# Linked Stress Release Model Object Creates a point process model object with class `"linksrm"`. ```r linksrm(data, gif, marks, params, gmap, mmap, TT) ``` ## Arguments - `data`: a `data.frame` containing the history of the process, denoted below as $Ht$. It should contain all variables that are required to evaluate the `gif` function and the mark distribution, though can contain others too. No history is represented as `NULL`. - `gif`: ground intensity function. At this stage, this can only be `linksrm_gif` or modifications of that function; see Details below. - `marks`: mark distribution. See topic `marks` for further details. - `params`: numeric vector of **all** model parameters. - `gmap`: `expression`, maps the model parameters (`params`) into the parameter sub-space of the ground intensity function; see Details below. - `mmap`: `expression`, maps the model parameters (`params`) into the parameter sub-space of the mark distribution; see Details below. - `TT`: vector of length 2, being the time interval over which the integral of the ground intensity function is to be evaluated. ## Details The linked stress release model has a slightly peculiar structure which makes it difficult to fit into the `mpp` class. While the region should be thought of as a mark, it is completely defined by the function `linksrm_gif`, and hence from the programming perspective the `region` mark is really tied in with the `gif` function. Hence at the moment, the linked stress release model is treated as a special case. There may be other models that could be grouped into this class. ## Examples ```r p <- c(-1.5, -1.5, 0.01, 0.03, 2, -0.5, 0.2, 1, 1*log(10), 3) TT <- c(0, 1000) rexptrunc_mark <- function(ti, data, params){ x <- rexp(n=1, params[1]) x[x > params[2]] <- params[2] names(x) <- "magnitude" return(x) } x <- linksrm(data=NULL, gif=linksrm_gif, marks=list(NULL, rexptrunc_mark), params=p, gmap=expression(params[1:8]), mmap=expression(params[9:10]), TT=TT) x <- simulate(x, seed=5) print(logLik(x)) # estimate parameters temp_map <- function(y, p){ # map only gif parameters into model object y$params[1:8] <- p return(y) } weight <- c(0.1, 0.1, 0.005, 0.005, 0.1, 0.1, 0.1, 0.1) # see manual page for linksrm_gif for modifications to # make calculations faster # for testing, restrict to 5 iterations z <- nlm(neglogLik, p[1:8], object=x, pmap=temp_map, hessian=TRUE, gradtol=1e-08, steptol=1e-10, print.level=2, iterlim=5, typsize=weight) param.names <- c("a1", "a2", "b1", "b2", "c11", "c12", "c21", "c22") param.est <- cbind(p[1:8], z$estimate, sqrt(diag(solve(z$hessian)))) dimnames(param.est) <- list(param.names, c("Actual", "Estimate", "StdErr")) print(param.est) # place parameter estimates into model object x <- temp_map(x, z$estimate) # plot ground intensity function par.default <- par(mfrow=c(2,1), mar=c(4.1, 4.1, 0.5, 1)) x$gif <- linksrm_gif plot(x, 1, xlab="") plot(x, 2) par(par.default) # plot "residuals" for each region tau <- residuals(x) par(mfrow=c(2,1)) for (i in 1:2){ plot(tau[[i]], ylab="Transformed Time", xlab="Event Number", main=paste("Region", i)) abline(a=0, b=1, lty=2, col="red") } # plot cusum of "residuals" for each region for (i in 1:2){ plot(tau[[i]] - 1:length(tau[[i]]), ylab="Cusum of Transformed Time", xlab="Event Number", main=paste("Region", i)) abline(h=0, lty=2, col="red") } par(mfrow=c(1,1)) ```

linksrm function