glm.hpp File Reference

Generalized Linear Models (GLM) More...

#include "statcpp/basic_statistics.hpp"
#include "statcpp/continuous_distributions.hpp"
#include "statcpp/linear_regression.hpp"
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <exception>
#include <limits>
#include <stdexcept>
#include <utility>
#include <vector>

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Classes
struct	statcpp::glm_result
	GLM result structure. More...
struct	statcpp::glm_residuals
	GLM residuals structure. More...

Namespaces
namespace	statcpp
namespace	statcpp::detail
	Internal helper functions.

Enumerations
enum class	statcpp::link_function {   statcpp::identity , statcpp::logit , statcpp::probit , statcpp::log ,   statcpp::inverse , statcpp::cloglog }
	Link function types. More...
enum class	statcpp::distribution_family { statcpp::gaussian , statcpp::binomial , statcpp::poisson , statcpp::gamma_family }
	Distribution family. More...

Functions
double	statcpp::detail::link_transform (double mu, link_function link)
	Link function g(mu) -> eta.
double	statcpp::detail::inverse_link (double eta, link_function link)
	Inverse link function g^{-1}(eta) -> mu.
double	statcpp::detail::link_derivative (double mu, link_function link)
	Derivative of link function d(eta)/d(mu) = g'(mu)
double	statcpp::detail::variance_function (double mu, distribution_family family)
	Variance function V(mu)
double	statcpp::detail::deviance_residual (double y, double mu, distribution_family family)
	Calculate deviance (for a single observation)
std::vector< double >	statcpp::detail::solve_weighted_least_squares (const std::vector< std::vector< double > > &X, const std::vector< double > &z, const std::vector< double > &w, std::vector< std::vector< double > > &XtWX_inv)
	Solve weighted least squares.
glm_result	statcpp::glm_fit (const std::vector< std::vector< double > > &X, const std::vector< double > &y, distribution_family family=distribution_family::gaussian, link_function link=link_function::identity, std::size_t max_iter=100, double tol=1e-8)
	Fit a generalized linear model.
glm_result	statcpp::logistic_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t max_iter=100, double tol=1e-8)
	Logistic regression.
double	statcpp::predict_probability (const glm_result &model, const std::vector< double > &x)
	Probability prediction with logistic regression.
std::vector< double >	statcpp::odds_ratios (const glm_result &model)
	Calculate odds ratios.
std::vector< std::pair< double, double > >	statcpp::odds_ratios_ci (const glm_result &model, double confidence=0.95)
	Confidence intervals for odds ratios.
glm_result	statcpp::poisson_regression (const std::vector< std::vector< double > > &X, const std::vector< double > &y, std::size_t max_iter=100, double tol=1e-8)
	Poisson regression.
double	statcpp::predict_count (const glm_result &model, const std::vector< double > &x)
	Expected count prediction with Poisson regression.
std::vector< double >	statcpp::incidence_rate_ratios (const glm_result &model)
	Calculate Incidence Rate Ratios.
glm_residuals	statcpp::compute_glm_residuals (const glm_result &model, const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Calculate GLM residuals.
double	statcpp::overdispersion_test (const glm_result &model, const std::vector< std::vector< double > > &X, const std::vector< double > &y)
	Overdispersion test (for Poisson regression)
double	statcpp::pseudo_r_squared_mcfadden (const glm_result &model)
	McFadden's pseudo R-squared.
double	statcpp::pseudo_r_squared_nagelkerke (const glm_result &model, const std::vector< double > &y, std::size_t n)
	Nagelkerke's pseudo R-squared.

Detailed Description

Generalized Linear Models (GLM)

Provides generalized linear models including logistic regression and Poisson regression. Uses the IRLS (Iteratively Reweighted Least Squares) algorithm for parameter estimation.

Definition in file glm.hpp.