smile.glm.model

Interface Model

All Superinterfaces:

java.io.Serializable

public interface Model
extends java.io.Serializable

The GLM model specification. The GLM consists of three elements:

1. An exponential family of probability distributions.
2. A linear predictor.
3. A link function provides the relationship between the linear predictor and the mean of the distribution function.

This class specifies the distribution and link function in the model.

An overdispersed exponential family of distributions is a generalization of an exponential family and the exponential dispersion model of distributions and includes those families of probability distributions, parameterized by θ and τ. The parameter θ is related to the mean of the distribution. The dispersion parameter τ typically is known and is usually related to the variance of the distribution.

There are many commonly used link functions, and their choice is informed by several considerations. There is always a well-defined canonical link function which is derived from the exponential of the response's density function. However, in some cases it makes sense to try to match the domain of the link function to the range of the distribution function's mean, or use a non-canonical link function for algorithmic purposes.

Method Summary

Modifier and Type	Method and Description
double	deviance(double[] y, double[] mu, double[] residuals) The deviance function.
double	dlink(double mu) The derivative of link function.
double	invlink(double eta) The inverse of link function.
double	link(double mu) The link function.
double	loglikelihood(double[] y, double[] mu) The log-likelihood function.
double	mustart(double y) The function to estimates the tarting values of means given y.
double	nullDeviance(double[] y, double mu) The NULL deviance function.
double	variance(double mu) The variance function.

Method Detail

link

double link(double mu)

The link function.

invlink

double invlink(double eta)

The inverse of link function.

dlink

double dlink(double mu)

The derivative of link function.

variance

double variance(double mu)

The variance function.

deviance

double deviance(double[] y,
                double[] mu,
                double[] residuals)

The deviance function.

nullDeviance

double nullDeviance(double[] y,
                    double mu)

The NULL deviance function.

loglikelihood

double loglikelihood(double[] y,
                     double[] mu)

The log-likelihood function.

mustart

double mustart(double y)

The function to estimates the tarting values of means given y.