scipy-yli/yli/regress.py

#   scipy-yli: Helpful SciPy utilities and recipes
#   Copyright © 2022–2023  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
import pandas as pd
import patsy
from scipy import stats
from scipy.special import expit
import statsmodels, statsmodels.miscmodels.ordinal_model
import statsmodels.api as sm
from statsmodels.iolib.table import SimpleTable
from statsmodels.stats.outliers_influence import variance_inflation_factor
from tqdm import tqdm

from datetime import datetime
import itertools
import warnings
import weakref

from .bayes_factors import BayesFactor, bayesfactor_afbf
from .config import config
from .shap import ShapResult
from .sig_tests import ChiSquaredResult, FTestResult
from .utils import Estimate, PValueStyle, as_numeric, check_nan, cols_for_formula, convert_pandas_nullable, fmt_p, formula_factor_ref_category, parse_patsy_term

def vif(df, formula=None, *, nan_policy='warn'):
	"""
	Calculate the variance inflation factor (VIF) for each variable in *df*
	
	:param df: Data to calculate the VIF for
	:type df: DataFrame
	:param formula: If specified, calculate the VIF only for the variables in the formula
	:type formula: str
	
	:return: The variance inflation factors
	:rtype: Series
	
	**Example:**
	
	.. code-block::
		
		df = pd.DataFrame({
			'D': [68.58, 67.33, 67.33, ...],
			'T1': [14, 10, 10, ...],
			'T2': [46, 73, 85, ...],
			...
		})
		yli.vif(df[['D', 'T1', 'T2', ...]])
	
	.. code-block:: text
		
		D     8.318301
		T1    6.081590
		T2    2.457122
		...
		dtype: float64
	
	The output shows the variance inflation factor for each variable in *df*.
	"""
	
	if formula:
		# Only consider columns in the formula
		df = df[cols_for_formula(formula, df)]
	
	# 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)

# ----------
# Regression

class LikelihoodRatioTestResult(ChiSquaredResult):
	"""
	Result of a likelihood ratio test for regression
	
	See :meth:`RegressionResult.lrtest_null`.
	"""
	
	def __init__(self, statistic, dof, pvalue):
		super().__init__(statistic, dof, pvalue)
	
	def _repr_html_(self):
		return 'LR({}) = {:.2f}; <i>p</i> {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, PValueStyle.RELATION | PValueStyle.HTML))
	
	def summary(self):
		"""
		Return a stringified summary of the likelihood ratio test
		
		:rtype: str
		"""
		
		return 'LR({}) = {:.2f}; p {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, PValueStyle.RELATION))

class RegressionResult:
	"""
	Result of a regression
	
	See :func:`yli.regress`.
	"""
	
	def __init__(self,
		model_class, df, dep, formula, nan_policy, model_kwargs, fit_kwargs,
		raw_result,
		full_name, model_name, fit_method,
		nobs, nevents, dof_model, fitted_dt, cov_type,
		terms,
		ll_model, ll_null,
		dof_resid, rsquared, f_statistic,
		comments,
		exp
	):
		# Data about how model fitted
		#: See :func:`yli.regress`
		self.model_class = model_class
		#: Data fitted (*weakref* to *DataFrame*)
		self.df = df
		#: See :func:`yli.regress`
		self.dep = dep
		#: See :func:`yli.regress`
		self.formula = formula
		#: See :func:`yli.regress`
		self.nan_policy = nan_policy
		#: See :func:`yli.regress`
		self.model_kwargs = model_kwargs
		#: See :func:`yli.regress`
		self.fit_kwargs = fit_kwargs
		
		#: Raw result from statsmodels *model.fit*
		self.raw_result = raw_result
		
		# Information for display
		#: Full name of the regression model type (*str*)
		self.full_name = full_name
		#: Short name of the regression model type (*str*)
		self.model_name = model_name
		#: Method for fitting the regression model (*str*)
		self.fit_method = fit_method
		
		# Basic fitted model information
		#: Number of observations (*int*)
		self.nobs = nobs
		#: Number of events (*int*, time-to-event models only)
		self.nevents = nevents
		#: Degrees of freedom for the model (*int*)
		self.dof_model = dof_model
		#: Date and time of fitting the model (Python *datetime*)
		self.fitted_dt = fitted_dt
		#: Method for computing the covariance matrix (*str*)
		self.cov_type = cov_type
		
		# Regression coefficients/p values
		#: Coefficients and *p* values for each term in the model (*dict* of :class:`SingleTerm` or :class:`CategoricalTerm`)
		self.terms = terms
		
		# Model log-likelihood
		#: Log-likelihood of fitted model (*float*)
		self.ll_model = ll_model
		#: Log-likelihood of null model (*float*)
		self.ll_null = ll_null
		
		# Extra statistics (not all regression models have these)
		#: Degrees of freedom for the residuals (*int*; *None* if N/A)
		self.dof_resid = dof_resid
		#: *R*:sup:`2` statistic (*float*; *None* if N/A)
		self.rsquared = rsquared
		#: *F* statistic (*float*; *None* if N/A)
		self.f_statistic = f_statistic
		
		#: Comments for the model (*List[str]*)
		self.comments = comments or []
		
		# Config for display style
		#: See :func:`yli.regress`
		self.exp = exp
	
	@property
	def pseudo_rsquared(self):
		"""McFadden's pseudo *R*:sup:`2` statistic"""
		
		return 1 - self.ll_model/self.ll_null
	
	def lrtest_null(self):
		"""
		Compute the likelihood ratio test comparing the model to the null model
		
		:rtype: :class:`LikelihoodRatioTestResult`
		"""
		
		statistic = -2 * (self.ll_null - self.ll_model)
		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
		
		:rtype: :class:`yli.sig_tests.FTestResult`
		"""
		
		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 a Bayes factor testing the hypothesis that the given beta is 0
		
		Uses the R *BFpack* library.
		
		Requires the regression to be from statsmodels.
		The term must be specified as the *raw name* from the statsmodels regression, available via :attr:`RegressionResult.raw_result`.
		
		:param term: Raw name of the term to be tested
		:type term: str
		
		:rtype: :class:`yli.bayes_factors.BayesFactor`
		"""
		
		# FIXME: Allow specifying our renamed terms
		
		# Get parameters required for AFBF
		params = pd.Series({raw_name.replace('[', '_').replace(']', '_'): beta for raw_name, beta in self.raw_result.params.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()
	
	def brant(self):
		"""
		Perform the Brant test for the parallel regression assumption in ordinal regression
		
		Applicable when the model was fitted using :class:`OrdinalLogit`.
		
		:rtype: :class:`BrantResult`
		
		**Example:**
		
		.. code-block::
			
			df = pd.DataFrame(...)
			model = yli.regress(yli.OrdinalLogit, df, 'apply', 'pared + public + gpa', exp=False)
			model.brant()
		
		.. code-block:: text
			
			          χ²  df     p   
			Omnibus  4.34  3   0.23  
			pared    0.13  1   0.72  
			public   3.44  1   0.06  
			gpa      0.18  1   0.67  
		
		The output shows the result of the Brant test. For example, for the omnibus test of the parallel regression assumption across all independent variables, the *χ*:sup:`2` statistic is 4.34, the *χ*:sup:`2` distribution has 3 degrees of freedom, and the test is not significant, with *p* value 0.23.
		
		**Reference:** Brant R. Assessing proportionality in the proportional odds model for ordinal logistic regression. *Biometrics*. 1990;46(4):1171–8. `doi:10.2307/2532457 <https://doi.org/10.2307/2532457>`_
		"""
		
		df = self.df()
		if df is None:
			raise Exception('Referenced DataFrame has been dropped')
		dep = self.dep
		
		# Check for/clean NaNs
		# NaN warning/error will already have been handled in regress, so here we pass nan_policy='omit'
		# Following this, we pass nan_policy='raise' to assert no NaNs remaining
		df = df[[dep] + cols_for_formula(self.formula, df)]
		df = check_nan(df, 'omit')
		
		# Ensure numeric type for dependent variable
		df[dep], dep_categories = as_numeric(df[dep])
		
		# Convert pandas nullable types for independent variables as this breaks statsmodels
		df = convert_pandas_nullable(df)
		
		# Precompute design matrix for RHS
		# This is also X+ in Brant paper
		dmatrix_right = patsy.dmatrix(self.formula, df, return_type='dataframe')
		dmatrix_right.reset_index(drop=True, inplace=True)  # Otherwise this confuses matrix multiplication
		
		# Fit individual logistic regressions
		logit_models = []
		for upper_limit in sorted(df[dep].unique())[:-1]:
			dep_dichotomous = (df[dep] <= upper_limit).astype(int).reset_index(drop=True)
			logit_result = sm.Logit(dep_dichotomous, dmatrix_right).fit(disp=False, **self.fit_kwargs)
			
			if not logit_result.mle_retvals['converged']:
				raise Exception('Maximum likelihood estimation failed to converge for {} <= {}. Check raw_result.mle_retvals.'.format(dep, upper_limit))
			
			if pd.isna(logit_result.bse).any():
				raise Exception('Regression returned NaN standard errors for {} <= {}.'.format(dep, upper_limit))
			
			logit_models.append(logit_result)
		
		logit_betas = np.array([model._results.params for model in logit_models]).T
		logit_pihat = np.array([expit(-model.fittedvalues) for model in logit_models]).T  # Predicted probabilities
		
		# vcov is the variance-covariance matrix of all individually fitted betas across all terms
		
		#                  |     model 1     |     model 2     |     model 3     | ...
		#                  | term 1 | term 2 | term 1 | term 2 | term 1 | term 2 | ...
		# model 1 | term 1 |
		#         | term 2 |
		# model 2 | term 1 |
		#         | term 2 |
		#   ...
		
		n_terms = len(dmatrix_right.columns) - 1  # number of beta terms (excluding intercept)
		n_betas = len(logit_models) * n_terms
		vcov = np.zeros((n_betas, n_betas))
		
		# Populate the variance-covariance matrix for comparisons between individually fitted models
		for j in range(0, len(logit_models) - 1):
			for l in range(j + 1, len(logit_models)):
				Wjj = np.diag(logit_pihat[:,j] - logit_pihat[:,j] * logit_pihat[:,j])
				Wjl = np.diag(logit_pihat[:,l] - logit_pihat[:,j] * logit_pihat[:,l])
				Wll = np.diag(logit_pihat[:,l] - logit_pihat[:,l] * logit_pihat[:,l])
				
				matrix_result = np.linalg.inv(dmatrix_right.T @ Wjj @ dmatrix_right) @ dmatrix_right.T @ Wjl @ dmatrix_right @ np.linalg.inv(dmatrix_right.T @ Wll @ dmatrix_right)
				j_vs_l_vcov = np.asarray(matrix_result)[1:,1:]  # Asymptotic covariance for j,l
				
				vcov[j*n_terms:(j+1)*n_terms, l*n_terms:(l+1)*n_terms] = j_vs_l_vcov
				vcov[l*n_terms:(l+1)*n_terms, j*n_terms:(j+1)*n_terms] = j_vs_l_vcov
		
		# Populate the variance-covariance matrix within each individually fitted model
		for i in range(len(logit_models)):
			vcov[i*n_terms:(i+1)*n_terms, i*n_terms:(i+1)*n_terms] = logit_models[i]._results.cov_params()[1:,1:]
		
		# ------------------
		# Perform Wald tests
		
		beta_names = ['{}_{}'.format(raw_name, i) for i in range(len(logit_models)) for raw_name in dmatrix_right.columns[1:]]
		wald_results = {}
		
		# Omnibus test
		constraints = [' = '.join('{}_{}'.format(raw_name, i) for i in range(len(logit_models))) for raw_name in dmatrix_right.columns[1:]]
		constraint = ', '.join(constraints)
		df = (len(logit_models) - 1) * (len(dmatrix_right.columns) - 1)  # df = (number of levels minus 2) * (number of terms excluding intercept)
		wald_result = _wald_test(beta_names, logit_betas[1:].ravel('F'), constraint, vcov, df)
		wald_results['Omnibus'] = ChiSquaredResult(wald_result.statistic, wald_result.df_denom, wald_result.pvalue)
		
		# Individual terms
		for raw_name in dmatrix_right.columns[1:]:
			constraint = ' = '.join('{}_{}'.format(raw_name, i) for i in range(len(logit_models)))
			df = len(logit_models) - 1  # df = (number of levels minus 2)
			wald_result = _wald_test(beta_names, logit_betas[1:].ravel('F'), constraint, vcov, df)
			wald_results[raw_name] = ChiSquaredResult(wald_result.statistic, wald_result.df_denom, wald_result.pvalue)
		
		return BrantResult(wald_results)
	
	def bootstrap(self, samples=1000):
		"""
		Use bootstrapping to recompute confidence intervals and *p* values for the terms in the regression model
		
		:param samples: Number of bootstrap samples to draw
		:type samples: int
		
		:rtype: :class:`yli.regress.RegressionResult`
		"""
		
		df = self.df()
		if df is None:
			raise Exception('Referenced DataFrame has been dropped')
		dep = self.dep
		
		# Check for/clean NaNs
		# NaN warning/error will already have been handled in regress, so here we pass nan_policy='omit'
		# Following this, we pass nan_policy='raise' to assert no NaNs remaining
		df = df[[dep] + cols_for_formula(self.formula, df)]
		df = check_nan(df, 'omit')
		
		# Ensure numeric type for dependent variable
		df[dep], dep_categories = as_numeric(df[dep])
		
		# Convert pandas nullable types for independent variables as this breaks statsmodels
		df = convert_pandas_nullable(df)
		
		# Precompute design matrices
		dmatrices = patsy.dmatrices(dep + ' ~ ' + self.formula, df, return_type='dataframe')
		
		# Fit full model
		#full_model = regress(self.model_class, df, dep, self.formula, nan_policy='raise', _dmatrices=dmatrices, model_kwargs=self.model_kwargs, fit_kwargs=self.fit_kwargs)
		
		# Initialise bootstrap_results
		bootstrap_results = {}  # Dict mapping term raw names to bootstrap betas
		for term in self.terms.values():
			if isinstance(term, SingleTerm):
				bootstrap_results[term.raw_name] = []
			else:
				for sub_term in term.categories.values():
					bootstrap_results[sub_term.raw_name] = []
		
		# Draw bootstrap samples and regress
		dmatrices = dmatrices[0].join(dmatrices[1])
		
		for i in tqdm(range(samples)):
			bootstrap_rows = dmatrices.sample(len(df), replace=True)
			model = self.model_class(endog=bootstrap_rows.iloc[:,0], exog=bootstrap_rows.iloc[:,1:], **self.model_kwargs)
			model.formula = dep + ' ~ ' + self.formula
			
			result = model.fit(disp=False, **self.fit_kwargs)
			
			for raw_name, raw_beta in zip(model.exog_names, result._results.params):
				bootstrap_results[raw_name].append(raw_beta)
		
		# Combine bootstrap results
		terms = {}
		for term_name, term in self.terms.items():
			if isinstance(term, SingleTerm):
				bootstrap_betas = bootstrap_results[term.raw_name]
				bootstrap_pvalue = sum(1 for b in bootstrap_betas if b < 0) / len(bootstrap_betas)
				bootstrap_pvalue = 2 * min(bootstrap_pvalue, 1 - bootstrap_pvalue)
				terms[term_name] = SingleTerm(term.raw_name, Estimate(term.beta.point, np.quantile(bootstrap_betas, config.alpha/2), np.quantile(bootstrap_betas, 1-config.alpha/2)), bootstrap_pvalue)
			else:
				categories = {}
				for sub_term_name, sub_term in term.categories.items():
					bootstrap_betas = bootstrap_results[sub_term.raw_name]
					bootstrap_pvalue = sum(1 for b in bootstrap_betas if b < 0) / len(bootstrap_betas)
					bootstrap_pvalue = 2 * min(bootstrap_pvalue, 1 - bootstrap_pvalue)
					categories[sub_term_name] = SingleTerm(sub_term.raw_name, Estimate(sub_term.beta.point, np.quantile(bootstrap_betas, config.alpha/2), np.quantile(bootstrap_betas, 1-config.alpha/2)), bootstrap_pvalue)
				terms[term_name] = CategoricalTerm(categories, term.ref_category)
		
		return RegressionResult(
			self.model_class, self.df, dep, self.formula, self.nan_policy, self.model_kwargs, self.fit_kwargs,
			None,
			self.full_name, self.model_name, self.fit_method,
			self.nobs, None, self.dof_model, datetime.now(), 'Bootstrap',
			terms,
			self.ll_model, self.ll_null,
			self.dof_resid, self.rsquared, self.f_statistic,
			self.comments,
			self.exp
		)
	
	def shap(self, **kwargs):
		"""
		Compute SHAP values for the model
		
		Uses the Python *shap* library.
		
		:param kwargs: Keyword arguments to pass to *shap.LinearExplainer*
		
		:rtype: :class:`yli.shap.ShapResult`
		
		**Reference:** Lundberg SM, Lee SI. A unified approach to interpreting model predictions. In: Guyon I, Von Luxburg U, Bengio S, et al., editors. *Advances in Neural Information Processing Systems*; 2017 Dec 4–9; Long Beach, CA. https://proceedings.neurips.cc/paper/2017/hash/8a20a8621978632d76c43dfd28b67767-Abstract.html
		"""
		
		import shap
		
		xdata = ShapResult._get_xdata(self)
		
		# Combine terms into single list
		params = []
		for term in self.terms.values():
			if isinstance(term, SingleTerm):
				params.append(term.beta.point)
			else:
				params.extend(s.beta.point for s in term.categories.values())
		
		explainer = shap.LinearExplainer((np.array(params[1:]), params[0]), xdata, **kwargs)  # FIXME: Assumes zeroth term is intercept
		shap_values = explainer.shap_values(xdata).astype('float')
		
		return ShapResult(weakref.ref(self), shap_values, list(xdata.columns))
	
	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')))
		if self.cov_type:
			left_col.append(('Std. Errors:', 'Non-Robust' if self.cov_type == 'nonrobust' else self.cov_type.upper() if self.cov_type.startswith('hc') else self.cov_type))
		
		# Right column
		right_col = []
		
		right_col.append(('No. Observations:', format(self.nobs, '.0f')))
		if self.nevents:
			right_col.append(('No. Events:', format(self.nevents, '.0f')))
		right_col.append(('Df. Model:', format(self.dof_model, '.0f')))
		if self.dof_resid:
			right_col.append(('Df. Residuals:', format(self.dof_resid, '.0f')))
		if self.rsquared:
			right_col.append(('<i>R</i><sup>2</sup>:' if html else 'R²:', format(self.rsquared, '.2f')))
		elif self.ll_null:
			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(f_result.pvalue, PValueStyle.VALUE_ONLY | PValueStyle.HTML)))
			else:
				right_col.append(('F:', format(f_result.statistic, '.2f')))
				right_col.append(('p (F):', fmt_p(f_result.pvalue, PValueStyle.VALUE_ONLY)))
		else:
			# Otherwise report likelihood ratio test as overall test
			right_col.append(('LL-Model:', format(self.ll_model, '.2f')))
			
			if self.ll_null:
				lrtest_result = self.lrtest_null()
				
				right_col.append(('LL-Null:', format(self.ll_null, '.2f')))
				if html:
					right_col.append(('<i>p</i> (LR):', fmt_p(lrtest_result.pvalue, PValueStyle.VALUE_ONLY | PValueStyle.HTML)))
				else:
					right_col.append(('p (LR):', fmt_p(lrtest_result.pvalue, PValueStyle.VALUE_ONLY)))
		
		return left_col, right_col
	
	def __repr__(self):
		if config.repr_is_summary:
			return self.summary()
		return super().__repr__()
	
	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">({: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)
		
		for term_name, term in self.terms.items():
			if isinstance(term, SingleTerm):
				# Single term
				
				# Exponentiate beta if requested
				beta = term.beta
				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_name, beta.point, beta.ci_lower, beta.ci_upper, fmt_p(term.pvalue, PValueStyle.TABULAR | PValueStyle.HTML))
			elif isinstance(term, CategoricalTerm):
				# Categorical term
				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)
				
				# Render reference category
				if term.ref_category is not None:
					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)
				
				# Loop over terms
				for sub_term_name, sub_term in term.categories.items():
					# Exponentiate beta if requested
					beta = sub_term.beta
					if self.exp:
						beta = np.exp(beta)
					
					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, PValueStyle.TABULAR | PValueStyle.HTML))
			else:
				raise Exception('Attempt to render unknown term type')
		
		out += '</table>'
		
		# TODO: Have a detailed view which shows SE, t/z, etc.
		
		if self.comments:
			out += '<ol>'
			for comment in self.comments:
				out += '<li>{}</li>'.format(comment)
			out += '</ol>'
		
		return out
	
	def summary(self):
		"""
		Return a stringified summary of the regression model
		
		:rtype: str
		"""
		
		# 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_name, term in self.terms.items():
			if isinstance(term, SingleTerm):
				# Single term
				
				# Exponentiate beta if requested
				beta = term.beta
				if self.exp:
					beta = np.exp(beta)
				
				# Add some extra padding
				table_data.append([term_name + '  ', format(beta.point, '.2f'), '({:.2f}'.format(beta.ci_lower), '-', '{:.2f})'.format(beta.ci_upper), '  ' + fmt_p(term.pvalue, PValueStyle.TABULAR)])
			elif isinstance(term, CategoricalTerm):
				# Categorical term
				table_data.append([term_name + '  ', '', '', '', '', ''])
				
				# Render reference category
				if term.ref_category is not None:
					table_data.append(['{}  '.format(term.ref_category), 'Ref.', '', '', '', ''])
				
				# Loop over terms
				for sub_term_name, sub_term in term.categories.items():
					# Exponentiate beta if requested
					beta = sub_term.beta
					if self.exp:
						beta = np.exp(beta)
					
					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, PValueStyle.TABULAR)])
			else:
				raise Exception('Attempt to render unknown term type')
		
		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   ', '({:g}% CI)'.format((1-config.alpha)*100))  # 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:])
		
		if self.comments:
			out += '\n'
			for i, comment in enumerate(self.comments):
				out += '\n{}. {}'.format(i + 1, comment)
		
		return out

class SingleTerm:
	"""A term in a :class:`RegressionResult` which is a single term"""
	
	def __init__(self, raw_name, beta, pvalue):
		#: Raw name of the term (*str*; e.g. in :attr:`RegressionResult.raw_result`)
		self.raw_name = raw_name
		#: :class:`yli.utils.Estimate` of the coefficient
		self.beta = beta
		#: *p* value for the coefficient (*float*)
		self.pvalue = pvalue

class CategoricalTerm:
	"""A group of terms in a :class:`RegressionResult` corresponding to a categorical variable"""
	
	def __init__(self, categories, ref_category):
		#: Terms for each of the categories, excluding the reference category (*dict* of :class:`SingleTerm`)
		self.categories = categories
		#: Name of the reference category (*str*)
		self.ref_category = ref_category

def regress(
	model_class, df, dep, formula, *,
	nan_policy='warn',
	model_kwargs=None, fit_kwargs=None,
	family=None, exposure=None, status=None,  # common model_kwargs
	cov_type=None, method=None, maxiter=None, start_params=None,  # common fit_kwargs
	bool_baselevels=False, exp=None,
	_dmatrices=None,
):
	"""
	Fit a statsmodels regression model
	
	:param model_class: Type of regression model to fit
	:type model_class: statsmodels model class
	:param df: Data to perform regression on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numeric)
	:type dep: str
	:param formula: Patsy formula for the regression model
	:type formula: str
	:param exposure: Column in *df* for the exposure variable (numeric, some models only)
	:type exposure: str
	:param status: Column in *df* for the status variable (time-to-event models only)
	:type status: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	:param model_kwargs: Keyword arguments to pass to *model_class* constructor
	:type model_kwargs: dict
	:param fit_kwargs: Keyword arguments to pass to *model.fit*
	:type fit_kwargs: dict
	:param family: See statsmodels *GLM* constructor
	:param cov_type: See statsmodels *model.fit*
	:param method: See statsmodels *model.fit*
	:param maxiter: See statsmodels *model.fit*
	:param start_params: See statsmodels *model.fit*
	:param bool_baselevels: Show reference categories for boolean independent variables even if reference category is *False*
	:type bool_baselevels: bool
	:param exp: Report exponentiated parameters rather than raw parameters, default (*None*) is to autodetect based on *model_class*
	:type exp: bool
	
	:rtype: :class:`yli.regress.RegressionResult`
	
	**Example:**
	
	.. code-block::
		
		df = pd.DataFrame({
			'Unhealthy': [False, False, False, ...],
			'Fibrinogen': [2.52, 2.46, 2.29, ...],
			'GammaGlobulin': [38, 36, 36, ...]
		})
		yli.regress(sm.Logit, df, 'Unhealthy', 'Fibrinogen + GammaGlobulin')
	
	.. code-block:: text
		
		             Logistic Regression Results              
		======================================================
		Dep. Variable:  Unhealthy  |  No. Observations:     32
		        Model:      Logit  |         Df. Model:      2
		       Method:        MLE  |     Df. Residuals:     29
		         Date: 2022-10-18  |         Pseudo R²:   0.26
		         Time:   19:00:34  |          LL-Model: -11.47
		  Std. Errors: Non-Robust  |           LL-Null: -15.44
		                           |            p (LR):  0.02*
		======================================================
		                exp(β)   (95% CI)          p   
		-----------------------------------------------
		  (Intercept)     0.00 (0.00 -  0.24)    0.03* 
		   Fibrinogen     6.80 (1.01 - 45.79)    0.049*
		GammaGlobulin     1.17 (0.92 -  1.48)    0.19  
		-----------------------------------------------
	
	The output summarises the results of the regression.
	Note that the parameter estimates are automatically exponentiated.
	For example, the odds ratio for unhealthiness per unit increase in fibrinogen is 6.80, with 95% confidence interval 1.01–45.79, and is significant with *p* value 0.049.
	"""
	
	# Populate model_kwargs
	if model_kwargs is None:
		model_kwargs = {}
	if family is not None:
		model_kwargs['family'] = family
	
	# Populate fit_kwargs
	if fit_kwargs is None:
		fit_kwargs = {}
	if cov_type is not None:
		fit_kwargs['cov_type'] = cov_type
	if method is not None:
		fit_kwargs['method'] = method
	if maxiter is not None:
		fit_kwargs['maxiter'] = maxiter
	if start_params is not None:
		fit_kwargs['start_params'] = start_params
	
	# Autodetect whether to exponentiate
	if exp is None:
		if model_class in (sm.Logit, sm.PHReg, sm.Poisson, OrdinalLogit, PenalisedLogit):
			exp = True
		else:
			exp = False
	
	df_ref = weakref.ref(df)
	
	if _dmatrices is None:
		# Check for/clean NaNs in input columns
		columns = [dep] + cols_for_formula(formula, df)
		if exposure is not None:
			columns.append(exposure)
		if status is not None:
			columns.append(status)
		
		df = df[columns]
		df = check_nan(df, nan_policy)
		
		# Ensure numeric type for dependent variable
		df[dep], dep_categories = as_numeric(df[dep])
		
		# Convert pandas nullable types for independent variables as this breaks statsmodels
		df = convert_pandas_nullable(df)
		
		# Construct design matrix from formula
		dmatrices = patsy.dmatrices(dep + ' ~ ' + formula, df, return_type='dataframe')
	else:
		dmatrices = _dmatrices
	
	if model_class in (sm.PHReg, OrdinalLogit):
		# Drop explicit intercept term
		# FIXME: Check before dropping
		dmatrices = (dmatrices[0], dmatrices[1].iloc[:,1:])
	
	# Add exposure to model
	if exposure is not None:
		if df[exposure].dtype == '<m8[ns]':
			model_kwargs['exposure'] = df[exposure].dt.total_seconds()
		else:
			model_kwargs['exposure'] = df[exposure]
	
	# Add status to model
	if status is not None:
		model_kwargs['status'] = df[status]
	
	# Fit model
	model = model_class(endog=dmatrices[0], exog=dmatrices[1], **model_kwargs)
	model.formula = dep + ' ~ ' + formula
	result = model.fit(disp=False, **fit_kwargs)
	
	if isinstance(result, RegressionResult):
		# Already processed!
		result.model_class = model_class
		result.df = df_ref
		result.dep = dep
		result.formula = formula
		result.nan_policy = nan_policy
		result.model_kwargs = model_kwargs
		result.fit_kwargs = fit_kwargs
		result.exp = exp
		return result
	
	# Check convergence
	if hasattr(result, 'mle_retvals') and not result.mle_retvals['converged']:
		warnings.warn('Maximum likelihood estimation failed to converge. Check raw_result.mle_retvals.')
	
	# Process terms
	terms = {}
	
	# Join term names manually because statsmodels wrapper is very slow
	#confint = result.conf_int(config.alpha)
	
	if hasattr(result, '_results'):
		confint = {k: v for k, v in zip(model.exog_names, result._results.conf_int(config.alpha))}
		pvalues = {k: v for k, v in zip(model.exog_names, result._results.pvalues)}
		params = result._results.params
	else:
		# e.g. PHReg
		confint = {k: v for k, v in zip(model.exog_names, result.conf_int(config.alpha))}
		pvalues = {k: v for k, v in zip(model.exog_names, result.pvalues)}
		params = result.params
	
	#for raw_name, raw_beta in result.params.items():
	for raw_name, raw_beta in zip(model.exog_names, params):
		beta = Estimate(raw_beta, confint[raw_name][0], confint[raw_name][1])
		
		# Rename terms
		if raw_name == 'Intercept':
			# Intercept term (single term)
			term = '(Intercept)'
			terms[term] = SingleTerm(raw_name, beta, pvalues[raw_name])
		elif model_class is OrdinalLogit and '/' in raw_name:
			# Group ordinal regression cutoffs
			if '(Cutoffs)' not in terms:
				terms['(Cutoffs)'] = CategoricalTerm({}, None)
			
			if dep_categories is None:
				term = raw_name
			else:
				# Need to convert factorised names back into original names
				bits = raw_name.split('/')
				term = dep_categories[round(float(bits[0]))] + '/' + dep_categories[round(float(bits[1]))]
			
			terms['(Cutoffs)'].categories[term] = SingleTerm(raw_name, beta, pvalues[raw_name])
		else:
			# Parse if required
			factor, column, contrast = parse_patsy_term(formula, df, raw_name)
			
			if contrast is not None:
				# Categorical term
				
				if bool_baselevels is False and contrast == 'True' and set(df[column].unique()) == set([True, False]):
					# Treat as single term
					terms[column] = SingleTerm(raw_name, beta, pvalues[raw_name])
				else:
					# Add a new categorical term if not exists
					if column not in terms:
						ref_category = formula_factor_ref_category(formula, df, factor)
						terms[column] = CategoricalTerm({}, ref_category)
					
					terms[column].categories[contrast] = SingleTerm(raw_name, beta, pvalues[raw_name])
			else:
				# Single term
				terms[column] = SingleTerm(raw_name, beta, pvalues[raw_name])
	
	# Fit null model (for ll_null)
	if hasattr(result, 'll_null'):
		ll_null = result.ll_null
	elif hasattr(result, 'llnull'):
		ll_null = result.llnull
	elif model_class is sm.PHReg:
		ll_null = model.loglike([0 for _ in result.params])
	else:
		# Construct null (intercept-only) model
		#result_null = model_class.from_formula(formula=dep + ' ~ 1', data=df).fit()
		dm_exog = pd.DataFrame(index=dmatrices[0].index)
		dm_exog['Intercept'] = pd.Series(dtype='float64')
		dm_exog['Intercept'].fillna(1, inplace=True)
		
		result_null = model_class(endog=dmatrices[0], exog=dm_exog).fit()
		ll_null = result_null.llf
	
	if model_class is sm.OLS:
		method_name = 'Least Squares'
	elif model_class is sm.PHReg:
		method_name = 'MPLE'
	else:
		# Parse raw regression results to get fit method
		# Avoid this in general as it can be expensive to summarise all the post hoc tests, etc.
		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}
		method_name = header_dict['Method:']
	
	# Get names to display
	if model_class is sm.PHReg:
		short_name = 'Cox'
	else:
		short_name = model_class.__name__
	
	if model_class is sm.Logit:
		full_name = 'Logistic Regression'
	elif model_class is OrdinalLogit:
		full_name = 'Ordinal Logistic Regression'
	else:
		full_name = '{} Regression'.format(short_name)
	if fit_kwargs.get('cov_type', 'nonrobust') != 'nonrobust':
		full_name = 'Robust {}'.format(full_name)
	
	return RegressionResult(
		model_class, df_ref, dep, formula, nan_policy, model_kwargs, fit_kwargs,
		result,
		full_name, short_name, method_name,
		getattr(result, 'nobs', len(df)), df[status].sum() if model_class is sm.PHReg else None, result.df_model, datetime.now(), getattr(result, 'cov_type', 'nonrobust'),
		terms,
		result.llf, ll_null,
		getattr(result, 'df_resid', None), getattr(result, 'rsquared', None), getattr(result, 'fvalue', None),
		[],
		exp
	)

def logit_then_regress(model_class, df, dep, formula, *, nan_policy='warn', **kwargs):
	"""
	Perform logistic regression, then use parameters as start parameters for desired regression
	
	:param model_class: Type of regression model to fit
	:type model_class: statsmodels model class
	:param df: Data to perform regression on
	:type df: DataFrame
	:param dep: Column in *df* for the dependent variable (numeric)
	:type dep: str
	:param formula: Patsy formula for the regression model
	:type formula: str
	:param nan_policy: How to handle *nan* values (see :ref:`nan-handling`)
	:type nan_policy: str
	:param kwargs: Passed through to :func:`yli.regress`
	
	:rtype: :class:`yli.regress.RegressionResult`
	"""
	
	# Check for/clean NaNs
	# Do this once here so we only get 1 warning
	df = df[[dep] + cols_for_formula(formula, df)]
	df = check_nan(df, nan_policy)
	
	# Perform logistic regression
	logit_result = regress(sm.Logit, df, dep, formula, **kwargs)
	logit_params = logit_result.raw_result.params
	
	# Check convergence
	if not logit_result.raw_result.mle_retvals['converged']:
		return None
	
	# Perform desired regression
	return regress(model_class, df, dep, formula, start_params=logit_params, **kwargs)

# -----------------------------
# Penalised logistic regression

class PenalisedLogit(statsmodels.discrete.discrete_model.BinaryModel):
	"""
	statsmodels-compatible model for computing Firth penalised logistic regression
	
	Uses the R *logistf* library.
	
	This class should be used in conjunction with :func:`yli.regress`.
	
	**Example:**
	
	.. code-block::
		
		df = pd.DataFrame({
			'Pred': [1] * 20 + [0] * 220,
			'Outcome': [1] * 40 + [0] * 200
		})
		yli.regress(yli.PenalisedLogit, df, 'Outcome', 'Pred', exp=False)
	
	.. code-block:: text
		
		          Penalised Logistic Regression Results          
		=========================================================
		Dep. Variable:      Outcome  |  No. Observations:     240
		        Model:        Logit  |         Df. Model:       1
		       Method: Penalised ML  |         Pseudo R²:    0.37
		         Date:   2022-10-19  |          LL-Model:  -66.43
		         Time:     07:50:40  |           LL-Null: -105.91
		  Std. Errors:   Non-Robust  |            p (LR): <0.001*
		=========================================================
		                β      (95% CI)          p   
		---------------------------------------------
		(Intercept)   -2.28 (-2.77 - -1.85)   <0.001*
		       Pred    5.99  (3.95 - 10.85)   <0.001*
		---------------------------------------------
	
	The output summarises the result of the regression.
	The summary table shows that a penalised method was applied.
	Note that because `exp=False` was passed, the parameter estimates are not automatically exponentiated.
	"""
	
	def fit(self, disp=False):
		import rpy2.robjects as ro
		import rpy2.robjects.packages
		import rpy2.robjects.pandas2ri
		
		# Assume data is already cleaned from regress()
		df = self.data.orig_endog.join(self.data.orig_exog)
		
		# 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
				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(
					None, None, None, None, None, None, None,  # Set in regress()
					model,
					'Penalised Logistic Regression', 'Logit', 'Penalised ML',
					model['n'][0], None, model['df'][0], datetime.now(), 'nonrobust',
					terms,
					model['loglik'][0], model['loglik'][1],
					None, None, None,
					[],
					None  # Set exp in regress()
				)

# ------------------------------------------------------
# Ordinal logistic regression (R/Stata parameterisation)

class OrdinalLogit(statsmodels.miscmodels.ordinal_model.OrderedModel):
	"""
	statsmodels-compatible model for computing ordinal logistic (or probit) regression
	
	The implementation subclasses statsmodels' native *OrderedModel*, but substitutes an alternative parameterisation used by R and Stata.
	In the native statsmodels implementation, the first cutoff parameter is the true cutoff, but further cutoff parameter are log differences between consecutive cutoffs.
	In this parameterisation, cutoff terms are represented directly in the model.
	
	**Example:**
	
	.. code-block::
		
		df = pd.DataFrame(...)
		yli.regress(yli.OrdinalLogit, df, 'apply', 'pared + public + gpa', exp=False)
	
	.. code-block:: text
		
		              Ordinal Logistic Regression Results              
		===============================================================
		Dep. Variable:              apply  |  No. Observations:     400
		        Model:       OrdinalLogit  |         Df. Model:       5
		       Method: Maximum Likelihood  |     Df. Residuals:     395
		         Date:         2022-12-02  |         Pseudo R²:    0.03
		         Time:           21:30:38  |          LL-Model: -358.51
		  Std. Errors:         Non-Robust  |           LL-Null: -370.60
		                                   |            p (LR): <0.001*
		===============================================================
		                                β      (95% CI)         p   
		------------------------------------------------------------
		                      pared    1.05  (0.53 - 1.57)   <0.001*
		                     public   -0.06 (-0.64 - 0.53)    0.84  
		                        gpa    0.62  (0.10 - 1.13)    0.02* 
		                  (Cutoffs)                                 
		   unlikely/somewhat likely    2.20  (0.68 - 3.73)    0.005*
		somewhat likely/very likely    4.30  (2.72 - 5.88)   <0.001*
		------------------------------------------------------------
	
	The output summarises the result of the regression.
	The parameters shown under "(Cutoffs)" are the cutoff values in the latent variable parameterisation of ordinal regression.
	Note that because `exp=False` was passed, the parameter estimates are not automatically exponentiated.
	"""
	
	def __init__(self, endog, exog, **kwargs):
		if 'distr' not in kwargs:
			kwargs['distr'] = 'logit'
		
		super().__init__(endog, exog, **kwargs)
	
	def transform_threshold_params(self, params):
		th_params = params[-(self.k_levels - 1):]
		thresh = np.concatenate(([-np.inf], th_params, [np.inf]))
		return thresh
	
	def transform_reverse_threshold_params(self, params):
		return params[:-1]

class _Dummy: pass

def _wald_test(param_names, params, formula, vcov, df):
	# Hack! Piggyback off statsmodels to compute a Wald test
	
	lmr = statsmodels.base.model.LikelihoodModelResults(model=None, params=None)
	lmr.model = _Dummy()
	lmr.model.data = _Dummy()
	lmr.model.data.cov_names = param_names
	lmr.params = params
	lmr.df_resid = df
	
	return lmr.wald_test(formula, cov_p=vcov, use_f=False, scalar=True)

class BrantResult:
	"""
	Result of a Brant test for ordinal regression
	
	See :meth:`RegressionResult.brant`.
	"""
	
	def __init__(self, tests):
		#: Results for Brant test on each coefficient (*Dict[str, ChiSquaredResult]*)
		self.tests = tests
	
	def __repr__(self):
		if config.repr_is_summary:
			return self.summary()
		return super().__repr__()
	
	def _repr_html_(self):
		out = '<table><caption>Brant Test Results</caption><thead><tr><th></th><th style="text-align:center"><i>χ</i><sup>2</sup></th><th style="text-align:center">df</th><th style="text-align:center"><i>p</i></th></thead><tbody>'
		
		for raw_name, test in self.tests.items():
			out += '<tr><th>{}</th><td>{:.2f}</td><td>{:.0f}</td><td style="text-align:left">{}</td></tr>'.format(raw_name, test.statistic, test.dof, fmt_p(test.pvalue, PValueStyle.TABULAR | PValueStyle.HTML))
		
		out += '</tbody></table>'
		return out
	
	def summary(self):
		"""
		Return a stringified summary of the *χ*:sup:`2` test
		
		:rtype: str
		"""
		
		table = pd.DataFrame([
			['{:.2f}'.format(test.statistic), '{:.0f}'.format(test.dof), fmt_p(test.pvalue, PValueStyle.TABULAR)]
			for test in self.tests.values()
		], index=self.tests.keys(), columns=['χ² ', 'df', 'p   '])
		
		return str(table)