scipy-yli/yli/regress.py

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# scipy-yli: Helpful SciPy utilities and recipes
# Copyright © 2022 Lee Yingtong Li (RunasSudo)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
import numpy as np
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import pandas as pd
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import patsy
from scipy import stats
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import statsmodels
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import statsmodels.api as sm
from statsmodels.iolib.table import SimpleTable
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from statsmodels.stats.outliers_influence import variance_inflation_factor
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from datetime import datetime
import itertools
from .bayes_factors import BayesFactor, bayesfactor_afbf
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from .utils import Estimate, check_nan, fmt_p_html, fmt_p_text
def vif(df, formula=None, nan_policy='warn'):
"""
Calculate the variance inflation factor for each variable in df
formula: If specified, calculate the VIF only for the variables in the formula
"""
if formula:
# Only consider columns in the formula
df = df[cols_for_formula(formula)]
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# Check for/clean NaNs
df = check_nan(df, nan_policy)
# Convert all to float64 otherwise statsmodels chokes with "ufunc 'isfinite' not supported for the input types ..."
df = pd.get_dummies(df, drop_first=True) # Convert categorical dtypes
df = df.astype('float64') # Convert all other dtypes
# Add intercept column
orig_columns = list(df.columns)
df['Intercept'] = [1] * len(df)
vifs = {}
for i, col in enumerate(orig_columns):
vifs[col] = variance_inflation_factor(df, i)
return pd.Series(vifs)
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def cols_for_formula(formula):
"""Return the columns corresponding to the Patsy formula"""
model_desc = patsy.ModelDesc.from_formula(formula)
cols = set()
for term in model_desc.rhs_termlist:
for factor in term.factors:
name = factor.name()
if '(' in name:
# FIXME: Is there a better way of doing this?
name = name[name.index('(')+1:name.index(')')]
cols.add(name)
return list(cols)
# ----------
# Regression
class LikelihoodRatioTestResult:
"""Result of a likelihood ratio test for regression"""
def __init__(self, statistic, dof, pvalue):
self.statistic = statistic
self.dof = dof
self.pvalue = pvalue
def _repr_html_(self):
return 'LR({}) = {:.2f}; <i>p</i> {}'.format(self.dof, self.statistic, fmt_p_html(self.pvalue))
def summary(self):
return 'LR({}) = {:.2f}; p {}'.format(self.dof, self.statistic, fmt_p_text(self.pvalue))
class FTestResult:
"""Result of an F test for regression"""
def __init__(self, statistic, dof_model, dof_resid, pvalue):
self.statistic = statistic
self.dof_model = dof_model
self.dof_resid = dof_resid
self.pvalue = pvalue
def _repr_html_(self):
return '<i>F</i>({}, {}) = {:.2f}; <i>p</i> {}'.format(self.dof_model, self.dof_resid, self.statistic, fmt_p_html(self.pvalue))
def summary(self):
return 'F({}, {}) = {:.2f}; p {}'.format(self.dof_model, self.dof_resid, self.statistic, fmt_p_text(self.pvalue))
class RegressionResult:
"""
Result of a regression
llf/llnull: Log-likelihood of model/null model
"""
def __init__(self,
raw_result,
full_name, model_name, fit_method,
dep, nobs, dof_model, fitted_dt,
beta, pvalues,
llf, llnull,
dof_resid, rsquared, f_statistic,
exp
):
# A copy of the raw result so we can access it
self.raw_result = raw_result
# Information for display
self.full_name = full_name
self.model_name = model_name
self.fit_method = fit_method
# Basic fitted model information
self.dep = dep
self.nobs = nobs
self.dof_model = dof_model
self.fitted_dt = fitted_dt
# Regression coefficients
self.beta = beta
self.pvalues = pvalues
# Model log-likelihood
self.llf = llf
self.llnull = llnull
# Extra statistics (not all regression models have these)
self.dof_resid = dof_resid
self.rsquared = rsquared
self.f_statistic = f_statistic
# Config for display style
self.exp = exp
@property
def pseudo_rsquared(self):
"""McFadden's pseudo R-squared"""
return 1 - self.llf/self.llnull
def lrtest_null(self):
"""Compute the likelihood ratio test comparing the model to the null model"""
statistic = -2 * (self.llnull - self.llf)
pvalue = 1 - stats.chi2.cdf(statistic, self.dof_model)
return LikelihoodRatioTestResult(statistic, self.dof_model, pvalue)
def ftest(self):
"""Perform the F test that all slopes are 0"""
pvalue = 1 - stats.f(self.dof_model, self.dof_resid).cdf(self.f_statistic)
return FTestResult(self.f_statistic, self.dof_model, self.dof_resid, pvalue)
def bayesfactor_beta_zero(self, term):
"""
Compute Bayes factor testing the hypothesis that the given beta is 0
Requires statsmodels regression
"""
# Get parameters required for AFBF
params = pd.Series({term.replace('[', '_').replace(']', '_'): beta.point for term, beta in self.beta.items()})
cov = self.raw_result.cov_params()
# Compute BF matrix
bf01 = bayesfactor_afbf(params, cov, self.nobs, '{} = 0'.format(term.replace('[', '_').replace(']', '_')))
bf01 = BayesFactor(bf01.factor, '0', '{} = 0'.format(term), '1', '{} ≠ 0'.format(term))
if bf01.factor >= 1:
return bf01
else:
return bf01.invert()
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def _header_table(self, html):
"""Return the entries for the header table"""
# Left column
left_col = []
left_col.append(('Dep. Variable:', self.dep))
left_col.append(('Model:', self.model_name))
left_col.append(('Method:', self.fit_method))
left_col.append(('Date:', self.fitted_dt.strftime('%Y-%m-%d')))
left_col.append(('Time:', self.fitted_dt.strftime('%H:%M:%S')))
left_col.append(('No. Observations:', format(self.nobs, '.0f')))
# Right column
right_col = []
if self.dof_resid:
right_col.append(('Df. Residuals:', format(self.dof_resid, '.0f')))
right_col.append(('Df. Model:', format(self.dof_model, '.0f')))
if self.rsquared:
right_col.append(('<i>R</i><sup>2</sup>:' if html else 'R²:', format(self.rsquared, '.2f')))
else:
right_col.append(('Pseudo <i>R</i><sup>2</sup>:' if html else 'Pseudo R²:', format(self.pseudo_rsquared, '.2f')))
if self.f_statistic:
# Report the F test if available
f_result = self.ftest()
if html:
right_col.append(('<i>F</i>:', format(f_result.statistic, '.2f')))
right_col.append(('<i>p</i> (<i>F</i>):', fmt_p_html(f_result.pvalue, True)))
else:
right_col.append(('F:', format(f_result.statistic, '.2f')))
right_col.append(('p (F):', fmt_p_text(f_result.pvalue, True)))
else:
# Otherwise report likelihood ratio test as overall test
lrtest_result = self.lrtest_null()
right_col.append(('LL-Model:', format(self.llf, '.2f')))
right_col.append(('LL-Null:', format(self.llnull, '.2f')))
if html:
right_col.append(('<i>p</i> (LR):', fmt_p_html(lrtest_result.pvalue, True)))
else:
right_col.append(('p (LR):', fmt_p_text(lrtest_result.pvalue, True)))
return left_col, right_col
def _repr_html_(self):
# Render header table
left_col, right_col = self._header_table(html=True)
out = '<table><caption>{} Results</caption>'.format(self.full_name)
for left_cell, right_cell in itertools.zip_longest(left_col, right_col):
out += '<tr><th>{}</th><td>{}</td><th>{}</th><td>{}</td></tr>'.format(
left_cell[0] if left_cell else '',
left_cell[1] if left_cell else '',
right_cell[0] if right_cell else '',
right_cell[1] if right_cell else ''
)
out += '</table>'
# Render coefficients table
out += '<table><tr><th></th><th style="text-align:center">{}</th><th colspan="3" style="text-align:center">(95% CI)</th><th style="text-align:center"><i>p</i></th></tr>'.format('exp(<i>β</i>)' if self.exp else '<i>β</i>')
for term, beta in self.beta.items():
# Exponentiate if requested
if self.exp:
beta = np.exp(beta)
out += '<tr><th>{}</th><td>{:.2f}</td><td style="padding-right:0">({:.2f}</td><td>–</td><td style="padding-left:0">{:.2f})</td><td style="text-align:left">{}</td></tr>'.format(term, beta.point, beta.ci_lower, beta.ci_upper, fmt_p_html(self.pvalues[term], True))
out += '</table>'
# TODO: Have a detailed view which shows SE, t/z, etc.
return out
def summary(self):
# Render header table
left_col, right_col = self._header_table(html=False)
# Ensure equal sizes for SimpleTable
if len(right_col) > len(left_col):
left_col.extend([('', '')] * (len(right_col) - len(left_col)))
elif len(left_col) > len(right_col):
right_col.extend([('', '')] * (len(left_col) - len(right_col)))
table1 = SimpleTable(np.concatenate([left_col, right_col], axis=1), title='{} Results'.format(self.full_name))
table1.insert_stubs(2, [' | '] * len(left_col))
# Get rid of last line (merge with next table)
table1_lines = table1.as_text().splitlines(keepends=False)
out = '\n'.join(table1_lines[:-1]) + '\n'
# Render coefficients table
table_data = []
for term, beta in self.beta.items():
# Exponentiate if requested
if self.exp:
beta = np.exp(estimate)
# Add some extra padding
table_data.append([term + ' ', format(beta.point, '.2f'), '({:.2f}'.format(beta.ci_lower), '-', '{:.2f})'.format(beta.ci_upper), ' ' + fmt_p_text(self.pvalues[term], True)])
table2 = SimpleTable(data=table_data, headers=['', 'exp(β)' if self.exp else 'β', '', '\ue000', '', ' p']) # U+E000 is in Private Use Area, mark middle of CI column
table2_text = table2.as_text().replace(' \ue000 ', '(95% CI)') # Render heading in the right spot
table2_lines = table2_text.splitlines(keepends=False)
# Render divider line between 2 tables
max_table_len = max(len(table1_lines[-1]), len(table2_lines[-1]))
out += '=' * max_table_len + '\n'
out += '\n'.join(table2_lines[1:])
return out
def regress(
model_class, df, dep, formula, *,
nan_policy='warn', exp=None
):
"""Fit a statsmodels regression model"""
# Autodetect whether to exponentiate
if exp is None:
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if model_class is sm.Logit or model_class is PenalisedLogit:
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exp = True
else:
exp = False
# Check for/clean NaNs
df = df[[dep] + cols_for_formula(formula)]
df = check_nan(df, nan_policy)
# Ensure numeric type for dependent variable
if df[dep].dtype != 'float64':
df[dep] = df[dep].astype('float64')
# Convert pandas nullable types for independent variables
for col in df.columns:
if df[col].dtype == 'Int64':
df[col] = df[col].astype('float64')
# Fit model
model = model_class.from_formula(formula=dep + ' ~ ' + formula, data=df)
result = model.fit()
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if isinstance(result, RegressionResult):
# Already processed!
result.exp = exp
return result
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confint = result.conf_int()
beta = {t: Estimate(b, confint[0][t], confint[1][t]) for t, b in result.params.items()}
# Fit null model (for llnull)
if hasattr(result, 'llnull'):
llnull = result.llnull
else:
result_null = model_class.from_formula(formula=dep + ' ~ 1', data=df).fit()
llnull = result_null.llf
# Parse raw regression results (to get fit method)
header_entries = np.vectorize(str.strip)(np.concatenate(np.split(np.array(result.summary().tables[0].data), 2, axis=1)))
header_dict = {x[0]: x[1] for x in header_entries}
return RegressionResult(
result,
'Logistic Regression' if model_class is sm.Logit else '{} Regression'.format(model_class.__name__), model_class.__name__, header_dict['Method:'],
dep, result.nobs, result.df_model, datetime.now(),
beta, result.pvalues,
result.llf, llnull,
getattr(result, 'df_resid', None), getattr(result, 'rsquared', None), getattr(result, 'fvalue', None),
exp
)
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# -----------------------------
# Penalised logistic regression
class PenalisedLogit(statsmodels.discrete.discrete_model.BinaryModel):
"""
Statsmodel-compatible model for computing Firth penalised logistic regression
Uses R "logistf" library
NB: This class expects to be used in the context of yli.regress()
"""
def fit(self):
import rpy2.robjects as ro
import rpy2.robjects.packages
import rpy2.robjects.pandas2ri
# Assume data is already cleaned from regress()
df = self.data.frame.copy()
# Convert bool to int otherwise rpy2 chokes
df = df.replace({False: 0, True: 1})
# Import logistf
ro.packages.importr('logistf')
with ro.conversion.localconverter(ro.default_converter + ro.pandas2ri.converter):
with ro.local_context() as lc:
# Convert DataFrame to R
lc['df'] = df
# Transfer other parameters to R
lc['formula_'] = self.formula
# Fit the model
model = ro.r('logistf(formula_, data=df)')
beta = {t: Estimate(b, ci0, ci1) for t, b, ci0, ci1 in zip(model['terms'], model['coefficients'], model['ci.lower'], model['ci.upper'])}
pvalues = {t: p for t, p in zip(model['terms'], model['prob'])}
return RegressionResult(
model,
'Penalised Logistic Regression', 'Logit', 'Penalised ML',
self.endog_names, model['n'][0], model['df'][0], datetime.now(),
beta, pvalues,
model['loglik'][0], model['loglik'][1],
None, None, None,
None # Set exp in regress()
)