"""Generalized linear mixed model"""
import warnings
import re
import numpy as np
import pandas as pd
from sklearn.utils.random import check_random_state
from category_encoders.ordinal import OrdinalEncoder
import category_encoders.utils as util
import statsmodels.formula.api as smf
from statsmodels.genmod.bayes_mixed_glm import BinomialBayesMixedGLM as bgmm
__author__ = 'Jan Motl'
[docs]class GLMMEncoder(util.BaseEncoder, util.SupervisedTransformerMixin):
"""Generalized linear mixed model.
Supported targets: binomial and continuous. For polynomial target support, see PolynomialWrapper.
This is a supervised encoder similar to TargetEncoder or MEstimateEncoder, but there are some advantages:
1. Solid statistical theory behind the technique. Mixed effects models are a mature branch of statistics.
2. No hyper-parameters to tune. The amount of shrinkage is automatically determined through the estimation
process. In short, the less observations a category has and/or the more the outcome varies for a category
then the higher the regularization towards "the prior" or "grand mean".
3. The technique is applicable for both continuous and binomial targets. If the target is continuous,
the encoder returns regularized difference of the observation's category from the global mean.
If the target is binomial, the encoder returns regularized log odds per category.
In comparison to JamesSteinEstimator, this encoder utilizes generalized linear mixed models from statsmodels library.
Note: This is an alpha implementation. The API of the method may change in the future.
Parameters
----------
verbose: int
integer indicating verbosity of the output. 0 for none.
cols: list
a list of columns to encode, if None, all string columns will be encoded.
drop_invariant: bool
boolean for whether or not to drop encoded columns with 0 variance.
return_df: bool
boolean for whether to return a pandas DataFrame from transform (otherwise it will be a numpy array).
handle_missing: str
options are 'return_nan', 'error' and 'value', defaults to 'value', which returns 0.
handle_unknown: str
options are 'return_nan', 'error' and 'value', defaults to 'value', which returns 0.
randomized: bool,
adds normal (Gaussian) distribution noise into training data in order to decrease overfitting (testing data are untouched).
sigma: float
standard deviation (spread or "width") of the normal distribution.
binomial_target: bool
if True, the target must be binomial with values {0, 1} and Binomial mixed model is used.
If False, the target must be continuous and Linear mixed model is used.
If None (the default), a heuristic is applied to estimate the target type.
Example
-------
>>> from category_encoders import *
>>> import pandas as pd
>>> from sklearn.datasets import fetch_openml
>>> bunch = fetch_openml(name="house_prices", as_frame=True)
>>> display_cols = ["Id", "MSSubClass", "MSZoning", "LotFrontage", "YearBuilt", "Heating", "CentralAir"]
>>> y = bunch.target > 200000
>>> X = pd.DataFrame(bunch.data, columns=bunch.feature_names)[display_cols]
>>> enc = GLMMEncoder(cols=['CentralAir', 'Heating']).fit(X, y)
>>> numeric_dataset = enc.transform(X)
>>> print(numeric_dataset.info())
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 1460 entries, 0 to 1459
Data columns (total 7 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Id 1460 non-null float64
1 MSSubClass 1460 non-null float64
2 MSZoning 1460 non-null object
3 LotFrontage 1201 non-null float64
4 YearBuilt 1460 non-null float64
5 Heating 1460 non-null float64
6 CentralAir 1460 non-null float64
dtypes: float64(6), object(1)
memory usage: 80.0+ KB
None
References
----------
.. [1] Data Analysis Using Regression and Multilevel/Hierarchical Models, page 253, from
https://faculty.psau.edu.sa/filedownload/doc-12-pdf-a1997d0d31f84d13c1cdc44ac39a8f2c-original.pdf
"""
prefit_ordinal = True
encoding_relation = util.EncodingRelation.ONE_TO_ONE
def __init__(self, verbose=0, cols=None, drop_invariant=False, return_df=True, handle_unknown='value',
handle_missing='value', random_state=None, randomized=False, sigma=0.05, binomial_target=None):
super().__init__(verbose=verbose, cols=cols, drop_invariant=drop_invariant, return_df=return_df,
handle_unknown=handle_unknown, handle_missing=handle_missing)
self.ordinal_encoder = None
self.mapping = None
self.random_state = random_state
self.randomized = randomized
self.sigma = sigma
self.binomial_target = binomial_target
def _fit(self, X, y, **kwargs):
y = y.astype(float)
self.ordinal_encoder = OrdinalEncoder(
verbose=self.verbose,
cols=self.cols,
handle_unknown='value',
handle_missing='value'
)
self.ordinal_encoder = self.ordinal_encoder.fit(X)
X_ordinal = self.ordinal_encoder.transform(X)
# Training
self.mapping = self._train(X_ordinal, y)
def _transform(self, X, y=None):
X = self.ordinal_encoder.transform(X)
if self.handle_unknown == 'error':
if X[self.cols].isin([-1]).any().any():
raise ValueError('Unexpected categories found in dataframe')
# Loop over the columns and replace the nominal values with the numbers
X = self._score(X, y)
return X
def _more_tags(self):
tags = super()._more_tags()
tags["predict_depends_on_y"] = True
return tags
def _train(self, X, y):
# Initialize the output
mapping = {}
# Estimate target type, if necessary
if self.binomial_target is None:
if len(y.unique()) <= 2:
binomial_target = True
else:
binomial_target = False
else:
binomial_target = self.binomial_target
# The estimation does not have to converge -> at least converge to the same value.
original_state = np.random.get_state()
np.random.seed(2001)
# Reset random state on completion
try:
for switch in self.ordinal_encoder.category_mapping:
col = switch.get('col')
values = switch.get('mapping')
data = self._rename_and_merge(X, y, col)
try:
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
if binomial_target:
# Classification, returns (regularized) log odds per category as stored in vc_mean
# Note: md.predict() returns: output = fe_mean + vcp_mean + vc_mean[category]
md = bgmm.from_formula('target ~ 1', {'a': '0 + C(feature)'}, data).fit_vb()
index_names = [int(float(re.sub(r'C\(feature\)\[(\S+)\]', r'\1', index_name))) for index_name in md.model.vc_names]
estimate = pd.Series(md.vc_mean, index=index_names)
else:
# Regression, returns (regularized) mean deviation of the observation's category from the global mean
md = smf.mixedlm('target ~ 1', data, groups=data['feature']).fit()
tmp = dict()
for key, value in md.random_effects.items():
tmp[key] = value[0]
estimate = pd.Series(tmp)
except np.linalg.LinAlgError:
# Singular matrix -> just return all zeros
estimate = pd.Series(np.zeros(len(values)), index=values)
# Ignore unique columns. This helps to prevent overfitting on id-like columns
if len(X[col].unique()) == len(y):
estimate[:] = 0
if self.handle_unknown == 'return_nan':
estimate.loc[-1] = np.nan
elif self.handle_unknown == 'value':
estimate.loc[-1] = 0
if self.handle_missing == 'return_nan':
estimate.loc[values.loc[np.nan]] = np.nan
elif self.handle_missing == 'value':
estimate.loc[-2] = 0
mapping[col] = estimate
finally:
np.random.set_state(original_state)
return mapping
def _score(self, X, y):
for col in self.cols:
# Score the column
X[col] = X[col].map(self.mapping[col])
# Randomization is meaningful only for training data -> we do it only if y is present
if self.randomized and y is not None:
random_state_generator = check_random_state(self.random_state)
X[col] = (X[col] * random_state_generator.normal(1., self.sigma, X[col].shape[0]))
return X
def _rename_and_merge(self, X, y, col):
"""
Statsmodels requires:
1) unique column names
2) non-numeric columns names
Solution: internally rename the columns.
"""
merged = pd.DataFrame()
merged['feature'] = X[col]
merged['target'] = y
return merged