hazrate.like: hazrate.like - Hazard rate likelihood

Description

Computes the hazard rate distance function.

Usage

hazrate.like(a, dist, covars)

Value

A list containing the following two components:

L.unscaled: A matrix of size $n$X$k$X$b$ containing likelihood values evaluated at distances in dist. Each row is associated with a single distance, and each column is associated with a single case (row of a). This matrix is "unscaled" because the underlying likelihood does not integrate to one. Values in L.unscaled are always greater than or equal to zero.
params: A $n$X$k$X$b$ array of the likelihood's (canonical) parameters, First page contains parameter values related to covariates (i.e., $s = exp(x'a)$), while subsequent pages contain other parameters. $b$ = 1 for halfnorm, negexp; $b$ = 2 for hazrate and others. Rows correspond to distances in dist. Columns correspond to rows from argument a.

Arguments

a: A vector or matrix of covariate and expansion term coefficients. Dimension is $k$ X $p$, where $k$ (i.e., nrow(a)) is the number of coefficient vectors to evaluate (cases) and $p$ (i.e., ncol(a)) is the number of covariate and expansion coefficients in the likelihood. If a is a dimensionless vector, it is interpreted to be a single row with $k$ = 1. Covariate coefficients in a are the first $q$ values ($q$ <= $p$), and must be on a log scale.
dist: A numeric vector of length $n$ or a single-column matrix (dimension $n$X1) containing detection distances at which to evaluate the likelihood.
covars: A numeric vector of length $q$ or matrix of dimension $n$X$q$ containing covariate values associated with distances in argument d

Details

The hazard rate likelihood is $$f(x|\sigma,k) = 1 - \exp(-(x/\sigma)^{-k})$$ where $\sigma$ determines location (i.e., distance at which the function equals 1 - exp(-1) = 0.632), and $k$ determines slope of the function at $\sigma$ (i.e., larger k equals steeper slope at $\sigma$). For distance analysis, the valid range for both $\sigma$ and k is $\geq 0$.

Examples

Run this code

d <- seq(0, 100, length=100)
covs <- matrix(1,length(d),1)
hazrate.like(c(log(20), 5), d, covs)

# Changing location parameter
plot(d, hazrate.like(c(log(20), 5), d, covs)$L.unscaled, type="l", col="red")
lines(d, hazrate.like(c(log(40), 5), d, covs)$L.unscaled, col="blue")
abline(h = 1 - exp(-1), lty = 2)
abline(v = c(20,40), lty = 2)

# Changing slope parameter
plot(d, hazrate.like(c(log(50), 20), d, covs)$L.unscaled, type="l", col="red")
lines(d, hazrate.like(c(log(50), 2), d, covs)$L.unscaled, col="blue")
abline(h = 1 - exp(-1), lty = 2)
abline(v = 50, lty = 2)