linksrm_convert {PtProcess}R Documentation

Parameter Conversion for Linked Stress Release Model

Description

Converts parameter values between two different parameterisations (described in Details below) of the linked stress release model.

Usage

linksrm_convert(params, abc=TRUE)

Arguments

params

a vector of parameter values of length n2+2nn^2+2n, where nn is the number of regions in the model.

abc

logical. If TRUE (default), then the input value of params is that of the abc parameterisation. See Details for further explanation.

Details

If abc == TRUE, the conditional intensity for the iith region is assumed to have the form

λg(t,iHt)=exp{ai+bi[tj=1ncijSj(t)]} \lambda_g(t,i | {\cal H}_t) = \exp\left\{ a_i + b_i\left[t - \sum_{j=1}^n c_{ij} S_j(t)\right]\right\}

with params=(a1,,an,b1,,bn,c11,c12,c13,,cnn) = (a_1, \cdots, a_n, b_1, \cdots, b_n, c_{11}, c_{12}, c_{13}, \cdots, c_{nn}).

If abc == FALSE, the conditional intensity for the iith region is assumed to have the form

λg(t,iHt)=exp{αi+νi[ρitj=1nθijSj(t)]} \lambda_g(t,i | {\cal H}_t) = \exp\left\{ \alpha_i + \nu_i\left[\rho_i t - \sum_{j=1}^n \theta_{ij} S_j(t)\right]\right\}

where θii=1\theta_{ii}=1 for all ii, n=length(params)+11n = \sqrt{\code{length(params)} + 1} - 1, and params

=(α1,,αn,ν1,,νn,ρ1,,ρn,θ12,θ13,,θ1n,θ21,θ23,,θn,n1). = (\alpha_1, \cdots, \alpha_n, \nu_1, \cdots, \nu_n, \rho_1, \cdots, \rho_n, \theta_{12}, \theta_{13}, \cdots, \theta_{1n}, \theta_{21}, \theta_{23}, \cdots, \theta_{n,n-1}).

Value

A list object with the following components is returned:

params

vector as specified in the function call.

a

vector of length nn as in the abc parameterisation.

b

vector of length nn as in the abc parameterisation.

c

n by nn matrix as in the abc parameterisation.

alpha

vector of length nn as in the alternative parameterisation.

nu

vector of length nn as in the alternative parameterisation.

rho

vector of length nn as in the alternative parameterisation.

theta

n by nn matrix with ones on the diagonal as in the alternative parameterisation.

See Also

linksrm_gif


[Package PtProcess version 3.3-16 Index]