1211 lines
44 KiB
Python
1211 lines
44 KiB
Python
# scipy-yli: Helpful SciPy utilities and recipes
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# Copyright © 2022–2023 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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import patsy
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from scipy import stats
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from scipy.special import expit
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import statsmodels, statsmodels.miscmodels.ordinal_model
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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 tqdm import tqdm
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from datetime import datetime
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import itertools
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import warnings
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import weakref
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from .bayes_factors import BayesFactor, bayesfactor_afbf
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from .config import config
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from .shap import ShapResult
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from .sig_tests import ChiSquaredResult, FTestResult
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from .utils import Estimate, PValueStyle, as_numeric, check_nan, cols_for_formula, convert_pandas_nullable, 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 (VIF) for each variable in *df*
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:param df: Data to calculate the VIF for
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:type df: DataFrame
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:param formula: If specified, calculate the VIF only for the variables in the formula
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:type formula: str
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:return: The variance inflation factors
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:rtype: Series
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**Example:**
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.. code-block::
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df = pd.DataFrame({
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'D': [68.58, 67.33, 67.33, ...],
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'T1': [14, 10, 10, ...],
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'T2': [46, 73, 85, ...],
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...
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})
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yli.vif(df[['D', 'T1', 'T2', ...]])
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.. code-block:: text
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D 8.318301
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T1 6.081590
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T2 2.457122
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...
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dtype: float64
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The output shows the variance inflation factor for each variable in *df*.
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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(ChiSquaredResult):
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"""
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Result of a likelihood ratio test for regression
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See :meth:`RegressionResult.lrtest_null`.
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"""
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def __init__(self, statistic, dof, pvalue):
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super().__init__(statistic, dof, 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, PValueStyle.RELATION | PValueStyle.HTML))
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def summary(self):
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"""
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Return a stringified summary of the likelihood ratio test
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:rtype: str
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"""
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return 'LR({}) = {:.2f}; p {}'.format(self.dof, self.statistic, fmt_p(self.pvalue, PValueStyle.RELATION))
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class RegressionResult:
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"""
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Result of a regression
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See :func:`yli.regress`.
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"""
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def __init__(self,
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model_class, df, dep, formula, nan_policy, model_kwargs, fit_kwargs,
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raw_result,
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full_name, model_name, fit_method,
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nobs, nevents, dof_model, fitted_dt, cov_type,
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terms,
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ll_model, ll_null,
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dof_resid, rsquared, f_statistic,
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comments,
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exp
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):
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# Data about how model fitted
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#: See :func:`yli.regress`
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self.model_class = model_class
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#: Data fitted (*weakref* to *DataFrame*)
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self.df = df
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#: See :func:`yli.regress`
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self.dep = dep
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#: See :func:`yli.regress`
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self.formula = formula
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#: See :func:`yli.regress`
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self.nan_policy = nan_policy
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#: See :func:`yli.regress`
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self.model_kwargs = model_kwargs
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#: See :func:`yli.regress`
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self.fit_kwargs = fit_kwargs
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#: Raw result from statsmodels *model.fit*
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self.raw_result = raw_result
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# Information for display
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#: Full name of the regression model type (*str*)
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self.full_name = full_name
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#: Short name of the regression model type (*str*)
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self.model_name = model_name
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#: Method for fitting the regression model (*str*)
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self.fit_method = fit_method
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# Basic fitted model information
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#: Number of observations (*int*)
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self.nobs = nobs
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#: Number of events (*int*, time-to-event models only)
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self.nevents = nevents
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#: Degrees of freedom for the model (*int*)
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self.dof_model = dof_model
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#: Date and time of fitting the model (Python *datetime*)
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self.fitted_dt = fitted_dt
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#: Method for computing the covariance matrix (*str*)
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self.cov_type = cov_type
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# Regression coefficients/p values
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#: Coefficients and *p* values for each term in the model (*dict* of :class:`SingleTerm` or :class:`CategoricalTerm`)
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self.terms = terms
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# Model log-likelihood
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#: Log-likelihood of fitted model (*float*)
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self.ll_model = ll_model
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#: Log-likelihood of null model (*float*)
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self.ll_null = ll_null
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# Extra statistics (not all regression models have these)
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#: Degrees of freedom for the residuals (*int*; *None* if N/A)
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self.dof_resid = dof_resid
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#: *R*:sup:`2` statistic (*float*; *None* if N/A)
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self.rsquared = rsquared
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#: *F* statistic (*float*; *None* if N/A)
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self.f_statistic = f_statistic
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#: Comments for the model (*List[str]*)
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self.comments = comments or []
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# Config for display style
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#: See :func:`yli.regress`
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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*:sup:`2` statistic"""
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return 1 - self.ll_model/self.ll_null
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def lrtest_null(self):
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"""
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Compute the likelihood ratio test comparing the model to the null model
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:rtype: :class:`LikelihoodRatioTestResult`
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"""
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statistic = -2 * (self.ll_null - self.ll_model)
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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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"""
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Perform the *F* test that all slopes are 0
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:rtype: :class:`yli.sig_tests.FTestResult`
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"""
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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 a Bayes factor testing the hypothesis that the given beta is 0
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Uses the R *BFpack* library.
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Requires the regression to be from statsmodels.
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The term must be specified as the *raw name* from the statsmodels regression, available via :attr:`RegressionResult.raw_result`.
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:param term: Raw name of the term to be tested
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:type term: str
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:rtype: :class:`yli.bayes_factors.BayesFactor`
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"""
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# FIXME: Allow specifying our renamed terms
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# Get parameters required for AFBF
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params = pd.Series({raw_name.replace('[', '_').replace(']', '_'): beta for raw_name, beta in self.raw_result.params.items()})
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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 brant(self):
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"""
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Perform the Brant test for the parallel regression assumption in ordinal regression
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Applicable when the model was fitted using :class:`OrdinalLogit`.
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:rtype: :class:`BrantResult`
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**Example:**
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.. code-block::
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df = pd.DataFrame(...)
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model = yli.regress(yli.OrdinalLogit, df, 'apply', 'pared + public + gpa', exp=False)
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model.brant()
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.. code-block:: text
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χ² df p
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Omnibus 4.34 3 0.23
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pared 0.13 1 0.72
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public 3.44 1 0.06
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gpa 0.18 1 0.67
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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.
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**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>`_
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"""
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df = self.df()
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if df is None:
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raise Exception('Referenced DataFrame has been dropped')
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dep = self.dep
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# Check for/clean NaNs
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# NaN warning/error will already have been handled in regress, so here we pass nan_policy='omit'
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# Following this, we pass nan_policy='raise' to assert no NaNs remaining
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df = df[[dep] + cols_for_formula(self.formula, df)]
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df = check_nan(df, 'omit')
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# Ensure numeric type for dependent variable
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df[dep], dep_categories = as_numeric(df[dep])
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# Convert pandas nullable types for independent variables as this breaks statsmodels
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df = convert_pandas_nullable(df)
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# Precompute design matrix for RHS
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# This is also X+ in Brant paper
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dmatrix_right = patsy.dmatrix(self.formula, df, return_type='dataframe')
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dmatrix_right.reset_index(drop=True, inplace=True) # Otherwise this confuses matrix multiplication
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# Fit individual logistic regressions
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logit_models = []
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for upper_limit in sorted(df[dep].unique())[:-1]:
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dep_dichotomous = (df[dep] <= upper_limit).astype(int).reset_index(drop=True)
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logit_result = sm.Logit(dep_dichotomous, dmatrix_right).fit(disp=False, **self.fit_kwargs)
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if not logit_result.mle_retvals['converged']:
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raise Exception('Maximum likelihood estimation failed to converge for {} <= {}. Check raw_result.mle_retvals.'.format(dep, upper_limit))
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if pd.isna(logit_result.bse).any():
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raise Exception('Regression returned NaN standard errors for {} <= {}.'.format(dep, upper_limit))
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logit_models.append(logit_result)
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logit_betas = np.array([model._results.params for model in logit_models]).T
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logit_pihat = np.array([expit(-model.fittedvalues) for model in logit_models]).T # Predicted probabilities
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# vcov is the variance-covariance matrix of all individually fitted betas across all terms
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# | model 1 | model 2 | model 3 | ...
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# | term 1 | term 2 | term 1 | term 2 | term 1 | term 2 | ...
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# model 1 | term 1 |
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# | term 2 |
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# model 2 | term 1 |
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# | term 2 |
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# ...
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n_terms = len(dmatrix_right.columns) - 1 # number of beta terms (excluding intercept)
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n_betas = len(logit_models) * n_terms
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vcov = np.zeros((n_betas, n_betas))
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# Populate the variance-covariance matrix for comparisons between individually fitted models
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for j in range(0, len(logit_models) - 1):
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for l in range(j + 1, len(logit_models)):
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Wjj = np.diag(logit_pihat[:,j] - logit_pihat[:,j] * logit_pihat[:,j])
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Wjl = np.diag(logit_pihat[:,l] - logit_pihat[:,j] * logit_pihat[:,l])
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Wll = np.diag(logit_pihat[:,l] - logit_pihat[:,l] * logit_pihat[:,l])
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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)
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j_vs_l_vcov = np.asarray(matrix_result)[1:,1:] # Asymptotic covariance for j,l
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vcov[j*n_terms:(j+1)*n_terms, l*n_terms:(l+1)*n_terms] = j_vs_l_vcov
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vcov[l*n_terms:(l+1)*n_terms, j*n_terms:(j+1)*n_terms] = j_vs_l_vcov
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# Populate the variance-covariance matrix within each individually fitted model
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for i in range(len(logit_models)):
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vcov[i*n_terms:(i+1)*n_terms, i*n_terms:(i+1)*n_terms] = logit_models[i]._results.cov_params()[1:,1:]
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# ------------------
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# Perform Wald tests
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beta_names = ['{}_{}'.format(raw_name, i) for i in range(len(logit_models)) for raw_name in dmatrix_right.columns[1:]]
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wald_results = {}
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# Omnibus test
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constraints = [' = '.join('{}_{}'.format(raw_name, i) for i in range(len(logit_models))) for raw_name in dmatrix_right.columns[1:]]
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constraint = ', '.join(constraints)
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df = (len(logit_models) - 1) * (len(dmatrix_right.columns) - 1) # df = (number of levels minus 2) * (number of terms excluding intercept)
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wald_result = _wald_test(beta_names, logit_betas[1:].ravel('F'), constraint, vcov, df)
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wald_results['Omnibus'] = ChiSquaredResult(wald_result.statistic, wald_result.df_denom, wald_result.pvalue)
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# Individual terms
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for raw_name in dmatrix_right.columns[1:]:
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constraint = ' = '.join('{}_{}'.format(raw_name, i) for i in range(len(logit_models)))
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df = len(logit_models) - 1 # df = (number of levels minus 2)
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wald_result = _wald_test(beta_names, logit_betas[1:].ravel('F'), constraint, vcov, df)
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wald_results[raw_name] = ChiSquaredResult(wald_result.statistic, wald_result.df_denom, wald_result.pvalue)
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return BrantResult(wald_results)
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def bootstrap(self, samples=1000):
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"""
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Use bootstrapping to recompute confidence intervals and *p* values for the terms in the regression model
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:param samples: Number of bootstrap samples to draw
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:type samples: int
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:rtype: :class:`yli.regress.RegressionResult`
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"""
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df = self.df()
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if df is None:
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raise Exception('Referenced DataFrame has been dropped')
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dep = self.dep
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# Check for/clean NaNs
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# NaN warning/error will already have been handled in regress, so here we pass nan_policy='omit'
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# Following this, we pass nan_policy='raise' to assert no NaNs remaining
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df = df[[dep] + cols_for_formula(self.formula, df)]
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df = check_nan(df, 'omit')
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# Ensure numeric type for dependent variable
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df[dep], dep_categories = as_numeric(df[dep])
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# Convert pandas nullable types for independent variables as this breaks statsmodels
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df = convert_pandas_nullable(df)
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# Precompute design matrices
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dmatrices = patsy.dmatrices(dep + ' ~ ' + self.formula, df, return_type='dataframe')
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# Fit full model
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#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)
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# Initialise bootstrap_results
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bootstrap_results = {} # Dict mapping term raw names to bootstrap betas
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for term in self.terms.values():
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if isinstance(term, SingleTerm):
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bootstrap_results[term.raw_name] = []
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else:
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for sub_term in term.categories.values():
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bootstrap_results[sub_term.raw_name] = []
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# Draw bootstrap samples and regress
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dmatrices = dmatrices[0].join(dmatrices[1])
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for i in tqdm(range(samples)):
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bootstrap_rows = dmatrices.sample(len(df), replace=True)
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model = self.model_class(endog=bootstrap_rows.iloc[:,0], exog=bootstrap_rows.iloc[:,1:], **self.model_kwargs)
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model.formula = dep + ' ~ ' + self.formula
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result = model.fit(disp=False, **self.fit_kwargs)
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for raw_name, raw_beta in zip(model.exog_names, result._results.params):
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bootstrap_results[raw_name].append(raw_beta)
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# Combine bootstrap results
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terms = {}
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for term_name, term in self.terms.items():
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if isinstance(term, SingleTerm):
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bootstrap_betas = bootstrap_results[term.raw_name]
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bootstrap_pvalue = sum(1 for b in bootstrap_betas if b < 0) / len(bootstrap_betas)
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bootstrap_pvalue = 2 * min(bootstrap_pvalue, 1 - bootstrap_pvalue)
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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)
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else:
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categories = {}
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for sub_term_name, sub_term in term.categories.items():
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bootstrap_betas = bootstrap_results[sub_term.raw_name]
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bootstrap_pvalue = sum(1 for b in bootstrap_betas if b < 0) / len(bootstrap_betas)
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bootstrap_pvalue = 2 * min(bootstrap_pvalue, 1 - bootstrap_pvalue)
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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)
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terms[term_name] = CategoricalTerm(categories, term.ref_category)
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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 (True/False or 1/0, 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)
|