Family: Class "Family"

In ppstat: Point Process Statistics

Description

An object of class Family specifies the family and corresponding phi function for a generalized linear point process model.

Objects from the Class

Objects can be created by calls of the form new("Family", name, link, phi, Dphi, D2phi).

Alternatively, the constructors Hawkes and Gibbs can be used.

Slots

name:

Object of class character.

link:

Object of class character.

phi:

Object of class function.

Dphi:

Object of class function.

D2phi:

Object of class function.

Methods

family

signature(object = "Family"): Returns the family name as a character.

Details

The family object is part of the model specification for a generalized linear point process model as implemented in the class PointProcessModel.

Two implemented families are the Hawkes and the Gibbs family. The link is the "inverse" of the phi function specified as a text string to facilitate the use of standard conventions, e.g. the log-link function corresponds to phi=exp.

Implemented standard link functions are, 'log', 'logit', 'cloglog', 'identity', 'root', 'logaffine'. The latter two require the specification of the additional parameter c, which by default is 0. For 'root' the resulting phi-function is

phi(x) = x^{c+1}1(x > 0)

and for 'logaffine'

phi(x) = exp(x)1(x <= c) + exp(c)(x - c + 1)1(x > c).

Using the identity link-function requires a constrained parameter space to ensure that the intensity for the point process model is positive. For this reason φ(x)=max(x,0) is often a better choice, which is obtained using the 'root' link with c=0 (the default).

Note that in order to prevent taking the logarithm of 0 in the computation of the minus-log-likelihood function, and thus preventing the minus-log-likelihood from taking the value Inf, the implementation modifies the standard link functions to be bounded below by .Machine$double.eps.

Author(s)

Niels Richard Hansen, [e-mail]

See Also

PointProcessModel, Hawkes and pointProcessModel.

Examples

showClass("Family")

## The Hawkes family with the log-link.
new("Family", 'Hawkes', link = 'log')
## Or using the constructor.
Hawkes(link = 'log')

## The default for the constructor is the root link.
Hawkes()

## The Hawkes family with the logaffine-link.
Hawkes(link = 'logaffine', c = 1) 

ppstat documentation built on May 2, 2019, 5:26 p.m.