.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/sampling/plot_b02nested.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_sampling_plot_b02nested.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_sampling_plot_b02nested.py:


Nested logit
============

Estimation of a nested logit model using sampling of alternatives.

:author: Michel Bierlaire
:date: Wed Nov  1 18:00:15 2023

.. GENERATED FROM PYTHON SOURCE LINES 11-33

.. code-block:: Python


    import pandas as pd
    from biogeme.sampling_of_alternatives import (
        SamplingContext,
        ChoiceSetsGeneration,
        GenerateModel,
        generate_segment_size,
    )
    from biogeme.expressions import Beta
    from biogeme.nests import OneNestForNestedLogit, NestsForNestedLogit
    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from specification_sampling import V, combined_variables
    from compare import compare
    from alternatives import (
        alternatives,
        ID_COLUMN,
        partitions,
        asian,
        all_alternatives,
    )








.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: Python

    logger = blog.get_screen_logger(level=blog.INFO)








.. GENERATED FROM PYTHON SOURCE LINES 37-45

.. code-block:: Python

    SAMPLE_SIZE = 20  # out of 100
    SAMPLE_SIZE_MEV = 33  # out of 33
    CHOICE_COLUMN = 'nested_0'
    PARTITION = 'downtown'
    MEV_PARTITION = 'uniform_asian'
    MODEL_NAME = f'nested_{PARTITION}_{SAMPLE_SIZE}'
    FILE_NAME = f'{MODEL_NAME}.dat'








.. GENERATED FROM PYTHON SOURCE LINES 46-50

.. code-block:: Python

    the_partition = partitions.get(PARTITION)
    if the_partition is None:
        raise ValueError(f'Unknown partition: {PARTITION}')








.. GENERATED FROM PYTHON SOURCE LINES 51-53

.. code-block:: Python

    segment_sizes = generate_segment_size(SAMPLE_SIZE, the_partition.number_of_segments())








.. GENERATED FROM PYTHON SOURCE LINES 54-55

We use all alternatives in the nest.

.. GENERATED FROM PYTHON SOURCE LINES 55-60

.. code-block:: Python

    mev_partition = partitions.get(MEV_PARTITION)
    if mev_partition is None:
        raise ValueError(f'Unknown partition: {MEV_PARTITION}')
    mev_segment_sizes = [SAMPLE_SIZE_MEV]








.. GENERATED FROM PYTHON SOURCE LINES 61-63

.. code-block:: Python

    observations = pd.read_csv('obs_choice.dat')








.. GENERATED FROM PYTHON SOURCE LINES 64-78

.. code-block:: Python

    context = SamplingContext(
        the_partition=the_partition,
        sample_sizes=segment_sizes,
        individuals=observations,
        choice_column=CHOICE_COLUMN,
        alternatives=alternatives,
        id_column=ID_COLUMN,
        biogeme_file_name=FILE_NAME,
        utility_function=V,
        combined_variables=combined_variables,
        mev_partition=mev_partition,
        mev_sample_sizes=mev_segment_sizes,
    )








.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: Python

    logger.info(context.reporting())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Size of the choice set: 100
    Main partition: 2 segment(s) of size 46, 54
    Main sample: 20: 10/46, 10/54
    Nbr of MEV alternatives: 33
    MEV partition: 1 segment(s) of size 33
    MEV sample: 33: 33/33
 




.. GENERATED FROM PYTHON SOURCE LINES 82-85

.. code-block:: Python

    the_data_generation = ChoiceSetsGeneration(context=context)
    the_model_generation = GenerateModel(context=context)








.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: Python

    biogeme_database = the_data_generation.sample_and_merge(recycle=False)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Generating 20 + 33 alternatives for 10000 observations 

      0%|          | 0/10000 [00:00<?, ?it/s]
      1%|          | 80/10000 [00:00<00:12, 794.30it/s]
      2%|▏         | 162/10000 [00:00<00:12, 809.32it/s]
      2%|▏         | 243/10000 [00:00<00:12, 802.39it/s]
      3%|▎         | 324/10000 [00:00<00:12, 802.40it/s]
      4%|▍         | 406/10000 [00:00<00:11, 807.01it/s]
      5%|▍         | 487/10000 [00:00<00:11, 802.54it/s]
      6%|▌         | 568/10000 [00:00<00:11, 797.74it/s]
      6%|▋         | 648/10000 [00:00<00:11, 794.93it/s]
      7%|▋         | 729/10000 [00:00<00:11, 798.59it/s]
      8%|▊         | 809/10000 [00:01<00:11, 794.76it/s]
      9%|▉         | 889/10000 [00:01<00:11, 795.77it/s]
     10%|▉         | 970/10000 [00:01<00:11, 798.77it/s]
     11%|█         | 1052/10000 [00:01<00:11, 804.48it/s]
     11%|█▏        | 1133/10000 [00:01<00:11, 801.92it/s]
     12%|█▏        | 1214/10000 [00:01<00:10, 800.67it/s]
     13%|█▎        | 1295/10000 [00:01<00:10, 792.49it/s]
     14%|█▍        | 1376/10000 [00:01<00:10, 794.83it/s]
     15%|█▍        | 1456/10000 [00:01<00:10, 792.32it/s]
     15%|█▌        | 1536/10000 [00:01<00:10, 790.00it/s]
     16%|█▌        | 1616/10000 [00:02<00:10, 785.48it/s]
     17%|█▋        | 1696/10000 [00:02<00:10, 788.59it/s]
     18%|█▊        | 1775/10000 [00:02<00:10, 785.20it/s]
     19%|█▊        | 1855/10000 [00:02<00:10, 787.53it/s]
     19%|█▉        | 1935/10000 [00:02<00:10, 790.90it/s]
     20%|██        | 2015/10000 [00:02<00:10, 785.24it/s]
     21%|██        | 2094/10000 [00:02<00:10, 770.94it/s]
     22%|██▏       | 2172/10000 [00:02<00:10, 766.16it/s]
     22%|██▏       | 2249/10000 [00:02<00:10, 757.04it/s]
     23%|██▎       | 2325/10000 [00:02<00:10, 750.69it/s]
     24%|██▍       | 2402/10000 [00:03<00:10, 756.29it/s]
     25%|██▍       | 2481/10000 [00:03<00:09, 765.47it/s]
     26%|██▌       | 2560/10000 [00:03<00:09, 772.20it/s]
     26%|██▋       | 2641/10000 [00:03<00:09, 783.29it/s]
     27%|██▋       | 2720/10000 [00:03<00:09, 781.71it/s]
     28%|██▊       | 2800/10000 [00:03<00:09, 785.64it/s]
     29%|██▉       | 2879/10000 [00:03<00:09, 785.86it/s]
     30%|██▉       | 2961/10000 [00:03<00:08, 794.53it/s]
     30%|███       | 3042/10000 [00:03<00:08, 796.98it/s]
     31%|███       | 3124/10000 [00:03<00:08, 801.18it/s]
     32%|███▏      | 3205/10000 [00:04<00:08, 800.60it/s]
     33%|███▎      | 3286/10000 [00:04<00:08, 796.99it/s]
     34%|███▎      | 3366/10000 [00:04<00:08, 797.69it/s]
     34%|███▍      | 3446/10000 [00:04<00:08, 792.94it/s]
     35%|███▌      | 3526/10000 [00:04<00:08, 794.35it/s]
     36%|███▌      | 3607/10000 [00:04<00:08, 798.98it/s]
     37%|███▋      | 3687/10000 [00:04<00:07, 795.83it/s]
     38%|███▊      | 3769/10000 [00:04<00:07, 800.45it/s]
     38%|███▊      | 3850/10000 [00:04<00:07, 795.01it/s]
     39%|███▉      | 3931/10000 [00:04<00:07, 798.00it/s]
     40%|████      | 4011/10000 [00:05<00:07, 794.91it/s]
     41%|████      | 4091/10000 [00:05<00:07, 794.11it/s]
     42%|████▏     | 4171/10000 [00:05<00:07, 794.85it/s]
     43%|████▎     | 4251/10000 [00:05<00:07, 794.33it/s]
     43%|████▎     | 4332/10000 [00:05<00:07, 797.84it/s]
     44%|████▍     | 4412/10000 [00:05<00:07, 796.59it/s]
     45%|████▍     | 4492/10000 [00:05<00:06, 796.48it/s]
     46%|████▌     | 4572/10000 [00:05<00:06, 792.33it/s]
     47%|████▋     | 4652/10000 [00:05<00:06, 793.64it/s]
     47%|████▋     | 4732/10000 [00:05<00:06, 793.78it/s]
     48%|████▊     | 4813/10000 [00:06<00:06, 797.15it/s]
     49%|████▉     | 4894/10000 [00:06<00:06, 800.06it/s]
     50%|████▉     | 4975/10000 [00:06<00:06, 801.56it/s]
     51%|█████     | 5056/10000 [00:06<00:06, 800.16it/s]
     51%|█████▏    | 5137/10000 [00:06<00:06, 799.02it/s]
     52%|█████▏    | 5217/10000 [00:06<00:06, 796.81it/s]
     53%|█████▎    | 5297/10000 [00:06<00:05, 795.42it/s]
     54%|█████▍    | 5377/10000 [00:06<00:05, 794.28it/s]
     55%|█████▍    | 5458/10000 [00:06<00:05, 798.62it/s]
     55%|█████▌    | 5538/10000 [00:06<00:05, 796.06it/s]
     56%|█████▌    | 5618/10000 [00:07<00:05, 795.52it/s]
     57%|█████▋    | 5698/10000 [00:07<00:05, 794.26it/s]
     58%|█████▊    | 5778/10000 [00:07<00:05, 788.48it/s]
     59%|█████▊    | 5857/10000 [00:07<00:05, 786.74it/s]
     59%|█████▉    | 5937/10000 [00:07<00:05, 789.87it/s]
     60%|██████    | 6016/10000 [00:07<00:05, 788.95it/s]
     61%|██████    | 6096/10000 [00:07<00:04, 791.09it/s]
     62%|██████▏   | 6176/10000 [00:07<00:04, 788.79it/s]
     63%|██████▎   | 6256/10000 [00:07<00:04, 790.96it/s]
     63%|██████▎   | 6336/10000 [00:08<00:04, 792.56it/s]
     64%|██████▍   | 6416/10000 [00:08<00:04, 792.67it/s]
     65%|██████▍   | 6497/10000 [00:08<00:04, 796.61it/s]
     66%|██████▌   | 6577/10000 [00:08<00:04, 792.19it/s]
     67%|██████▋   | 6657/10000 [00:08<00:04, 789.39it/s]
     67%|██████▋   | 6738/10000 [00:08<00:04, 794.25it/s]
     68%|██████▊   | 6818/10000 [00:08<00:04, 790.89it/s]
     69%|██████▉   | 6898/10000 [00:08<00:03, 792.43it/s]
     70%|██████▉   | 6978/10000 [00:08<00:03, 794.19it/s]
     71%|███████   | 7058/10000 [00:08<00:03, 793.50it/s]
     71%|███████▏  | 7139/10000 [00:09<00:03, 795.46it/s]
     72%|███████▏  | 7219/10000 [00:09<00:03, 796.49it/s]
     73%|███████▎  | 7299/10000 [00:09<00:03, 796.52it/s]
     74%|███████▍  | 7380/10000 [00:09<00:03, 797.97it/s]
     75%|███████▍  | 7460/10000 [00:09<00:03, 796.74it/s]
     75%|███████▌  | 7541/10000 [00:09<00:03, 800.13it/s]
     76%|███████▌  | 7622/10000 [00:09<00:02, 801.85it/s]
     77%|███████▋  | 7703/10000 [00:09<00:02, 796.69it/s]
     78%|███████▊  | 7784/10000 [00:09<00:02, 798.53it/s]
     79%|███████▊  | 7864/10000 [00:09<00:02, 795.47it/s]
     79%|███████▉  | 7944/10000 [00:10<00:02, 792.58it/s]
     80%|████████  | 8024/10000 [00:10<00:02, 793.29it/s]
     81%|████████  | 8104/10000 [00:10<00:02, 794.29it/s]
     82%|████████▏ | 8184/10000 [00:10<00:02, 795.60it/s]
     83%|████████▎ | 8266/10000 [00:10<00:02, 801.06it/s]
     83%|████████▎ | 8347/10000 [00:10<00:02, 797.27it/s]
     84%|████████▍ | 8427/10000 [00:10<00:01, 794.30it/s]
     85%|████████▌ | 8507/10000 [00:10<00:01, 790.25it/s]
     86%|████████▌ | 8587/10000 [00:10<00:01, 790.93it/s]
     87%|████████▋ | 8667/10000 [00:10<00:01, 791.47it/s]
     87%|████████▋ | 8747/10000 [00:11<00:01, 792.64it/s]
     88%|████████▊ | 8827/10000 [00:11<00:01, 793.65it/s]
     89%|████████▉ | 8908/10000 [00:11<00:01, 798.37it/s]
     90%|████████▉ | 8989/10000 [00:11<00:01, 800.95it/s]
     91%|█████████ | 9070/10000 [00:11<00:01, 800.38it/s]
     92%|█████████▏| 9152/10000 [00:11<00:01, 804.64it/s]
     92%|█████████▏| 9233/10000 [00:11<00:00, 801.85it/s]
     93%|█████████▎| 9314/10000 [00:11<00:00, 803.86it/s]
     94%|█████████▍| 9395/10000 [00:11<00:00, 802.79it/s]
     95%|█████████▍| 9476/10000 [00:11<00:00, 804.63it/s]
     96%|█████████▌| 9557/10000 [00:12<00:00, 802.73it/s]
     96%|█████████▋| 9638/10000 [00:12<00:00, 800.25it/s]
     97%|█████████▋| 9719/10000 [00:12<00:00, 799.25it/s]
     98%|█████████▊| 9801/10000 [00:12<00:00, 804.38it/s]
     99%|█████████▉| 9882/10000 [00:12<00:00, 803.90it/s]
    100%|█████████▉| 9963/10000 [00:12<00:00, 804.60it/s]
    100%|██████████| 10000/10000 [00:13<00:00, 738.33it/s]
    Define new variables 

    Defining new variables...:   0%|          | 0/20 [00:00<?, ?it/s]
    Defining new variables...:   5%|▌         | 1/20 [00:00<00:05,  3.37it/s]
    Defining new variables...:  10%|█         | 2/20 [00:00<00:05,  3.19it/s]
    Defining new variables...:  15%|█▌        | 3/20 [00:00<00:05,  3.13it/s]
    Defining new variables...:  20%|██        | 4/20 [00:01<00:05,  3.11it/s]
    Defining new variables...:  25%|██▌       | 5/20 [00:01<00:04,  3.06it/s]
    Defining new variables...:  30%|███       | 6/20 [00:01<00:04,  3.06it/s]
    Defining new variables...:  35%|███▌      | 7/20 [00:02<00:04,  3.06it/s]
    Defining new variables...:  40%|████      | 8/20 [00:02<00:03,  3.05it/s]
    Defining new variables...:  45%|████▌     | 9/20 [00:02<00:03,  3.04it/s]
    Defining new variables...:  50%|█████     | 10/20 [00:03<00:03,  3.03it/s]
    Defining new variables...:  55%|█████▌    | 11/20 [00:03<00:02,  3.04it/s]
    Defining new variables...:  60%|██████    | 12/20 [00:03<00:02,  3.04it/s]
    Defining new variables...:  65%|██████▌   | 13/20 [00:04<00:02,  3.04it/s]
    Defining new variables...:  70%|███████   | 14/20 [00:04<00:01,  3.04it/s]
    Defining new variables...:  75%|███████▌  | 15/20 [00:04<00:01,  3.04it/s]
    Defining new variables...:  80%|████████  | 16/20 [00:05<00:01,  3.04it/s]
    Defining new variables...:  85%|████████▌ | 17/20 [00:05<00:00,  3.04it/s]
    Defining new variables...:  90%|█████████ | 18/20 [00:05<00:00,  3.04it/s]
    Defining new variables...:  95%|█████████▌| 19/20 [00:06<00:00,  3.04it/s]
    Defining new variables...: 100%|██████████| 20/20 [00:06<00:00,  3.02it/s]
    Defining new variables...: 100%|██████████| 20/20 [00:17<00:00,  1.13it/s]
    File nested_downtown_20.dat has been created. 




.. GENERATED FROM PYTHON SOURCE LINES 89-90

Definition of the nest.

.. GENERATED FROM PYTHON SOURCE LINES 90-99

.. code-block:: Python

    mu_asian = Beta('mu_asian', 1.0, 1.0, None, 0)
    nest_asian = OneNestForNestedLogit(
        nest_param=mu_asian, list_of_alternatives=asian, name='asian'
    )
    nests = NestsForNestedLogit(
        choice_set=all_alternatives,
        tuple_of_nests=(nest_asian,),
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    The following elements do not appear in any nest and are assumed each to be alone in a separate nest: {2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 39, 41, 42, 43, 44, 46, 48, 49, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 73, 74, 75, 77, 82, 83, 84, 85, 86, 88, 90, 93, 95, 96, 97, 99}. If it is not the intention, check the assignment of alternatives to nests. 




.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. code-block:: Python

    logprob = the_model_generation.get_nested_logit(nests)








.. GENERATED FROM PYTHON SOURCE LINES 103-106

.. code-block:: Python

    the_biogeme = bio.BIOGEME(biogeme_database, logprob)
    the_biogeme.modelName = MODEL_NAME





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Biogeme parameters read from biogeme.toml. 




.. GENERATED FROM PYTHON SOURCE LINES 107-108

Calculate the null log likelihood for reporting.

.. GENERATED FROM PYTHON SOURCE LINES 108-112

.. code-block:: Python

    the_biogeme.calculate_null_loglikelihood(
        {i: 1 for i in range(context.total_sample_size)}
    )





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    np.float64(-29957.32273553647)



.. GENERATED FROM PYTHON SOURCE LINES 113-114

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 114-116

.. code-block:: Python

    results = the_biogeme.estimate(recycle=False)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    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 __nested_downtown_20.iter 
    Cannot read file __nested_downtown_20.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.    beta_chinese  beta_ethiopian     beta_french     beta_indian   beta_japanese     beta_korean   beta_lebanese   beta_log_dist    beta_mexican      beta_price     beta_rating        mu_asian     Function    Relgrad   Radius      Rho      
        0          -0.094          -0.044           0.023           -0.12            0.12          -0.067          0.0027              -1            0.68           -0.51            0.47             1.2      2.4e+04      0.081       10     0.92   ++ 
        1            0.18            0.52            0.83            0.39               1            0.24            0.78           -0.61             1.2            -0.4            0.76             1.4      2.3e+04      0.024    1e+02        1   ++ 
        2            0.52            0.51            0.76            0.83             1.1            0.56            0.72           -0.62             1.2           -0.42            0.79             1.7      2.3e+04      0.012    1e+03      1.1   ++ 
        3            0.63             0.5            0.75            0.91             1.2            0.64            0.72            -0.6             1.2           -0.41            0.77             1.9      2.3e+04     0.0032    1e+04      1.2   ++ 
        4            0.69             0.5            0.75            0.97             1.2            0.69            0.71           -0.59             1.2           -0.41            0.76               2      2.3e+04    0.00042    1e+05      1.1   ++ 
        5            0.69             0.5            0.75            0.97             1.2            0.69            0.71           -0.59             1.2           -0.41            0.76               2      2.3e+04    6.3e-06    1e+05        1   ++ 
    Results saved in file nested_downtown_20.html 
    Results saved in file nested_downtown_20.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 117-119

.. code-block:: Python

    print(results.short_summary())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Results for model nested_downtown_20
    Nbr of parameters:              12
    Sample size:                    10000
    Excluded data:                  0
    Null log likelihood:            -29957.32
    Final log likelihood:           -22979.19
    Likelihood ratio test (null):           13956.26
    Rho square (null):                      0.233
    Rho bar square (null):                  0.233
    Akaike Information Criterion:   45982.39
    Bayesian Information Criterion: 46068.91





.. GENERATED FROM PYTHON SOURCE LINES 120-123

.. code-block:: Python

    estimated_parameters = results.get_estimated_parameters()
    estimated_parameters






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>beta_chinese</th>
          <td>0.700229</td>
          <td>0.071300</td>
          <td>9.820906</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_ethiopian</th>
          <td>0.503377</td>
          <td>0.040232</td>
          <td>12.511976</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_french</th>
          <td>0.744952</td>
          <td>0.048852</td>
          <td>15.249200</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_indian</th>
          <td>0.976977</td>
          <td>0.063607</td>
          <td>15.359560</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_japanese</th>
          <td>1.236949</td>
          <td>0.054294</td>
          <td>22.782394</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_korean</th>
          <td>0.696263</td>
          <td>0.061596</td>
          <td>11.303638</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_lebanese</th>
          <td>0.713084</td>
          <td>0.049902</td>
          <td>14.289703</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_log_dist</th>
          <td>-0.588648</td>
          <td>0.012729</td>
          <td>-46.243923</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_mexican</th>
          <td>1.204193</td>
          <td>0.029153</td>
          <td>41.306497</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_price</th>
          <td>-0.404956</td>
          <td>0.012275</td>
          <td>-32.989608</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>beta_rating</th>
          <td>0.763591</td>
          <td>0.015256</td>
          <td>50.052379</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>mu_asian</th>
          <td>2.019067</td>
          <td>0.059071</td>
          <td>34.180512</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 124-126

.. code-block:: Python

    df, msg = compare(estimated_parameters)








.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: Python

    print(df)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

                  Name  True Value  Estimated Value    T-Test
    0      beta_rating        0.75         0.763591 -0.890885
    1       beta_price       -0.40        -0.404956  0.403743
    2     beta_chinese        0.75         0.700229  0.698055
    3    beta_japanese        1.25         1.236949  0.240375
    4      beta_korean        0.75         0.696263  0.872402
    5      beta_indian        1.00         0.976977  0.361951
    6      beta_french        0.75         0.744952  0.103343
    7     beta_mexican        1.25         1.204193  1.571277
    8    beta_lebanese        0.75         0.713084  0.739766
    9   beta_ethiopian        0.50         0.503377 -0.083940
    10   beta_log_dist       -0.60        -0.588648 -0.891786
    11        mu_asian        2.00         2.019067 -0.322789




.. GENERATED FROM PYTHON SOURCE LINES 130-131

.. code-block:: Python

    print(msg)




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Parameters not estimated: ['mu_downtown']





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (1 minutes 16.858 seconds)


.. _sphx_glr_download_auto_examples_sampling_plot_b02nested.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_b02nested.ipynb <plot_b02nested.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b02nested.py <plot_b02nested.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_b02nested.zip <plot_b02nested.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_