residuals: Residuals of a Point Process Model

In PtProcess: Time Dependent Point Process Modelling

Description

Provides methods for the generic function residuals.

Usage

## S3 method for class 'mpp'
residuals(object, ...)
## S3 method for class 'linksrm'
residuals(object, ...)

Arguments

object	an object with class mpp or linksrm.
...	other arguments.

Details

Let ti be the times of the observed events. Then the transformed times are defined as

tau_i = integral_0^{ti} of {lambda_g(t|Ht) dt}.

If the proposed point process model is correct, then the transformed time points will form a stationary Poisson process with rate parameter one. A plot of transformed time points versus the cumulative number of events should then roughly follow the straight line y = x. Significant departures from this line indicate a weakness in the model. Further details can be found in Ogata (1988) and Aalen & Hoem (1978).

See Baddeley et al (2005) and Zhuang (2006) for extensions of these methodologies.

Value

Returns a time series object with class "ts" in the case of mpp. In the case of linksrm a list is returned with the number of components being equal to the number of regions, and with each component being a time series object.

References

Cited references are listed on the PtProcess manual page.

Examples

TT <- c(0, 1000)
bvalue <- 1
params <- c(-2.5, 0.01, 0.8, bvalue*log(10))

x <- mpp(data=NULL,
         gif=srm_gif,
         marks=list(NULL, rexp_mark),
         params=params,
         gmap=expression(params[1:3]),
         mmap=expression(params[4]),
         TT=TT)
x <- simulate(x, seed=5)

tau <- residuals(x)

plot(tau, ylab="Transformed Time", xlab="Event Number")
abline(a=0, b=1, lty=2, col="red")

#   represent as a cusum
plot(tau - 1:length(tau), ylab="Cusum of Transformed Time", xlab="Event Number")
abline(h=0, lty=2, col="red")

PtProcess documentation built on May 4, 2021, 1:06 a.m.