From aa88239cb11a6da546c821254a71c90b75995812 Mon Sep 17 00:00:00 2001
From: RunasSudo <runassudo@yingtongli.me>
Date: Fri, 21 Apr 2023 15:27:42 +1000
Subject: [PATCH] Implement deviance chi-squared test for Poisson regression

---
 yli/regress.py   | 16 ++++++++++++++++
 yli/sig_tests.py |  2 +-
 2 files changed, 17 insertions(+), 1 deletion(-)

diff --git a/yli/regress.py b/yli/regress.py
index 289b810..4470ae0 100644
--- a/yli/regress.py
+++ b/yli/regress.py
@@ -237,6 +237,7 @@ class RegressionModel:
 		self.rsquared = None
 		self.ll_model = None
 		self.ll_null = None
+		self.ll_saturated = None
 		self.f_statistic = None
 		
 		# Parameters
@@ -480,6 +481,18 @@ class RegressionModel:
 		else:
 			return bf01.invert()
 	
+	def deviance_chi2(self):
+		"""
+		Perform the deviance *χ*:sup:`2` test for goodness of fit
+		
+		:rtype: :class:`yli.sig_tests.ChiSquaredResult`
+		"""
+		
+		deviance_model = 2 * (self.ll_saturated - self.ll_model)
+		pvalue = 1 - stats.chi2.cdf(deviance_model, df=self.dof_resid)
+		
+		return ChiSquaredResult(deviance_model, int(self.dof_resid), pvalue)
+	
 	def ftest(self):
 		"""
 		Perform the *F* test that all slopes are 0
@@ -1131,6 +1144,9 @@ class Poisson(RegressionModel):
 		result.ll_model = raw_result.llf
 		result.ll_null = raw_result.llnull
 		
+		# Compute saturated log-likelihood
+		result.ll_saturated = float(sm.families.Poisson().loglike(data_dep + 1e-10, data_dep + 1e-10))
+		
 		result.terms = raw_terms_from_statsmodels_result(raw_result)
 		result.vcov = raw_result.cov_params()
 		
diff --git a/yli/sig_tests.py b/yli/sig_tests.py
index 24b6d98..cd17aef 100644
--- a/yli/sig_tests.py
+++ b/yli/sig_tests.py
@@ -583,7 +583,7 @@ class ChiSquaredResult:
 	"""
 	Result of a generic test with *χ*:sup:`2`-distributed test statistic
 	
-	See :meth:`yli.logrank`.
+	See :meth:`yli.logrank`, :meth:`yli.regress.RegressionModel.deviance_chi2`.
 	
 	See also :class:`yli.regress.BrantResult`, :class:`yli.regress.LikelihoodRatioTestResult`, :class:`PearsonChiSquaredResult`.
 	"""