/*
Copyright (C) 2012, University of Cambridge, Department of Psychiatry.
Created by Rudolf Cardinal (rnc1001@cam.ac.uk).
This file is part of CamCOPS.
CamCOPS is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
CamCOPS 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with CamCOPS. If not, see <https://www.gnu.org/licenses/>.
*/
#pragma once
// #define LINK_FUNCTION_FAMILY_USE_AIC
#include <functional>
#include <QString>
#include "maths/include_eigen_dense.h" // IWYU pragma: keep
// Represents a link function family for a generalized linear model.
class LinkFunctionFamily
{
public:
using LinkFnType = std::function<Eigen::ArrayXXd(const Eigen::ArrayXXd&)>;
using InvLinkFnType = std::function<Eigen::ArrayXXd(const Eigen::ArrayXXd&)>;
using DerivativeInvLinkFnType = std::function<Eigen::ArrayXXd(const Eigen::ArrayXXd&)>;
using VarianceFnType = std::function<Eigen::ArrayXXd(const Eigen::ArrayXXd&)>;
using DevResidsFnType = std::function<Eigen::ArrayXd(
const Eigen::ArrayXd&, // y
const Eigen::ArrayXd&, // mu
const Eigen::ArrayXd& // wt
)>;
using ValidEtaFnType = std::function<bool(const Eigen::ArrayXd&)>;
using ValidMuFnType = std::function<bool(const Eigen::ArrayXd&)>;
using InitializeFnType = std::function<bool( // returns: OK?
QStringList&, // errors
const LinkFunctionFamily&, // family
Eigen::ArrayXd&, // y
Eigen::ArrayXd&, // n
Eigen::ArrayXd&, // m
Eigen::ArrayXd&, // weights
Eigen::ArrayXd&, // start
Eigen::ArrayXd&, // etastart
Eigen::ArrayXd& // mustart
)>;
#ifdef LINK_FUNCTION_FAMILY_USE_AIC
using AICFnType = std::function<double(
const Eigen::ArrayXd&, // y, definitely vector (from glm.fit)
const Eigen::ArrayXd&, // n (NO IDEA from R glm.fit)
const Eigen::ArrayXd&, // mu, definitely vector (from glm.fit)
const Eigen::ArrayXd&, // wt, definitely vector (from glm.fit)
double // dev, definitely scalar (from glm.fit)
)>;
#endif
LinkFunctionFamily(
const QString& family_name,
const LinkFnType& link_fn,
const InvLinkFnType& inv_link_fn,
const DerivativeInvLinkFnType& derivative_inv_link_fn,
const VarianceFnType& variance_fn,
const DevResidsFnType& dev_resids_fn,
const ValidEtaFnType& valid_eta_fn,
const ValidMuFnType& valid_mu_fn,
const InitializeFnType& initialize_fn
#ifdef LINK_FUNCTION_FAMILY_USE_AIC
, const AICFnType& aic_fn
#endif
);
public:
// For nasty hacks, like R does ;)
QString family_name; // "family" in R
// Link function, giving eta = link(mu):
LinkFnType link_fn;
// Inverse link function, giving mu = invlink(eta):
InvLinkFnType inv_link_fn;
// Derivative of the inverse link function ("mu.eta" in R).
// This gives d(mu)/d(eta) as a function of eta.
DerivativeInvLinkFnType derivative_inv_link_fn;
// Variance function: gives the variance as a function of the mean; "the
// part of the variance that depends on" the mean; V(mu).
// https://en.wikipedia.org/wiki/Variance_function
// If the variance is independent of the mean, then this should return a
// constant, probably 1.
VarianceFnType variance_fn;
// As per "dev.resids" in "?family" in R:
// Function giving the deviance for each observation as a
// function of ‘(y, mu, wt)’, used by the ‘residuals’ method
// when computing deviance residuals.
// For example, the unit deviance for the normal distribution is given by
// d(y, mu) = (y - mu)^2
// ... https://en.wikipedia.org/wiki/Deviance_(statistics)
// and so that is what statsfunc::gaussianDevResids() provides, as one of
// the functions that might be used here.
DevResidsFnType dev_resids_fn;
// Validate the linear predictors
ValidEtaFnType valid_eta_fn;
// Validate the means
ValidMuFnType valid_mu_fn;
// GLM initialization (ugly eval() code in R)
InitializeFnType initialize_fn;
#ifdef LINK_FUNCTION_FAMILY_USE_AIC
// AIC (Aikake information criterion) calculation ("aic" in R)
AICFnType aic_fn;
#endif
};
extern const QString LINK_FAMILY_NAME_GAUSSIAN;
extern const QString LINK_FAMILY_NAME_BINOMIAL;
extern const QString LINK_FAMILY_NAME_POISSON;
// Some concrete link function families:
extern const LinkFunctionFamily LINK_FN_FAMILY_GAUSSIAN; // default for glm() in R
extern const LinkFunctionFamily LINK_FN_FAMILY_LOGIT;
extern const LinkFunctionFamily LINK_FN_FAMILY_POISSON;