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NO2

  • Author: givasile
  • Runtime: ~1.5 min
  • Description: Global and regional effects (PDP, RHALE, SHAP-DP) of wind speed on NOβ‚‚ concentration in Oslo, explaining a neural network and revealing interactions with wind direction and traffic volume.
  • πŸ“„ The whole notebook in one page: PDP report

The NO2 is a subsample of 500 observations from a data set that originate in a study where air pollution at a road is related to traffic volume and meteorological variables, collected by the Norwegian Public Roads Administration. The response variable (column 1) consist of hourly values of the logarithm of the concentration of NO2 (particles), measured at Alnabru in Oslo, Norway, between October 2001 and August 2003.

The predictor variables (columns 2 to 8) are the logarithm of the number of cars per hour, temperature 2 meter above ground (degree C), wind speed (meters/second), the temperature difference between 25 and 2 meters above ground (degree C), wind direction (degrees between 0 and 360), hour of day and day number from October 1. 2001.

import effector
import numpy as np
import tensorflow as tf
from tensorflow import keras
import random

np.random.seed(42)
tf.random.set_seed(42)
random.seed(42)

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1784066952.812651   23030 cpu_feature_guard.cc:227] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

Preprocess the data

import openml

no2 = openml.datasets.get_dataset(547)

X, y, categorical_indicator, attribute_names = no2.get_data(
    target=no2.default_target_attribute
)

print("Design matrix shape: {}".format(X.shape))
print("---------------------------------")
for col_name in X.columns:
    print("Feature: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(col_name, len(X[col_name].unique()), X[col_name].mean(), X[col_name].std(), X[col_name].min(), X[col_name].max()))

print("\nTarget shape: {}".format(y.shape))
print("---------------------------------")
print("Target: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format("no2_concentration", len(y.unique()), y.mean(), y.std(), y.min(), y.max()))

Design matrix shape: (500, 7)
---------------------------------
Feature: cars_per_hour  , unique:  464, Mean:   6.97, Std:   1.09, Min:   4.13, Max:   8.35
Feature: temperature_at_2m, unique:  223, Mean:   0.85, Std:   6.52, Min: -18.60, Max:  21.10
Feature: wind_speed     , unique:   78, Mean:   3.06, Std:   1.78, Min:   0.30, Max:   9.90
Feature: temperature_diff_2m_25m, unique:   61, Mean:   0.15, Std:   1.07, Min:  -5.40, Max:   4.30
Feature: wind_direction , unique:  373, Mean: 143.37, Std:  86.51, Min:   2.00, Max: 359.00
Feature: hour_of_day    , unique:   24, Mean:  12.38, Std:   6.80, Min:   1.00, Max:  24.00
Feature: day            , unique:  287, Mean: 310.47, Std: 200.98, Min:  32.00, Max: 608.00

Target shape: (500,)
---------------------------------
Target: no2_concentration, unique:  385, Mean:   3.70, Std:   0.75, Min:   1.22, Max:   6.40

def preprocess(X, y):
    # Standarize X
    X_df = X
    x_mean = X_df.mean()
    x_std = X_df.std()
    X_df = (X_df - X_df.mean()) / X_df.std()

    # Standarize Y
    Y_df = y
    y_mean = Y_df.mean()
    y_std = Y_df.std()
    Y_df = (Y_df - Y_df.mean()) / Y_df.std()
    return X_df, Y_df, x_mean, x_std, y_mean, y_std

# shuffle and standarize all features
X_df, Y_df, x_mean, x_std, y_mean, y_std = preprocess(X, y)

def split(X_df, Y_df):
    # shuffle indices
    indices = X_df.index.tolist()
    np.random.shuffle(indices)

    # data split
    train_size = int(0.8 * len(X_df))

    X_train = X_df.iloc[indices[:train_size]]
    Y_train = Y_df.iloc[indices[:train_size]]
    X_test = X_df.iloc[indices[train_size:]]
    Y_test = Y_df.iloc[indices[train_size:]]

    return X_train, Y_train, X_test, Y_test

# train/test split
X_train, Y_train, X_test, Y_test = split(X_df, Y_df)

Fit a Neural Network

We train a deep fully-connected Neural Network with 3 hidden layers for \(10\) epochs. The model achieves a root mean squared error on the test of about \(0.7\) units.

# Train - Evaluate - Explain a neural network
model = keras.Sequential([
    keras.layers.Dense(1024, activation="relu"),
    keras.layers.Dense(512, activation="relu"),
    keras.layers.Dense(256, activation="relu"),
    keras.layers.Dense(1)
])

optimizer = keras.optimizers.Adam(learning_rate=0.001)
model.compile(optimizer=optimizer, loss="mse", metrics=["mae", keras.metrics.RootMeanSquaredError()])
model.fit(X_train, Y_train, batch_size=512, epochs=10, verbose=0)
print("train [mse, mae, rmse]:", [round(v, 3) for v in model.evaluate(X_train, Y_train, verbose=0)])
print("test  [mse, mae, rmse]:", [round(v, 3) for v in model.evaluate(X_test, Y_test, verbose=0)])

train [mse, mae, rmse]: [0.336, 0.448, 0.58]
test  [mse, mae, rmse]: [0.498, 0.562, 0.706]

Explain

We will focus on the feature wind_speed (wind speed) because its global effect is quite heterogeneous and the heterogeneity can be further explained using regional effects.

def model_jac(x):
    x_tensor = tf.convert_to_tensor(x, dtype=tf.float32)
    with tf.GradientTape() as t:
        t.watch(x_tensor)
        pred = model(x_tensor)
        grads = t.gradient(pred, x_tensor)
    return grads.numpy()

def model_forward(x):
    return model(x).numpy().squeeze()

scale_y = {"mean": y_mean, "std": y_std}
scale_x_list =[{"mean": x_mean.iloc[i], "std": x_std.iloc[i]} for i in range(len(x_mean))]
feature_names = X_df.columns.to_list()
target_name = "no2_concentration"
y_limits=(2.5,5.5)
dy_limits = (-0.3,0.1)
foi = 2

# the full schema: names and the inverse scaling β€” reports and rules
# render in raw units automatically
schema = effector.Schema(
    feature_names=feature_names,
    scale_x_list=scale_x_list,
    scale_y=scale_y,
    target_name=target_name,
)

Global Effect

Overview of All Features

We start by examining all features. Feature effect methods are generally more meaningful for numerical features. To compare effects across features more easily, we standardize the y_limits. 

pdp = effector.PDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=2000)
for i in range(len(feature_names)):
    pdp.plot(feature=i, centering=True, scale_x=scale_x_list[i], scale_y=scale_y, show_avg_output=True, nof_ice=200, y_limits=y_limits)

png

png

png

png

png

png

png

y_limits = (3,4.5)

PDP

pdp = effector.PDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=5000)
pdp.plot(feature=foi, centering=True, scale_x=scale_x_list[foi], scale_y=scale_y, show_avg_output=True, nof_ice=200, y_limits=y_limits)

png

RHALE

rhale = effector.RHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, schema=schema)
rhale.plot(feature=foi, heterogeneity="std", centering=True, scale_x=scale_x_list[foi], scale_y=scale_y, show_avg_output=True, y_limits=y_limits, dy_limits=dy_limits)

png

shap_dp = effector.ShapDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=500)
shap_dp.plot(feature=foi, centering=True, scale_x=scale_x_list[foi], scale_y=scale_y, show_avg_output=True, y_limits=y_limits)

png

Importance and one-click explanation

Beyond per-feature curves, every global effect exposes an importance score (the dispersion of the mean effect β€” the ΞΌ-twin of heterogeneity), and effector.explain(...) runs the whole pipeline (fit β†’ rank β†’ regional search) and returns a self-contained Report.

# per-feature importance = dispersion of the mean effect (mu-twin of heterogeneity)
pdp_imp = effector.PDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=2000)
print("importances:", dict(zip(feature_names, np.round(pdp_imp.importances(), 3))))

# one-click auto-explanation -> Report (serializable; self-contained HTML)
report = effector.explain(X_train.to_numpy(), model_forward, y=np.asarray(Y_train).squeeze(), method="pdp", schema=schema, nof_instances=2000)
report.show()

# the whole notebook, in one page: the report published with this example
from pathlib import Path
_out = Path("reports") / "04_no2"
_out.mkdir(parents=True, exist_ok=True)
report.to_html(_out / "report_pdp.html")

importances: {'cars_per_hour': np.float64(0.741), 'temperature_at_2m': np.float64(0.255), 'wind_speed': np.float64(0.259), 'temperature_diff_2m_25m': np.float64(0.245), 'wind_direction': np.float64(0.073), 'hour_of_day': np.float64(0.169), 'day': np.float64(0.051)}


[effector] global effects   (GAM)  -> 89.3% of the model's variance
           regional effects (CALM) -> 95.5%

  ════════════════════════════════════════════════════════════════════════
  PDP report  Β·  target: no2_concentration
  ════════════════════════════════════════════════════════════════════════

  DATA & MODEL
  ────────────────────────────────────────────────────────────────────────
    instances     400
    features      7  Β·  7 continuous
    model output  mean 3.69 Β· std 0.585 Β· range [2.03, 4.86]
    model RΒ²      0.656  (on this subsample)

  EXPLAINED VARIANCE
  ────────────────────────────────────────────────────────────────────────
    step         split on                 solo     Ξ”RΒ²      RΒ²       heter
    ──────────────────────────────────────────────────────────────────────
    GAM          (all features global)       β€”       β€”   89.3%           β€”
  + wind_speed   cars_per_hour, wind…    +4.0%   +4.0%   93.3% 0.19 β†’ 0.10
  + temperature_dcars_per_hour, wind…    +3.6%   +2.2%   95.5% 0.16 β†’ 0.12
    ──────────────────────────────────────────────────────────────────────
    FINAL                                                95.5%

  REJECTED SPLITS                                            min gain 1.0%
  ────────────────────────────────────────────────────────────────────────
    feature      split on                 solo     Ξ”RΒ²    reason
    ──────────────────────────────────────────────────────────────────────
  βœ— cars_per_hourhour_of_day, temper…    +2.3%   -0.8%    redundant
  βœ— wind_directiocars_per_hour, temp…    +3.7%   -1.3%    redundant

    βœ— redundant: it would explain variance on its own (see solo),
      but the accepted splits already account for it.

  FEATURES                                ranked, in the selected snapshot
  ────────────────────────────────────────────────────────────────────────
    feature        importance                          heter      #regions
    ──────────────────────────────────────────────────────────────────────
    cars_per_hour      0.7413  β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ     0.1999             1
    temperature_at     0.2547  β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ                 0.1472             1
    wind_speed         0.2443  β–ˆβ–ˆβ–ˆβ–ˆβ–ˆβ–ˆ                 0.0977             4
    temperature_di     0.2076  β–ˆβ–ˆβ–ˆβ–ˆβ–ˆ                  0.1166             4
    ──────────────────────────────────────────────────────────────────────
    the features above carry 83% of the total importance mass



Feature 2 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
wind_speed πŸ”Ή [id: 0 | heter: 0.19 | inst: 400 | w: 1.00]
    wind_direction < 127.60 πŸ”Ή [id: 1 | heter: 0.12 | inst: 210 | w: 0.53]
        cars_per_hour < 7.54 πŸ”Ή [id: 2 | heter: 0.11 | inst: 124 | w: 0.31]
        cars_per_hour β‰₯ 7.54 πŸ”Ή [id: 3 | heter: 0.08 | inst: 86 | w: 0.21]
    wind_direction β‰₯ 127.60 πŸ”Ή [id: 4 | heter: 0.13 | inst: 190 | w: 0.47]
        cars_per_hour < 6.74 πŸ”Ή [id: 5 | heter: 0.13 | inst: 57 | w: 0.14]
        cars_per_hour β‰₯ 6.74 πŸ”Ή [id: 6 | heter: 0.09 | inst: 133 | w: 0.33]
--------------------------------------------------
Feature 2 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0πŸ”Ήheter: 0.19
    Level 1πŸ”Ήheter: 0.12 | πŸ”»0.07 (36.06%)
        Level 2πŸ”Ήheter: 0.10 | πŸ”»0.03 (20.99%)




Feature 3 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
temperature_diff_2m_25m πŸ”Ή [id: 0 | heter: 0.16 | inst: 400 | w: 1.00]
    cars_per_hour < 7.34 πŸ”Ή [id: 1 | heter: 0.15 | inst: 193 | w: 0.48]
        wind_speed < 3.09 πŸ”Ή [id: 2 | heter: 0.13 | inst: 113 | w: 0.28]
        wind_speed β‰₯ 3.09 πŸ”Ή [id: 3 | heter: 0.14 | inst: 80 | w: 0.20]
    cars_per_hour β‰₯ 7.34 πŸ”Ή [id: 4 | heter: 0.12 | inst: 207 | w: 0.52]
        wind_direction < 163.20 πŸ”Ή [id: 5 | heter: 0.09 | inst: 104 | w: 0.26]
        wind_direction β‰₯ 163.20 πŸ”Ή [id: 6 | heter: 0.11 | inst: 103 | w: 0.26]
--------------------------------------------------
Feature 3 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0πŸ”Ήheter: 0.16
    Level 1πŸ”Ήheter: 0.13 | πŸ”»0.03 (16.24%)
        Level 2πŸ”Ήheter: 0.12 | πŸ”»0.02 (11.72%)




/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  fig.tight_layout()

Conclusion

All methods consistently indicate that NOβ‚‚ concentration decreases as wind speed increases. This aligns with physical intuition: higher wind speeds help disperse pollutants more effectively.

The steepest drop occurs at low to moderate wind speeds, where even small increases in wind can significantly improve dispersion.

At high wind speeds, the behavior varies slightly by method:

  • PDP shows the decline gradually slowing.

  • rHALE suggests a flattening effectβ€”indicating a threshold beyond which additional wind has minimal extra impact.

  • SHAP sometimes even shows a slight uptick at the highest wind speeds, possibly due to interactions with other features like wind direction or traffic.

Regional Effect

y_limits = (3,4.5)

Regional PDP

pdp_reg = effector.PDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=5_000)
pdp_reg.fit("all", centering=True)
part_pdp = pdp_reg.find_regions(foi, finder="best")
part_pdp.show(scale_x_list=scale_x_list)

Feature 2 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
wind_speed πŸ”Ή [id: 0 | heter: 0.19 | inst: 400 | w: 1.00]
    wind_direction < 127.60 πŸ”Ή [id: 1 | heter: 0.12 | inst: 210 | w: 0.53]
        cars_per_hour < 7.54 πŸ”Ή [id: 2 | heter: 0.11 | inst: 124 | w: 0.31]
        cars_per_hour β‰₯ 7.54 πŸ”Ή [id: 3 | heter: 0.08 | inst: 86 | w: 0.21]
    wind_direction β‰₯ 127.60 πŸ”Ή [id: 4 | heter: 0.13 | inst: 190 | w: 0.47]
        cars_per_hour < 6.74 πŸ”Ή [id: 5 | heter: 0.13 | inst: 57 | w: 0.14]
        cars_per_hour β‰₯ 6.74 πŸ”Ή [id: 6 | heter: 0.09 | inst: 133 | w: 0.33]
--------------------------------------------------
Feature 2 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0πŸ”Ήheter: 0.19
    Level 1πŸ”Ήheter: 0.12 | πŸ”»0.07 (36.06%)
        Level 2πŸ”Ήheter: 0.10 | πŸ”»0.03 (20.99%)

# plot the level-1 subregions (region ids depend on the fitted tree)
for r in part_pdp:
    if r.level == 1:
        part_pdp.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

for r in part_pdp:
    if r.level == 2:
        part_pdp.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

png

png

Regional RHALE

rhale_reg = effector.RHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, schema=schema)
rhale_reg.fit("all", centering=True)
part_rhale = rhale_reg.find_regions(foi, finder="best")
part_rhale.show(scale_x_list=scale_x_list)

Feature 2 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
wind_speed πŸ”Ή [id: 0 | heter: 0.15 | inst: 400 | w: 1.00]
    wind_direction < 127.60 πŸ”Ή [id: 1 | heter: 0.11 | inst: 210 | w: 0.53]
        cars_per_hour < 7.54 πŸ”Ή [id: 2 | heter: 0.09 | inst: 124 | w: 0.31]
        cars_per_hour β‰₯ 7.54 πŸ”Ή [id: 3 | heter: 0.07 | inst: 86 | w: 0.21]
    wind_direction β‰₯ 127.60 πŸ”Ή [id: 4 | heter: 0.08 | inst: 190 | w: 0.47]
        cars_per_hour < 6.94 πŸ”Ή [id: 5 | heter: 0.07 | inst: 63 | w: 0.16]
        cars_per_hour β‰₯ 6.94 πŸ”Ή [id: 6 | heter: 0.06 | inst: 127 | w: 0.32]
--------------------------------------------------
Feature 2 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0πŸ”Ήheter: 0.15
    Level 1πŸ”Ήheter: 0.09 | πŸ”»0.05 (36.12%)
        Level 2πŸ”Ήheter: 0.07 | πŸ”»0.02 (20.36%)

for r in part_rhale:
    if r.level == 1:
        part_rhale.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits, dy_limits=dy_limits)

png

png

for r in part_rhale:
    if r.level == 2:
        part_rhale.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits, dy_limits=dy_limits)

png

png

png

png

Regional SHAP-DP

shap_dp_reg = effector.ShapDP(data=X_train.to_numpy(), model=model_forward, schema=schema, nof_instances=500)
shap_dp_reg.fit("all", centering=True)
part_shap = shap_dp_reg.find_regions(foi, finder="best")
part_shap.show(scale_x_list=scale_x_list)

Feature 2 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
wind_speed πŸ”Ή [id: 0 | heter: 0.06 | inst: 400 | w: 1.00]
    wind_direction < 145.40 πŸ”Ή [id: 1 | heter: 0.05 | inst: 213 | w: 0.53]
        cars_per_hour < 7.34 πŸ”Ή [id: 2 | heter: 0.04 | inst: 115 | w: 0.29]
        cars_per_hour β‰₯ 7.34 πŸ”Ή [id: 3 | heter: 0.03 | inst: 98 | w: 0.24]
    wind_direction β‰₯ 145.40 πŸ”Ή [id: 4 | heter: 0.04 | inst: 187 | w: 0.47]
        temperature_diff_2m_25m < -0.07 πŸ”Ή [id: 5 | heter: 0.02 | inst: 72 | w: 0.18]
        temperature_diff_2m_25m β‰₯ -0.07 πŸ”Ή [id: 6 | heter: 0.04 | inst: 115 | w: 0.29]
--------------------------------------------------
Feature 2 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0πŸ”Ήheter: 0.06
    Level 1πŸ”Ήheter: 0.05 | πŸ”»0.02 (30.71%)
        Level 2πŸ”Ήheter: 0.04 | πŸ”»0.01 (19.89%)

for r in part_shap:
    if r.level == 1:
        part_shap.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

for r in part_shap:
    if r.level == 2:
        part_shap.plot(r.idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

png

png

Conclusion

Regional methods reveal two distinct patterns:

  • Low wind directions (≀ ~127–145Β°):, the dispersion appears more effective
  • High wind directions (> ~127–145Β°):, NOβ‚‚ remains steady or even slightly increases with stronger winds. This may be due to topographical blocking or pollutant recirculation depending on the local layout.

Diving deeper we observe that the relationship between wind speed and NOβ‚‚ further depends on traffic volume, revealing interaction effects:

  • At low wind directions::
  • If cars/hour ≀ 8, the drop in NOβ‚‚ with wind is more pronounced.
  • If cars/hour > 8, the drop becomes smoother, suggesting higher emissions dampen the wind’s dispersive power.
  • At high wind directions:
  • If cars/hour ≀ 7, NOβ‚‚ still decreases slightly even with higher wind.
  • If cars/hour > 7, the trend either flattens (SHAP-DP) or shows a slight increase (PDP, rHALE), potentially due to congestion-induced buildup or ineffective dispersal under certain wind conditions.

Cross-method sanity check

The one-liner effector.explain with every engine this notebook's model supports. Everything must run end to end; the closing table puts the reads side by side. Where methods disagree β€” ranking, accepted splits, RΒ² β€” that is a property of the data/model worth a closer look, not an error.

from pathlib import Path
_out = Path("reports") / "04_no2"
_out.mkdir(parents=True, exist_ok=True)

# === cross-method sweep: effector.explain on every applicable engine ======
sweep_reports = {}
for _m in ["pdp", "derpdp", "ale", "rhale", "shapdp"]:
    _kw = {"nof_instances": 300} if _m == "shapdp" else {}
    print(f"--- {_m} " + "-" * 50)
    sweep_reports[_m] = effector.explain(
        X_train.to_numpy(), model_forward, model_jac,
        y=np.asarray(Y_train).squeeze(), method=_m, schema=schema, **_kw
    )
    if _m != "pdp":  # the published report is the narrated one above
        sweep_reports[_m].to_html(_out / f"report_{_m}.html")

print()
print(f"{'method':<8} {'ranking (plotted)':<44} {'GAM R2':>8} {'final R2':>9}  splits")
for _m, _r in sweep_reports.items():
    _rank = " > ".join(fr.name for fr in _r.features)
    _ev = _r.explained_variance
    if _ev:
        _sp = "; ".join(f"{s['name']} on {s['on']}" for s in _ev["stages"]) or "none"
        print(f"{_m:<8} {_rank:<44} {_ev['gam_r2']:>7.1%} {_ev['regional_r2']:>8.1%}  {_sp}")
    else:
        print(f"{_m:<8} {_rank:<44} {'-':>7} {'-':>8}  (derivative scale: no variance ledger)")

print(f"\nreports stored in {_out}/")

--- pdp --------------------------------------------------


[effector] global effects   (GAM)  -> 89.3% of the model's variance
           regional effects (CALM) -> 95.5%
--- derpdp --------------------------------------------------


/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  fig.tight_layout()


--- ale --------------------------------------------------


[effector] global effects   (GAM)  -> 87.6% of the model's variance
           regional effects (CALM) -> 95.5%


/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  fig.tight_layout()


--- rhale --------------------------------------------------


[effector] global effects   (GAM)  -> 86.9% of the model's variance
           regional effects (CALM) -> 95.5%


/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  fig.tight_layout()


--- shapdp --------------------------------------------------


[effector] global effects   (GAM)  -> 90.2% of the model's variance
           regional effects (CALM) -> 95.3%


/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
  fig.tight_layout()



method   ranking (plotted)                              GAM R2  final R2  splits
pdp      cars_per_hour > temperature_at_2m > wind_speed > temperature_diff_2m_25m   89.3%    95.5%  wind_speed on cars_per_hour, wind_direction; temperature_diff_2m_25m on cars_per_hour, wind_direction, wind_speed
derpdp   cars_per_hour > wind_speed > temperature_diff_2m_25m > temperature_at_2m       -        -  (derivative scale: no variance ledger)
ale      cars_per_hour > temperature_at_2m > temperature_diff_2m_25m > wind_speed   87.6%    95.5%  wind_speed on cars_per_hour, wind_direction; temperature_at_2m on day, hour_of_day
rhale    cars_per_hour > temperature_at_2m > wind_speed > temperature_diff_2m_25m   86.9%    95.5%  wind_speed on cars_per_hour, wind_direction; temperature_at_2m on day, hour_of_day
shapdp   cars_per_hour > temperature_at_2m > wind_speed > temperature_diff_2m_25m   90.2%    95.3%  wind_speed on cars_per_hour, temperature_diff_2m_25m, wind_direction; cars_per_hour on temperature_at_2m, temperature_diff_2m_25m

reports stored in reports/04_no2/