integrateOneStepLines: Integrate Line-transect One-step function

In Rdistance: Density and Abundance from Distance-Sampling Surveys

Integrate Line-transect One-step function

Description

Compute exact integral of the one-step distance function for line transects.

Usage

integrateOneStepLines(object, newdata = NULL, Units = NULL)

Arguments

object	Either an Rdistance fitted distance function (an object that inherits from class "dfunc"; usually produced by a call to dfuncEstim), or a matrix of canonical distance function parameters (e.g., matrix(exp(fit$par),1)). If a matrix, each row corresponds to a distance function and each column is a parameter. The first column is the parameter related to sighting covariates and must be transformed to the "real" space (i.e., inverse link, which is exp(), must be applied outside this routine). If object is a matrix, it should not have measurement units because only derived quantities (e.g., ESW) have units; Rdistance function parameters themselves never have units.
newdata	A data frame containing new values for the distance function covariates. If NULL and object is a fitted distance function, the observed covariates stored in object are used (behavior similar to predict.lm). Argument newdata is ignored if object is a matrix.
Units	Physical units of sighting distances if object is a matrix. Sighting distance units can differ from units of w.lo or w.hi. Ignored if object is a fitted distance function.

Details

Returned integrals are

\int_0^{w} (\frac{p}{\theta_i}I(0\leq x \leq \theta_i) + \frac{1-p}{w - \theta_i}I(\theta_i < x \leq w)) dx = \frac{\theta_i}{p},

where w = w.hi - w.lo, \theta_i is the estimated one-step distance function threshold for the i-th observed distance, and p is the estimated one-step proportion.

Value

A vector of areas under the distance functions represented in object. If object is a distance function and newdata is specified, the returned vector's length is nrow(newdata). If object is a distance function and newdata is NULL, returned vector's length is length(distances(object)). If object is a matrix, return's length is nrow(object).

Note

Users will not normally call this function. It is called internally by nLL and effectiveDistance.

See Also

integrateNumeric; integrateNegexpLines; integrateHalfnormLines

Examples

# A oneStep distance function on simulated data
whi <- 250
T <- 100  # true threshold
p <- 0.85 # true proportion <T
n <- 200  # num simulated points
x <- c( runif(n*p, min=0, max=T), runif(n*(1-p), min=T, max=whi))
x <- setUnits(x, "m")
tranID <- sample(rep(1:10, each=n/10), replace=FALSE)
detectDf <- data.frame(transect = tranID, dist = x)
siteDf <- data.frame(transect = 1:10
               , length = rep(setUnits(10,"m"), 10))
distDf <- RdistDf(siteDf, detectDf)

# Estimation
fit <- dfuncEstim(distDf
                 , formula = dist ~ 1
                 , likelihood = "oneStep"
                 , w.hi = setUnits(whi, "m")
                 )
table(integrateOneStepLines(fit))
table(ESW(fit))

# Check:
T.hat <- exp(fit$par[1])
p.hat <- fit$par[2]
gAtT <- ((1-p.hat) * T.hat) / (p.hat * (whi - T.hat))

plot(fit)
abline(h = gAtT, col="blue")

areaLE.T <- (1.0) * T.hat
areaGT.T <- gAtT * (whi - T.hat)
areaLE.T + areaGT.T  # ESW

# Equivalent
T.hat / p.hat

Rdistance documentation built on Jan. 10, 2026, 1:07 a.m.