Initial implementation of Brant test
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@ -19,7 +19,7 @@ from .config import config
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from .descriptives import auto_descriptives
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from .distributions import beta_oddsratio, beta_ratio, hdi, transformed_dist
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from .io import pickle_read_compressed, pickle_read_encrypted, pickle_write_compressed, pickle_write_encrypted
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from .regress import OrdinalLogit, PenalisedLogit, logit_then_regress, regress, regress_bootstrap, vif
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from .regress import OrdinalLogit, PenalisedLogit, brant, logit_then_regress, regress, regress_bootstrap, vif
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from .sig_tests import anova_oneway, auto_univariable, chi2, mannwhitney, pearsonr, ttest_ind
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def reload_me():
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165
yli/regress.py
165
yli/regress.py
@ -31,7 +31,7 @@ import warnings
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from .bayes_factors import BayesFactor, bayesfactor_afbf
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from .config import config
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from .sig_tests import FTestResult
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from .sig_tests import ChiSquaredResult, FTestResult
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from .utils import Estimate, PValueStyle, 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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@ -94,7 +94,7 @@ def vif(df, formula=None, *, nan_policy='warn'):
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# ----------
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# Regression
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class LikelihoodRatioTestResult:
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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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@ -102,17 +102,7 @@ class LikelihoodRatioTestResult:
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"""
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def __init__(self, statistic, dof, pvalue):
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#: Likelihood ratio test statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom for the likelihood ratio test statistic (*int*)
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self.dof = dof
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#: *p* value for the likelihood ratio test (*float*)
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self.pvalue = pvalue
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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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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@ -913,3 +903,152 @@ class OrdinalLogit(statsmodels.miscmodels.ordinal_model.OrderedModel):
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def transform_reverse_threshold_params(self, params):
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return params[:-1]
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class _Dummy: pass
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def _wald_test(param_names, params, formula, vcov, df):
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# Hack! Piggyback off statsmodels to compute a Wald test
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lmr = statsmodels.base.model.LikelihoodModelResults(model=None, params=None)
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lmr.model = _Dummy()
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lmr.model.data = _Dummy()
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lmr.model.data.cov_names = param_names
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lmr.params = params
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lmr.df_resid = df
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return lmr.wald_test(formula, cov_p=vcov, use_f=False, scalar=True)
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class BrantResult:
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# TODO: Documentation
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def __init__(self, tests):
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#: Results for Brant test on each coefficient (*Dict[str, ChiSquaredResult]*)
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self.tests = tests
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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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>'
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for raw_name, test in self.tests.items():
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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))
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out += '</tbody></table>'
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return out
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def summary(self):
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"""
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Return a stringified summary of the *χ*:sup:`2` test
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:rtype: str
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"""
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# FIXME
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return 'FIXME'
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def brant(
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df, dep, formula, *,
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nan_policy='warn',
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fit_kwargs=None,
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method=None, maxiter=None, start_params=None, # common fit_kwargs
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):
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# TODO: Documentation
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if fit_kwargs is None:
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fit_kwargs = {}
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if method is not None:
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fit_kwargs['method'] = method
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if maxiter is not None:
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fit_kwargs['maxiter'] = maxiter
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if start_params is not None:
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fit_kwargs['start_params'] = start_params
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# Check for/clean NaNs
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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(formula, df)]
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df = check_nan(df, nan_policy)
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# Ensure numeric type for dependent variable
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if df[dep].dtype != 'float64':
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df[dep] = df[dep].astype('float64')
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# Convert pandas nullable types for independent variables 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(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]: # FIXME: Sort order
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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, **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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@ -483,7 +483,35 @@ def mannwhitney(df, dep, ind, *, nan_policy='warn', brunnermunzel=True, use_cont
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# ------------------------
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# Pearson chi-squared test
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class PearsonChiSquaredResult:
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class ChiSquaredResult:
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# TODO: Documentation
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def __init__(self, statistic, dof, pvalue):
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#: *χ*:sup:`2` statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom for the *χ*:sup:`2` distribution (*int*)
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self.dof = dof
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#: *p* value for the *χ*:sup:`2` test (*float*)
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self.pvalue = pvalue
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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return '<i>χ</i><sup>2</sup>({}) = {:.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 *χ*:sup:`2` test
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:rtype: str
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"""
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return 'χ²({}) = {:.2f}; p {}'.format(self.ct, self.dof, self.statistic, fmt_p(self.pvalue, PValueStyle.RELATION))
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class PearsonChiSquaredResult(ChiSquaredResult):
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"""
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Result of a Pearson *χ*:sup:`2` test
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@ -491,24 +519,15 @@ class PearsonChiSquaredResult:
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"""
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def __init__(self, ct, statistic, dof, pvalue, oddsratio=None, riskratio=None):
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super().__init__(statistic, dof, pvalue)
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#: Contingency table for the observations (*DataFrame*)
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self.ct = ct
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#: *χ*:sup:`2` statistic (*float*)
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self.statistic = statistic
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#: Degrees of freedom for the *χ*:sup:`2` distribution (*int*)
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self.dof = dof
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#: *p* value for the *χ*:sup:`2` test (*float*)
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self.pvalue = pvalue
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#: Odds ratio (*float*; *None* if not a 2×2 table)
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self.oddsratio = oddsratio
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#: Risk ratio (*float*; *None* if not a 2×2 table)
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self.riskratio = riskratio
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def __repr__(self):
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if config.repr_is_summary:
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return self.summary()
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return super().__repr__()
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def _repr_html_(self):
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if self.oddsratio is not None:
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return '{0}<br><i>χ</i><sup>2</sup>({1}) = {2:.2f}; <i>p</i> {3}<br>OR ({4:g}% CI) = {5}<br>RR ({4:g}% CI) = {6}'.format(
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