487 lines
16 KiB
Python
487 lines
16 KiB
Python
# scipy-yli: Helpful SciPy utilities and recipes
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# Copyright © 2022 Lee Yingtong Li (RunasSudo)
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU Affero General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU Affero General Public License for more details.
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#
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# You should have received a copy of the GNU Affero General Public License
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# along with this program. If not, see <https://www.gnu.org/licenses/>.
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import numpy as np
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import pandas as pd
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from scipy import stats
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import statsmodels
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import statsmodels.api as sm
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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
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import itertools
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from .bayes_factors import BayesFactor, bayesfactor_afbf
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from .config import config
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from .sig_tests import FTestResult
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from .utils import Estimate, check_nan, cols_for_formula, fmt_p, formula_factor_ref_category, parse_patsy_term
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def vif(df, formula=None, nan_policy='warn'):
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"""
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Calculate the variance inflation factor for each variable in df
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formula: If specified, calculate the VIF only for the variables in the formula
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"""
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if formula:
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# Only consider columns in the formula
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df = df[cols_for_formula(formula, df)]
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# Check for/clean NaNs
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df = check_nan(df, nan_policy)
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# Convert all to float64 otherwise statsmodels chokes with "ufunc 'isfinite' not supported for the input types ..."
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df = pd.get_dummies(df, drop_first=True) # Convert categorical dtypes
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df = df.astype('float64') # Convert all other dtypes
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# Add intercept column
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orig_columns = list(df.columns)
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df['Intercept'] = [1] * len(df)
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vifs = {}
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for i, col in enumerate(orig_columns):
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vifs[col] = variance_inflation_factor(df, i)
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return pd.Series(vifs)
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# ----------
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# Regression
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class LikelihoodRatioTestResult:
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"""Result of a likelihood ratio test for regression"""
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def __init__(self, statistic, dof, pvalue):
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self.statistic = statistic
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self.dof = dof
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self.pvalue = pvalue
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def _repr_html_(self):
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return 'LR({}) = {:.2f}; <i>p</i> {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, html=True))
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def summary(self):
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return 'LR({}) = {:.2f}; p {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, html=False))
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class RegressionResult:
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"""
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Result of a regression
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llf/llnull: Log-likelihood of model/null model
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"""
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def __init__(self,
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raw_result,
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full_name, model_name, fit_method,
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dep, nobs, dof_model, fitted_dt,
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terms,
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llf, llnull,
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dof_resid, rsquared, f_statistic,
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exp
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):
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# A copy of the raw result so we can access it
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self.raw_result = raw_result
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# Information for display
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self.full_name = full_name
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self.model_name = model_name
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self.fit_method = fit_method
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# Basic fitted model information
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self.dep = dep
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self.nobs = nobs
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self.dof_model = dof_model
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self.fitted_dt = fitted_dt
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# Regression coefficients/p values
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self.terms = terms
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# Model log-likelihood
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self.llf = llf
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self.llnull = llnull
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# Extra statistics (not all regression models have these)
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self.dof_resid = dof_resid
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self.rsquared = rsquared
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self.f_statistic = f_statistic
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# Config for display style
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self.exp = exp
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@property
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def pseudo_rsquared(self):
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"""McFadden's pseudo R-squared"""
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return 1 - self.llf/self.llnull
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def lrtest_null(self):
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"""Compute the likelihood ratio test comparing the model to the null model"""
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statistic = -2 * (self.llnull - self.llf)
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pvalue = 1 - stats.chi2.cdf(statistic, self.dof_model)
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return LikelihoodRatioTestResult(statistic, self.dof_model, pvalue)
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def ftest(self):
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"""Perform the F test that all slopes are 0"""
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pvalue = 1 - stats.f(self.dof_model, self.dof_resid).cdf(self.f_statistic)
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return FTestResult(self.f_statistic, self.dof_model, self.dof_resid, pvalue)
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def bayesfactor_beta_zero(self, term):
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"""
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Compute Bayes factor testing the hypothesis that the given beta is 0
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Requires statsmodels regression
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"""
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# Get parameters required for AFBF
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params = pd.Series({term.raw_name.replace('[', '_').replace(']', '_'): term.beta.point for term in self.terms.values()})
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cov = self.raw_result.cov_params()
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# Compute BF matrix
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bf01 = bayesfactor_afbf(params, cov, self.nobs, '{} = 0'.format(term.replace('[', '_').replace(']', '_')))
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bf01 = BayesFactor(bf01.factor, '0', '{} = 0'.format(term), '1', '{} ≠ 0'.format(term))
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if bf01.factor >= 1:
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return bf01
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else:
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return bf01.invert()
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def _header_table(self, html):
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"""Return the entries for the header table"""
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# Left column
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left_col = []
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left_col.append(('Dep. Variable:', self.dep))
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left_col.append(('Model:', self.model_name))
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left_col.append(('Method:', self.fit_method))
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left_col.append(('Date:', self.fitted_dt.strftime('%Y-%m-%d')))
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left_col.append(('Time:', self.fitted_dt.strftime('%H:%M:%S')))
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left_col.append(('No. Observations:', format(self.nobs, '.0f')))
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# Right column
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right_col = []
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if self.dof_resid:
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right_col.append(('Df. Residuals:', format(self.dof_resid, '.0f')))
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right_col.append(('Df. Model:', format(self.dof_model, '.0f')))
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if self.rsquared:
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right_col.append(('<i>R</i><sup>2</sup>:' if html else 'R²:', format(self.rsquared, '.2f')))
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else:
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right_col.append(('Pseudo <i>R</i><sup>2</sup>:' if html else 'Pseudo R²:', format(self.pseudo_rsquared, '.2f')))
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if self.f_statistic:
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# Report the F test if available
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f_result = self.ftest()
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if html:
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right_col.append(('<i>F</i>:', format(f_result.statistic, '.2f')))
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right_col.append(('<i>p</i> (<i>F</i>):', fmt_p(f_result.pvalue, html=True, nospace=True)))
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else:
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right_col.append(('F:', format(f_result.statistic, '.2f')))
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right_col.append(('p (F):', fmt_p(f_result.pvalue, html=False, nospace=True)))
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else:
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# Otherwise report likelihood ratio test as overall test
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lrtest_result = self.lrtest_null()
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right_col.append(('LL-Model:', format(self.llf, '.2f')))
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right_col.append(('LL-Null:', format(self.llnull, '.2f')))
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if html:
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right_col.append(('<i>p</i> (LR):', fmt_p(lrtest_result.pvalue, html=True, nospace=True)))
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else:
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right_col.append(('p (LR):', fmt_p(lrtest_result.pvalue, html=False, nospace=True)))
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return left_col, right_col
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def _repr_html_(self):
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# Render header table
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left_col, right_col = self._header_table(html=True)
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out = '<table><caption>{} Results</caption>'.format(self.full_name)
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for left_cell, right_cell in itertools.zip_longest(left_col, right_col):
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out += '<tr><th>{}</th><td>{}</td><th>{}</th><td>{}</td></tr>'.format(
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left_cell[0] if left_cell else '',
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left_cell[1] if left_cell else '',
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right_cell[0] if right_cell else '',
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right_cell[1] if right_cell else ''
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)
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out += '</table>'
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# Render coefficients table
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out += '<table><tr><th></th><th style="text-align:center">{}</th><th colspan="3" style="text-align:center">({:g}% CI)</th><th style="text-align:center"><i>p</i></th></tr>'.format('exp(<i>β</i>)' if self.exp else '<i>β</i>', (1-config.alpha)*100)
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for term_name, term in self.terms.items():
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if isinstance(term, SingleTerm):
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# Single term
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# Exponentiate beta if requested
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beta = term.beta
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if self.exp:
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beta = np.exp(beta)
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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_name, beta.point, beta.ci_lower, beta.ci_upper, fmt_p(term.pvalue, html=True, nospace=True))
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elif isinstance(term, CategoricalTerm):
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# Categorical term
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out += '<tr><th>{}</th><td></td><td style="padding-right:0"></td><td></td><td style="padding-left:0"></td><td></td></tr>'.format(term_name)
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# Render reference category
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out += '<tr><td style="text-align:right;font-style:italic">{}</td><td>Ref.</td><td style="padding-right:0"></td><td></td><td style="padding-left:0"></td><td></td></tr>'.format(term.ref_category)
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# Loop over terms
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for sub_term_name, sub_term in term.categories.items():
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# Exponentiate beta if requested
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beta = sub_term.beta
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if self.exp:
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beta = np.exp(beta)
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out += '<tr><td style="text-align:right;font-style:italic">{}</td><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(sub_term_name, beta.point, beta.ci_lower, beta.ci_upper, fmt_p(sub_term.pvalue, html=True, nospace=True))
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else:
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raise Exception('Attempt to render unknown term type')
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out += '</table>'
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# TODO: Have a detailed view which shows SE, t/z, etc.
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return out
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def summary(self):
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# Render header table
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left_col, right_col = self._header_table(html=False)
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# Ensure equal sizes for SimpleTable
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if len(right_col) > len(left_col):
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left_col.extend([('', '')] * (len(right_col) - len(left_col)))
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elif len(left_col) > len(right_col):
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right_col.extend([('', '')] * (len(left_col) - len(right_col)))
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table1 = SimpleTable(np.concatenate([left_col, right_col], axis=1), title='{} Results'.format(self.full_name))
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table1.insert_stubs(2, [' | '] * len(left_col))
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# Get rid of last line (merge with next table)
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table1_lines = table1.as_text().splitlines(keepends=False)
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out = '\n'.join(table1_lines[:-1]) + '\n'
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# Render coefficients table
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table_data = []
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for term_name, term in self.terms.items():
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if isinstance(term, SingleTerm):
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# Single term
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# Exponentiate beta if requested
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beta = term.beta
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if self.exp:
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beta = np.exp(beta)
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# Add some extra padding
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table_data.append([term_name + ' ', format(beta.point, '.2f'), '({:.2f}'.format(beta.ci_lower), '-', '{:.2f})'.format(beta.ci_upper), ' ' + fmt_p(term.pvalue, html=False, nospace=True)])
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elif isinstance(term, CategoricalTerm):
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# Categorical term
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table_data.append([term_name + ' ', '', '', '', '', ''])
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# Render reference category
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table_data.append(['{} '.format(term.ref_category), 'Ref.', '', '', '', ''])
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# Loop over terms
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for sub_term_name, sub_term in term.categories.items():
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# Exponentiate beta if requested
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beta = sub_term.beta
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if self.exp:
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beta = np.exp(beta)
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table_data.append([sub_term_name + ' ', format(beta.point, '.2f'), '({:.2f}'.format(beta.ci_lower), '-', '{:.2f})'.format(beta.ci_upper), ' ' + fmt_p(sub_term.pvalue, html=False, nospace=True)])
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else:
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raise Exception('Attempt to render unknown term type')
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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
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table2_text = table2.as_text().replace(' \ue000 ', '({:g}% CI)'.format((1-config.alpha)*100)) # Render heading in the right spot
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table2_lines = table2_text.splitlines(keepends=False)
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# Render divider line between 2 tables
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max_table_len = max(len(table1_lines[-1]), len(table2_lines[-1]))
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out += '=' * max_table_len + '\n'
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out += '\n'.join(table2_lines[1:])
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return out
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class SingleTerm:
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"""
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A term in a RegressionResult which is a single term
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raw_name: The raw name of the term (e.g. in RegressionResult.raw_result data)
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beta: An Estimate of the coefficient
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pvalue: The p value
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"""
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def __init__(self, raw_name, beta, pvalue):
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self.raw_name = raw_name
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self.beta = beta
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self.pvalue = pvalue
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class CategoricalTerm:
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"""A group of terms in a RegressionResult corresponding to a categorical variable"""
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def __init__(self, categories, ref_category):
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self.categories = categories
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self.ref_category = ref_category
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def regress(
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model_class, df, dep, formula, *,
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nan_policy='warn',
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bool_baselevels=False, exp=None
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):
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"""
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Fit a statsmodels regression model
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bool_baselevels: Show reference categories for boolean independent variables even if reference category is False
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exp: Report exponentiated parameters rather than raw parameters
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"""
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# Autodetect whether to exponentiate
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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
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else:
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exp = False
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# Check for/clean NaNs
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df = df[[dep] + cols_for_formula(formula, df)]
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df = check_nan(df, nan_policy)
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# Ensure numeric type for dependent variable
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if df[dep].dtype != 'float64':
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df[dep] = df[dep].astype('float64')
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# Convert pandas nullable types for independent variables
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for col in df.columns:
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if df[col].dtype == 'Int64':
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df[col] = df[col].astype('float64')
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# Fit model
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model = model_class.from_formula(formula=dep + ' ~ ' + formula, data=df)
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result = model.fit()
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if isinstance(result, RegressionResult):
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# Already processed!
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result.exp = exp
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return result
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# Process terms
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terms = {}
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confint = result.conf_int(config.alpha)
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for raw_name, raw_beta in result.params.items():
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beta = Estimate(raw_beta, confint[0][raw_name], confint[1][raw_name])
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# Rename terms
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if raw_name == 'Intercept':
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# Intercept term (single term)
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term = '(Intercept)'
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terms[term] = SingleTerm(raw_name, beta, result.pvalues[raw_name])
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else:
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# Parse if required
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factor, column, contrast = parse_patsy_term(formula, df, raw_name)
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if contrast is not None:
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# Categorical term
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if bool_baselevels is False and contrast == 'True' and set(df[column].unique()) == set([True, False]):
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# Treat as single term
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terms[column] = SingleTerm(raw_name, beta, result.pvalues[raw_name])
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else:
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# Add a new categorical term if not exists
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if column not in terms:
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ref_category = formula_factor_ref_category(formula, df, factor)
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terms[column] = CategoricalTerm({}, ref_category)
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terms[column].categories[contrast] = SingleTerm(raw_name, beta, result.pvalues[raw_name])
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else:
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# Single term
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terms[column] = SingleTerm(raw_name, beta, result.pvalues[raw_name])
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# Fit null model (for llnull)
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if hasattr(result, 'llnull'):
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llnull = result.llnull
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else:
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result_null = model_class.from_formula(formula=dep + ' ~ 1', data=df).fit()
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llnull = result_null.llf
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# Parse raw regression results (to get fit method)
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header_entries = np.vectorize(str.strip)(np.concatenate(np.split(np.array(result.summary().tables[0].data), 2, axis=1)))
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header_dict = {x[0]: x[1] for x in header_entries}
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return RegressionResult(
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result,
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'Logistic Regression' if model_class is sm.Logit else '{} Regression'.format(model_class.__name__), model_class.__name__, header_dict['Method:'],
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dep, result.nobs, result.df_model, datetime.now(),
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terms,
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result.llf, llnull,
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getattr(result, 'df_resid', None), getattr(result, 'rsquared', None), getattr(result, 'fvalue', None),
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exp
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)
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# -----------------------------
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# Penalised logistic regression
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class PenalisedLogit(statsmodels.discrete.discrete_model.BinaryModel):
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"""
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Statsmodel-compatible model for computing Firth penalised logistic regression
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Uses R "logistf" library
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NB: This class expects to be used in the context of yli.regress()
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"""
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def fit(self):
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import rpy2.robjects as ro
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import rpy2.robjects.packages
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import rpy2.robjects.pandas2ri
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# Assume data is already cleaned from regress()
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df = self.data.frame.copy()
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# Convert bool to int otherwise rpy2 chokes
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df = df.replace({False: 0, True: 1})
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# Import logistf
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ro.packages.importr('logistf')
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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
|
|
lc['alpha'] = config.alpha
|
|
|
|
# Fit the model
|
|
model = ro.r('logistf(formula_, data=df, alpha=alpha)')
|
|
|
|
# TODO: Handle categorical terms?
|
|
terms = {t: SingleTerm(t, Estimate(b, ci0, ci1), p) for t, b, ci0, ci1, p in zip(model['terms'], model['coefficients'], model['ci.lower'], model['ci.upper'], model['prob'])}
|
|
|
|
return RegressionResult(
|
|
model,
|
|
'Penalised Logistic Regression', 'Logit', 'Penalised ML',
|
|
self.endog_names, model['n'][0], model['df'][0], datetime.now(),
|
|
terms,
|
|
model['loglik'][0], model['loglik'][1],
|
|
None, None, None,
|
|
None # Set exp in regress()
|
|
)
|