0.23    +
  520      1.9e+04     0.0013   0.0052     0.57    +
  521      1.9e+04     0.0018   0.0052     0.36    +
  522      1.9e+04     0.0012   0.0052     0.59    +
  523      1.9e+04     0.0016   0.0052     0.42    +
  524      1.9e+04     0.0011   0.0052     0.63    +
  525      1.9e+04     0.0016   0.0052     0.39    +
  526      1.9e+04     0.0011   0.0052     0.55    +
  527      1.9e+04     0.0015   0.0052     0.45    +
  528      1.9e+04      0.001   0.0052     0.61    +
  529      1.9e+04     0.0015   0.0052      0.4    +
  530      1.9e+04     0.0011   0.0052     0.48    +
  531      1.9e+04     0.0014   0.0052     0.49    +
  532      1.9e+04    0.00094   0.0052     0.63    +
  533      1.9e+04     0.0015   0.0052     0.39    +
  534      1.9e+04     0.0011   0.0052     0.37    +
  535      1.9e+04     0.0013   0.0052     0.53    +
  536      1.9e+04    0.00074   0.0052     0.77    +
  537      1.9e+04     0.0012   0.0052     0.39    +
  538      1.9e+04      0.001   0.0052     0.43    +
  539      1.9e+04     0.0014   0.0052     0.45    +
  540      1.9e+04     0.0009   0.0052     0.55    +
  541      1.9e+04     0.0014   0.0052     0.46    +
  542      1.9e+04    0.00084   0.0052     0.45    +
  543      1.9e+04     0.0011   0.0052     0.34    +
  544      1.9e+04    0.00081   0.0052     0.66    +
  545      1.9e+04     0.0015   0.0052     0.32    +
  546      1.9e+04     0.0015   0.0026    0.046    -
  547      1.9e+04    0.00068   0.0026     0.71    +
  548      1.9e+04     0.0011   0.0026     0.17    +
  549      1.9e+04    0.00064   0.0026     0.78    +
  550      1.9e+04     0.0009   0.0026     0.53    +
  551      1.9e+04    0.00052   0.0026     0.88    +
  552      1.9e+04    0.00087   0.0026     0.42    +
  553      1.9e+04    0.00056   0.0026      0.8    +
  554      1.9e+04    0.00086   0.0026     0.54    +
  555      1.9e+04    0.00052   0.0026     0.82    +
  556      1.9e+04    0.00084   0.0026     0.42    +
  557      1.9e+04     0.0005   0.0026     0.83    +
  558      1.9e+04    0.00087   0.0026     0.53    +
  559      1.9e+04    0.00052   0.0026     0.78    +
  560      1.9e+04    0.00085   0.0026     0.47    +
  561      1.9e+04    0.00047   0.0026     0.82    +
  562      1.9e+04    0.00088   0.0026      0.5    +
  563      1.9e+04    0.00049   0.0026     0.76    +
  564      1.9e+04    0.00086   0.0026     0.49    +
  565      1.9e+04    0.00046   0.0026      0.8    +
  566      1.9e+04    0.00087   0.0026     0.49    +
  567      1.9e+04    0.00046   0.0026     0.76    +
  568      1.9e+04    0.00085   0.0026     0.48    +
  569      1.9e+04    0.00044   0.0026     0.77    +
  570      1.9e+04    0.00085   0.0026     0.48    +
  571      1.9e+04    0.00044   0.0026     0.76    +
  572      1.9e+04    0.00084   0.0026     0.48    +
  573      1.9e+04    0.00042   0.0026     0.75    +
  574      1.9e+04    0.00084   0.0026     0.48    +
  575      1.9e+04    0.00042   0.0026     0.75    +
  576      1.9e+04    0.00084   0.0026     0.48    +
  577      1.9e+04    0.00041   0.0026     0.74    +
  578      1.9e+04    0.00083   0.0026     0.47    +
  579      1.9e+04     0.0004   0.0026     0.73    +
  580      1.9e+04    0.00083   0.0026     0.47    +
  581      1.9e+04    0.00039   0.0026     0.73    +
  582      1.9e+04    0.00082   0.0026     0.47    +
  583      1.9e+04    0.00038   0.0026     0.72    +
  584      1.9e+04    0.00082   0.0026     0.47    +
  585      1.9e+04    0.00037   0.0026     0.71    +
  586      1.9e+04    0.00081   0.0026     0.47    +
  587      1.9e+04    0.00037   0.0026     0.71    +
  588      1.9e+04    0.00081   0.0026     0.47    +
  589      1.9e+04    0.00036   0.0026      0.7    +
  590      1.9e+04     0.0008   0.0026     0.47    +
  591      1.9e+04    0.00035   0.0026      0.7    +
  592      1.9e+04     0.0008   0.0026     0.47    +
  593      1.9e+04    0.00034   0.0026     0.69    +
  594      1.9e+04    0.00079   0.0026     0.47    +
  595      1.9e+04    0.00034   0.0026     0.69    +
  596      1.9e+04    0.00078   0.0026     0.47    +
  597      1.9e+04    0.00033   0.0026     0.68    +
  598      1.9e+04    0.00078   0.0026     0.47    +
  599      1.9e+04    0.00032   0.0026     0.68    +
  600      1.9e+04    0.00077   0.0026     0.47    +
  601      1.9e+04    0.00032   0.0026     0.68    +
  602      1.9e+04    0.00076   0.0026     0.47    +
  603      1.9e+04    0.00032   0.0026     0.68    +
  604      1.9e+04    0.00075   0.0026     0.46    +
  605      1.9e+04    0.00032   0.0026     0.66    +
  606      1.9e+04    0.00079   0.0026     0.43    +
  607      1.9e+04    0.00032   0.0026     0.58    +
  608      1.9e+04    0.00069   0.0026     0.49    +
  609      1.9e+04    0.00031   0.0026     0.78    +
  610      1.9e+04    0.00079   0.0026     0.44    +
  611      1.9e+04    0.00033   0.0026     0.55    +
  612      1.9e+04     0.0007   0.0026     0.49    +
  613      1.9e+04     0.0003   0.0026     0.77    +
  614      1.9e+04    0.00079   0.0026     0.43    +
  615      1.9e+04    0.00034   0.0026     0.52    +
  616      1.9e+04    0.00069   0.0026      0.5    +
  617      1.9e+04     0.0003   0.0026     0.79    +
  618      1.9e+04    0.00079   0.0026     0.42    +
  619      1.9e+04    0.00035   0.0026     0.49    +
  620      1.9e+04    0.00067   0.0026      0.5    +
  621      1.9e+04    0.00029   0.0026     0.82    +
  622      1.9e+04     0.0008   0.0026     0.42    +
  623      1.9e+04    0.00036   0.0026     0.44    +
  624      1.9e+04    0.00065   0.0026     0.51    +
  625      1.9e+04    0.00028   0.0026     0.87    +
  626      1.9e+04    0.00081   0.0026     0.41    +
  627      1.9e+04    0.00039   0.0026     0.37    +
  628      1.9e+04    0.00062   0.0026     0.51    +
  629      1.9e+04    0.00027    0.026     0.93   ++
  630      1.9e+04    0.00027    0.013     -1.8    -
  631      1.9e+04    0.00027   0.0065     -1.4    -
  632      1.9e+04    0.00027   0.0032    -0.72    -
  633      1.9e+04    0.00093   0.0032     0.24    +
  634      1.9e+04    0.00093   0.0016    -0.12    -
  635      1.9e+04    0.00041   0.0016     0.73    +
  636      1.9e+04    0.00093   0.0016      0.2    +
  637      1.9e+04    0.00054   0.0016     0.46    +
  638      1.9e+04    0.00051   0.0016     0.51    +
  639      1.9e+04    0.00034    0.016     0.93   ++
  640      1.9e+04    0.00034   0.0081     -1.7    -
  641      1.9e+04    0.00034    0.004    -0.99    -
  642      1.9e+04    0.00034    0.002    -0.32    -
  643      1.9e+04    0.00068    0.002     0.24    +
  644      1.9e+04    0.00038    0.002     0.57    +
  645      1.9e+04    0.00058    0.002     0.52    +
  646      1.9e+04    0.00033    0.002     0.83    +
  647      1.9e+04    0.00061    0.002     0.38    +
  648      1.9e+04    0.00032    0.002     0.76    +
  649      1.9e+04    0.00062    0.002     0.49    +
  650      1.9e+04    0.00032    0.002     0.72    +
  651      1.9e+04    0.00064    0.002     0.46    +
  652      1.9e+04    0.00032    0.002     0.73    +
  653      1.9e+04    0.00065    0.002     0.47    +
  654      1.9e+04    0.00031    0.002     0.71    +
  655      1.9e+04    0.00065    0.002     0.47    +
  656      1.9e+04    0.00031    0.002     0.72    +
  657      1.9e+04    0.00065    0.002     0.47    +
  658      1.9e+04    0.00031    0.002     0.71    +
  659      1.9e+04    0.00065    0.002     0.47    +
  660      1.9e+04    0.00031    0.002     0.72    +
  661      1.9e+04    0.00065    0.002     0.47    +
  662      1.9e+04     0.0003    0.002     0.71    +
  663      1.9e+04    0.00065    0.002     0.47    +
  664      1.9e+04     0.0003    0.002     0.72    +
  665      1.9e+04    0.00065    0.002     0.47    +
  666      1.9e+04     0.0003    0.002     0.71    +
  667      1.9e+04    0.00064    0.002     0.48    +
  668      1.9e+04     0.0003    0.002     0.72    +
  669      1.9e+04    0.00065    0.002     0.47    +
  670      1.9e+04     0.0003    0.002     0.72    +
  671      1.9e+04    0.00064    0.002     0.48    +
  672      1.9e+04    0.00029    0.002     0.73    +
  673      1.9e+04    0.00064    0.002     0.47    +
  674      1.9e+04     0.0003    0.002     0.71    +
  675      1.9e+04    0.00064    0.002     0.46    +
  676      1.9e+04     0.0003    0.002     0.71    +
  677      1.9e+04    0.00066    0.002     0.44    +
  678      1.9e+04    0.00029    0.002     0.65    +
  679      1.9e+04    0.00056    0.002     0.48    +
  680      1.9e+04    0.00028    0.002     0.87    +
  681      1.9e+04    0.00069    0.002     0.44    +
  682      1.9e+04     0.0003    0.002     0.54    +
  683      1.9e+04    0.00059    0.002     0.51    +
  684      1.9e+04    0.00027     0.02     0.91   ++
  685      1.9e+04    0.00027     0.01       -2    -
  686      1.9e+04    0.00027    0.005     -1.5    -
  687      1.9e+04    0.00027   0.0025     -0.6    -
  688      1.9e+04    0.00079   0.0025      0.3    +
  689      1.9e+04    0.00079   0.0013    -0.11    -
  690      1.9e+04    0.00036   0.0013     0.75    +
  691      1.9e+04    0.00054   0.0013     0.39    +
  692      1.9e+04    0.00035   0.0013      0.7    +
  693      1.9e+04    0.00038   0.0013     0.56    +
  694      1.9e+04    0.00031    0.013     0.95   ++
  695      1.9e+04    0.00031   0.0063     -1.2    -
  696      1.9e+04    0.00031   0.0032    -0.49    -
  697      1.9e+04    0.00091   0.0032     0.11    +
  698      1.9e+04    0.00068   0.0032     0.31    +
  699      1.9e+04    0.00064   0.0032     0.15    +
  700      1.9e+04    0.00079   0.0032     0.11    +
  701      1.9e+04    0.00079   0.0032     0.44    +
  702      1.9e+04    0.00079   0.0016    -0.49    -
  703      1.9e+04    0.00041   0.0016      0.4    +
  704      1.9e+04    0.00051   0.0016     0.54    +
  705      1.9e+04    0.00029    0.016      1.1   ++
  706      1.9e+04    0.00029   0.0079     -1.8    -
  707      1.9e+04    0.00029   0.0039       -1    -
  708      1.9e+04    0.00029    0.002    -0.29    -
  709      1.9e+04     0.0008    0.002     0.27    +
  710      1.9e+04    0.00047    0.002     0.35    +
  711      1.9e+04    0.00059    0.002     0.45    +
  712      1.9e+04     0.0003    0.002     0.62    +
  713      1.9e+04    0.00058    0.002     0.52    +
  714      1.9e+04    0.00027    0.002     0.82    +
  715      1.9e+04    0.00066    0.002     0.46    +
  716      1.9e+04    0.00029    0.002     0.58    +
  717      1.9e+04    0.00053    0.002     0.51    +
  718      1.9e+04    0.00025     0.02     0.97   ++
  719      1.9e+04    0.00025   0.0099     -1.7    -
  720      1.9e+04    0.00025   0.0049     -1.3    -
  721      1.9e+04    0.00025   0.0025     -0.5    -
  722      1.9e+04    0.00025   0.0012    0.052    -
  723      1.9e+04      0.001   0.0012     0.22    +
  724      1.9e+04    0.00054   0.0012     0.17    +
  725      1.9e+04    0.00034   0.0012     0.69    +
  726      1.9e+04    0.00044   0.0012     0.84    +
  727      1.9e+04     0.0003    0.012     0.93   ++
  728      1.9e+04     0.0003   0.0062     -1.7    -
  729      1.9e+04     0.0003   0.0031    -0.72    -
  730      1.9e+04     0.0003   0.0015    0.072    -
  731      1.9e+04    0.00034   0.0015     0.59    +
  732      1.9e+04    0.00036   0.0015     0.72    +
  733      1.9e+04    0.00045   0.0015     0.57    +
  734      1.9e+04    0.00033   0.0015     0.78    +
  735      1.9e+04    0.00041   0.0015     0.63    +
  736      1.9e+04    0.00027    0.015     0.98   ++
  737      1.9e+04    0.00027   0.0077     -1.7    -
  738      1.9e+04    0.00027   0.0039    -0.73    -
  739      1.9e+04    0.00027   0.0019    0.089    -
  740      1.9e+04    0.00044   0.0019     0.73    +
  741      1.9e+04    0.00028   0.0019     0.85    +
  742      1.9e+04    0.00034   0.0019     0.48    +
  743      1.9e+04    0.00042   0.0019     0.52    +
  744      1.9e+04    0.00042   0.0019     0.58    +
  745      1.9e+04    0.00048   0.0019      0.2    +
  746      1.9e+04     0.0005   0.0019      0.6    +
  747      1.9e+04     0.0003    0.019        1   ++
  748      1.9e+04     0.0003   0.0096     -1.9    -
  749      1.9e+04     0.0003   0.0048     -1.3    -
  750      1.9e+04     0.0003   0.0024    -0.63    -
  751      1.9e+04     0.0003   0.0012   -0.014    -
  752      1.9e+04    0.00053   0.0012     0.33    +
  753      1.9e+04     0.0003   0.0012     0.82    +
  754      1.9e+04    0.00049   0.0012     0.54    +
  755      1.9e+04     0.0003    0.012     0.93   ++
  756      1.9e+04     0.0003    0.006     -1.5    -
  757      1.9e+04     0.0003    0.003    -0.75    -
  758      1.9e+04     0.0003   0.0015   -0.059    -
  759      1.9e+04    0.00044   0.0015     0.44    +
  760      1.9e+04    0.00031   0.0015     0.68    +
  761      1.9e+04    0.00046   0.0015     0.57    +
  762      1.9e+04     0.0003    0.015     0.93   ++
  763      1.9e+04     0.0003   0.0075     -2.3    -
  764      1.9e+04     0.0003   0.0038     -1.1    -
  765      1.9e+04     0.0003   0.0019    -0.22    -
  766      1.9e+04    0.00056   0.0019     0.37    +
  767      1.9e+04    0.00039   0.0019     0.38    +
  768      1.9e+04    0.00053   0.0019      0.5    +
  769      1.9e+04     0.0003   0.0019     0.68    +
  770      1.9e+04    0.00058   0.0019     0.49    +
  771      1.9e+04    0.00028   0.0019     0.66    +
  772      1.9e+04    0.00054   0.0019     0.52    +
  773      1.9e+04    0.00026   0.0019     0.89    +
  774      1.9e+04    0.00071   0.0019     0.41    +
  775      1.9e+04    0.00034   0.0019     0.29    +
  776      1.9e+04    0.00052   0.0019     0.56    +
  777      1.9e+04    0.00021    0.019      1.1   ++
  778      1.9e+04    0.00021   0.0094     -2.3    -
  779      1.9e+04    0.00021   0.0047     -1.4    -
  780      1.9e+04    0.00021   0.0024    -0.46    -
  781      1.9e+04    0.00073   0.0024     0.28    +
  782      1.9e+04    0.00044   0.0024     0.39    +
  783      1.9e+04    0.00062   0.0024     0.27    +
  784      1.9e+04    0.00054   0.0024     0.16    +
  785      1.9e+04    0.00067   0.0024     0.39    +
  786      1.9e+04    0.00067   0.0012    0.028    -
  787      1.9e+04    0.00031   0.0012     0.66    +
  788      1.9e+04    0.00048   0.0012     0.47    +
  789      1.9e+04    0.00029    0.012     0.92   ++
  790      1.9e+04    0.00029   0.0059     -1.9    -
  791      1.9e+04    0.00029   0.0029     -1.1    -
  792      1.9e+04    0.00029   0.0015    -0.37    -
  793      1.9e+04    0.00059   0.0015     0.31    +
  794      1.9e+04    0.00032   0.0015     0.58    +
  795      1.9e+04    0.00048   0.0015     0.52    +
  796      1.9e+04    0.00027    0.015     0.93   ++
  797      1.9e+04    0.00027   0.0073     -2.3    -
  798      1.9e+04    0.00027   0.0037     -1.2    -
  799      1.9e+04    0.00027   0.0018    -0.33    -
  800      1.9e+04     0.0005   0.0018      0.3    +
  801      1.9e+04    0.00031   0.0018     0.61    +
  802      1.9e+04    0.00052   0.0018      0.5    +
  803      1.9e+04    0.00029   0.0018     0.65    +
  804      1.9e+04    0.00056   0.0018     0.45    +
  805      1.9e+04     0.0003   0.0018     0.62    +
  806      1.9e+04    0.00062   0.0018     0.37    +
  807      1.9e+04    0.00029   0.0018     0.59    +
  808      1.9e+04    0.00058   0.0018     0.49    +
  809      1.9e+04    0.00025    0.018     0.93   ++
  810      1.9e+04    0.00025   0.0092     -2.5    -
  811      1.9e+04    0.00025   0.0046     -1.6    -
  812      1.9e+04    0.00025   0.0023    -0.73    -
  813      1.9e+04    0.00081   0.0023     0.14    +
  814      1.9e+04    0.00044   0.0023     0.29    +
  815      1.9e+04    0.00067   0.0023     0.37    +
  816      1.9e+04    0.00054   0.0023     0.12    +
  817      1.9e+04    0.00077   0.0023     0.36    +
  818      1.9e+04    0.00048   0.0023     0.33    +
  819      1.9e+04      0.001   0.0023     0.14    +
  820      1.9e+04    0.00047   0.0023     0.45    +
  821      1.9e+04    0.00077   0.0023     0.25    +
  822      1.9e+04    0.00045   0.0023     0.18    +
  823      1.9e+04    0.00061   0.0023     0.37    +
  824      1.9e+04    0.00051   0.0023      0.2    +
  825      1.9e+04    0.00076   0.0023     0.38    +
  826      1.9e+04    0.00031   0.0023     0.58    +
  827      1.9e+04    0.00089   0.0023     0.21    +
  828      1.9e+04    0.00089   0.0011    -0.12    -
  829      1.9e+04    0.00031   0.0011     0.81    +
  830      1.9e+04    0.00079   0.0011     0.24    +
  831      1.9e+04    0.00034   0.0011     0.44    +
  832      1.9e+04    0.00033   0.0011      0.5    +
  833      1.9e+04    0.00026    0.011        1   ++
  834      1.9e+04    0.00026   0.0057     -1.7    -
  835      1.9e+04    0.00026   0.0029       -1    -
  836      1.9e+04    0.00026   0.0014    -0.32    -
  837      1.9e+04    0.00039   0.0014      0.5    +
  838      1.9e+04    0.00031   0.0014     0.77    +
  839      1.9e+04    0.00045   0.0014     0.46    +
  840      1.9e+04    0.00032   0.0014     0.63    +
  841      1.9e+04    0.00043   0.0014     0.52    +
  842      1.9e+04     0.0003   0.0014     0.74    +
  843      1.9e+04    0.00049   0.0014     0.46    +
  844      1.9e+04     0.0003   0.0014     0.69    +
  845      1.9e+04    0.00049   0.0014     0.51    +
  846      1.9e+04    0.00028   0.0014     0.84    +
  847      1.9e+04    0.00054   0.0014     0.42    +
  848      1.9e+04    0.00029   0.0014     0.67    +
  849      1.9e+04     0.0005   0.0014     0.51    +
  850      1.9e+04    0.00027    0.014      0.9   ++
  851      1.9e+04    0.00027   0.0072     -2.3    -
  852      1.9e+04    0.00027   0.0036     -1.3    -
  853      1.9e+04    0.00027   0.0018    -0.39    -
  854      1.9e+04    0.00048   0.0018     0.28    +
  855      1.9e+04     0.0003   0.0018     0.65    +
  856      1.9e+04    0.00052   0.0018     0.46    +
  857      1.9e+04    0.00031   0.0018     0.49    +
  858      1.9e+04    0.00058   0.0018     0.41    +
  859      1.9e+04    0.00029   0.0018     0.54    +
  860      1.9e+04    0.00052   0.0018     0.36    +
  861      1.9e+04    0.00028   0.0018     0.67    +
  862      1.9e+04    0.00063   0.0018     0.39    +
  863      1.9e+04    0.00029   0.0018      0.5    +
  864      1.9e+04    0.00057   0.0018     0.45    +
  865      1.9e+04    0.00026   0.0018     0.84    +
  866      1.9e+04    0.00064   0.0018     0.38    +
  867      1.9e+04    0.00029   0.0018     0.48    +
  868      1.9e+04    0.00058   0.0018     0.48    +
  869      1.9e+04    0.00024    0.018     0.97   ++
  870      1.9e+04    0.00024    0.009     -2.4    -
  871      1.9e+04    0.00024   0.0045     -1.7    -
  872      1.9e+04    0.00024   0.0022    -0.76    -
  873      1.9e+04    0.00024   0.0011   -0.059    -
  874      1.9e+04    0.00024  0.00056    -0.28    -
  875      1.9e+04    0.00077  0.00056      0.3    +
  876      1.9e+04    0.00027   0.0056     0.95   ++
  877      1.9e+04    0.00027   0.0028     -1.4    -
  878      1.9e+04    0.00027   0.0014    -0.86    -
  879      1.9e+04    0.00027   0.0007    -0.38    -
  880      1.9e+04    0.00038   0.0007     0.86    +
  881      1.9e+04     0.0003    0.007     0.96   ++
  882      1.9e+04    0.00039    0.007     0.54    +
  883      1.9e+04    0.00039   0.0035    -0.51    -
  884      1.9e+04    0.00048    0.035     0.94   ++
  885      1.9e+04    0.00048    0.018     -1.8    -
  886      1.9e+04    0.00048   0.0088     -1.5    -
  887      1.9e+04    0.00048   0.0044    -0.94    -
  888      1.9e+04    0.00048   0.0022    -0.33    -
  889      1.9e+04    0.00026   0.0022     0.44    +
  890      1.9e+04    0.00059   0.0022      0.5    +
  891      1.9e+04    0.00042   0.0022     0.28    +
  892      1.9e+04    0.00072   0.0022     0.34    +
  893      1.9e+04    0.00072   0.0011    -0.16    -
  894      1.9e+04    0.00029   0.0011     0.78    +
  895      1.9e+04    0.00029  0.00055    0.045    -
  896      1.9e+04    0.00033  0.00055     0.55    +
  897      1.9e+04    0.00026   0.0055      1.1   ++
  898      1.9e+04    0.00026   0.0027    -0.37    -
  899      1.9e+04    0.00026   0.0014    0.013    -
  900      1.9e+04     0.0006   0.0014     0.36    +
  901      1.9e+04     0.0004   0.0014     0.43    +
  902      1.9e+04    0.00046   0.0014     0.52    +
  903      1.9e+04    0.00025    0.014        1   ++
  904      1.9e+04    0.00025   0.0068     -2.1    -
  905      1.9e+04    0.00025   0.0034     -1.4    -
  906      1.9e+04    0.00025   0.0017    -0.63    -
  907      1.9e+04    0.00025  0.00086     0.02    -
  908      1.9e+04    0.00026  0.00086     0.65    +
  909      1.9e+04    0.00025   0.0086        1   ++
  910      1.9e+04    0.00025   0.0043    -0.71    -
  911      1.9e+04    0.00025   0.0021    -0.24    -
  912      1.9e+04    0.00081   0.0021     0.18    +
  913      1.9e+04    0.00057   0.0021     0.31    +
  914      1.9e+04    0.00065   0.0021     0.33    +
  915      1.9e+04    0.00065   0.0011     0.08    -
  916      1.9e+04    0.00032   0.0011     0.65    +
  917      1.9e+04    0.00032  0.00053    0.063    -
  918      1.9e+04    0.00026  0.00053     0.61    +
  919      1.9e+04    0.00028   0.0053      1.1   ++
  920      1.9e+04    0.00028   0.0027   -0.038    -
  921      1.9e+04    0.00093   0.0027      0.3    +
  922      1.9e+04    0.00093   0.0013     -0.3    -
  923      1.9e+04     0.0005   0.0013     0.37    +
  924      1.9e+04    0.00045   0.0013     0.36    +
  925      1.9e+04    0.00031   0.0013     0.63    +
  926      1.9e+04    0.00044   0.0013     0.51    +
  927      1.9e+04    0.00028   0.0013     0.83    +
  928      1.9e+04    0.00048   0.0013      0.4    +
  929      1.9e+04    0.00029   0.0013     0.67    +
  930      1.9e+04    0.00047   0.0013     0.49    +
  931      1.9e+04    0.00028   0.0013     0.78    +
  932      1.9e+04     0.0005   0.0013     0.44    +
  933      1.9e+04    0.00028   0.0013     0.71    +
  934      1.9e+04    0.00049   0.0013     0.47    +
  935      1.9e+04    0.00028   0.0013     0.76    +
  936      1.9e+04    0.00052   0.0013     0.44    +
  937      1.9e+04    0.00028   0.0013     0.69    +
  938      1.9e+04     0.0005   0.0013     0.46    +
  939      1.9e+04    0.00027   0.0013     0.77    +
  940      1.9e+04    0.00053   0.0013     0.43    +
  941      1.9e+04    0.00028   0.0013     0.66    +
  942      1.9e+04     0.0005   0.0013     0.47    +
  943      1.9e+04    0.00027   0.0013     0.81    +
  944      1.9e+04    0.00055   0.0013     0.41    +
  945      1.9e+04    0.00028   0.0013     0.61    +
  946      1.9e+04    0.00049   0.0013     0.47    +
  947      1.9e+04    0.00026   0.0013     0.85    +
  948      1.9e+04    0.00057   0.0013     0.39    +
  949      1.9e+04    0.00029   0.0013     0.58    +
  950      1.9e+04    0.00049   0.0013     0.46    +
  951      1.9e+04    0.00026   0.0013     0.82    +
  952      1.9e+04    0.00056   0.0013      0.4    +
  953      1.9e+04    0.00029   0.0013     0.58    +
  954      1.9e+04    0.00049   0.0013     0.46    +
  955      1.9e+04    0.00026   0.0013     0.82    +
  956      1.9e+04    0.00056   0.0013      0.4    +
  957      1.9e+04    0.00029   0.0013     0.58    +
  958      1.9e+04    0.00049   0.0013     0.46    +
  959      1.9e+04    0.00026   0.0013      0.8    +
  960      1.9e+04    0.00055   0.0013     0.41    +
  961      1.9e+04    0.00028   0.0013      0.6    +
  962      1.9e+04     0.0005   0.0013     0.46    +
  963      1.9e+04    0.00026   0.0013      0.8    +
  964      1.9e+04    0.00055   0.0013     0.41    +
  965      1.9e+04    0.00028   0.0013      0.6    +
  966      1.9e+04     0.0005   0.0013     0.46    +
  967      1.9e+04    0.00026   0.0013     0.78    +
  968      1.9e+04    0.00054   0.0013     0.42    +
  969      1.9e+04    0.00028   0.0013     0.62    +
  970      1.9e+04     0.0005   0.0013     0.46    +
  971      1.9e+04    0.00026   0.0013     0.77    +
  972      1.9e+04    0.00054   0.0013     0.42    +
  973      1.9e+04    0.00028   0.0013     0.62    +
  974      1.9e+04     0.0005   0.0013     0.45    +
  975      1.9e+04    0.00026   0.0013     0.76    +
  976      1.9e+04    0.00053   0.0013     0.43    +
  977      1.9e+04    0.00028   0.0013     0.63    +
  978      1.9e+04     0.0005   0.0013     0.45    +
  979      1.9e+04    0.00027   0.0013     0.75    +
  980      1.9e+04    0.00053   0.0013     0.43    +
  981      1.9e+04    0.00027   0.0013     0.64    +
  982      1.9e+04     0.0005   0.0013     0.45    +
  983      1.9e+04    0.00027   0.0013     0.73    +
  984      1.9e+04    0.00052   0.0013     0.43    +
  985      1.9e+04    0.00027   0.0013     0.66    +
  986      1.9e+04     0.0005   0.0013     0.45    +
  987      1.9e+04    0.00027   0.0013     0.72    +
  988      1.9e+04    0.00052   0.0013     0.44    +
  989      1.9e+04    0.00027   0.0013     0.67    +
  990      1.9e+04     0.0005   0.0013     0.45    +
  991      1.9e+04    0.00027   0.0013     0.71    +
  992      1.9e+04    0.00051   0.0013     0.44    +
  993      1.9e+04    0.00027   0.0013     0.68    +
  994      1.9e+04    0.00051   0.0013     0.44    +
  995      1.9e+04    0.00027   0.0013     0.69    +
  996      1.9e+04    0.00051   0.0013     0.44    +
  997      1.9e+04    0.00027   0.0013     0.68    +
  998      1.9e+04    0.00051   0.0013     0.44    +
  999      1.9e+04    0.00027   0.0013     0.68    +
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
Results saved in file b01one_latent_regression.html
Results saved in file b01one_latent_regression.pickle
print(f'Estimated betas: {len(results.data.betaValues)}')
print(f'final log likelihood: {results.data.logLike:.3f}')
print(f'Output file: {results.data.htmlFileName}')
results.write_latex()
print(f'LaTeX file: {results.data.latexFileName}')
Estimated betas: 33
final log likelihood: -18669.552
Output file: b01one_latent_regression.html
Results saved in file b01one_latent_regression.tex
LaTeX file: b01one_latent_regression.tex
results.get_estimated_parameters()
Value Rob. Std err Rob. t-test Rob. p-value
B_Envir02_F1 -0.671273 0.097669 -6.872966 6.288081e-12
B_Envir03_F1 0.989374 0.371295 2.664655 7.706735e-03
B_Mobil11_F1 0.835982 0.353844 2.362571 1.814866e-02
B_Mobil14_F1 1.035533 0.376805 2.748193 5.992477e-03
B_Mobil16_F1 0.800743 0.345501 2.317629 2.046947e-02
B_Mobil17_F1 0.653985 0.348497 1.876585 6.057501e-02
INTER_Envir02 1.543392 0.269465 5.727611 1.018550e-08
INTER_Envir03 5.404574 0.956086 5.652809 1.578466e-08
INTER_Mobil11 5.863455 0.910094 6.442695 1.173703e-10
INTER_Mobil14 5.784569 0.964224 5.999197 1.982951e-09
INTER_Mobil16 5.484541 0.887010 6.183182 6.282233e-10
INTER_Mobil17 5.086870 0.899083 5.657842 1.532880e-08
SIGMA_STAR_Envir01 1.256476 2.608340 0.481715 6.300087e-01
SIGMA_STAR_Envir02 1.120950 0.043925 25.519377 0.000000e+00
SIGMA_STAR_Envir03 1.068524 0.038331 27.876393 0.000000e+00
SIGMA_STAR_Mobil11 1.082617 0.050021 21.643369 0.000000e+00
SIGMA_STAR_Mobil14 1.049818 0.038435 27.313768 0.000000e+00
SIGMA_STAR_Mobil16 1.095804 0.044687 24.521819 0.000000e+00
SIGMA_STAR_Mobil17 1.109011 0.046279 23.963362 0.000000e+00
beta_ScaledIncome_10_inf 0.073692 0.027507 2.679056 7.383009e-03
beta_ScaledIncome_4_6 -0.176435 0.080479 -2.192297 2.835807e-02
beta_ScaledIncome_6_8 0.214425 0.098746 2.171480 2.989489e-02
beta_ScaledIncome_8_10 -0.448493 0.131220 -3.417877 6.311158e-04
beta_ScaledIncome_minus_inf_4 0.068610 0.045134 1.520139 1.284761e-01
coef_age_65_more 0.086783 0.085731 1.012268 3.114100e-01
coef_haveChildren -0.035896 0.051929 -0.691246 4.894107e-01
coef_haveGA -0.512347 0.175536 -2.918752 3.514358e-03
coef_highEducation -0.206542 0.041936 -4.925128 8.430509e-07
coef_individualHouse -0.074936 0.041909 -1.788075 7.376396e-02
coef_intercept -2.524363 0.128951 -19.576169 0.000000e+00
coef_male 0.053167 0.042191 1.260146 2.076166e-01
coef_moreThanOneBike -0.238825 0.056510 -4.226223 2.376462e-05
coef_moreThanOneCar 0.454595 0.082717 5.495754 3.890451e-08


Total running time of the script: (2 minutes 46.429 seconds)

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