#include <yat/regression/NegativeBinomial.h>

Inheritance diagram for theplu::yat::regression::NegativeBinomial:

Public Member Functions
double	alpha (void) const
	alpha parameter More...

const utility::Matrix &	covariance (void) const
	Covariance of parameters. More...

void	fit (const utility::Matrix &x, const utility::VectorBase &y)
	fit model parameters More...

const utility::Vector &	fit_parameters (void) const

double	predict (const utility::VectorBase &x) const

Detailed Description

Negative Binomial regression models count data from a negative binomial distribution, $y \in NB(r;p)$ , for which the mean is $\mu = \frac{pr}{1-p}$ is modeled as $log(\mu) = \beta_0 + \beta_1 x_1 + ... + \beta_p x_p$ and the variance $V = \frac{pr}{(1-p)^2} = \alpha m(x)$ where $\alpha$ is the dispersion parameter $( \ge 1 )$ describing how wider the distribution is compared to Poisson; for $\alpha = 1$ the models equals Poisson regression.

Since: new in yat 0.15

Member Function Documentation

◆ alpha()

double theplu::yat::regression::NegativeBinomial::alpha ( void ) const

alpha parameter

The alpha parameter describves the dispersion of the data. Greater alpha implies greater dispersion and unity alpha means the model is same as Poisson regression.

◆ covariance()

const utility::Matrix& theplu::yat::regression::NegativeBinomial::covariance ( void ) const

Covariance of parameters.

Covariance matrix is inferred as $\alpha \left( X' W X \right)^{-1}$ where $ W $ is a diagonal matrix with element $W_{ii} = \mu_i$

◆ fit()

void theplu::yat::regression::NegativeBinomial::fit	(	const utility::Matrix &	x,
		const utility::VectorBase &	y
	)

virtual

fit model parameters

The parameters are tuned to minimise deviation between data and model $2 \sum_i y_i \ln (y_i / \mu_i)$

Each row in x represents a sample.

Implements theplu::yat::regression::Multivariate.

◆ fit_parameters()

const utility::Vector& theplu::yat::regression::NegativeBinomial::fit_parameters ( void ) const

virtual

Returns: model parameters

Implements theplu::yat::regression::Multivariate.

◆ predict()

double theplu::yat::regression::NegativeBinomial::predict ( const utility::VectorBase & x ) const

virtual

Predicted value given x. The prediction is calculated as $\exp{\beta_0 + \beta_1 x_1 +...+\beta_p x_p}$

Implements theplu::yat::regression::Multivariate.

The documentation for this class was generated from the following file:

yat/regression/NegativeBinomial.h

Public Member Functions

Detailed Description

Member Function Documentation

◆ alpha()

◆ covariance()

◆ fit()

◆ fit_parameters()

◆ predict()