expected.n: Expected Number of Individuals

Description

Computes the expected number of individuals detected across a detector layout or at each cluster of detectors.

Usage

expected.n(object, session = NULL, group = NULL, bycluster
    = FALSE, splitmask = FALSE)

Arguments

object

secr object output from secr.fit

session

character session vector

group

group -- for future use

bycluster

logical to output the expected number for clusters of detectors rather than whole array

splitmask

logical for computation method (see Details)

Value

The expected count (bycluster = FALSE) or a vector of expected counts, one per cluster. For multi-session data, a list of such vectors.

Warning

This function changed slightly between 2.1.0 and 2.1.1, and now performs as indicated here when bycluster = TRUE and clusters are not specified. Detectors are assumed to be independent (as with detector types `proximity', `count' etc.). The computed E(n) does not apply when there is competition among detectors, e.g., when detector = `multi'. The prediction of density at present considers only the base level of density covariates, such as cell-specific habitat variables.

Details

The expected number of individuals detected is $E(n) = \int p.(X) D(X) dX$ where the integration is a summation over object$mask. $p.(X)$ is the probability an individual at $X$ will be detected at least once either on the whole detector layout (bycluster = FALSE) or on the detectors in a single cluster (see pdot for more on $p.$). $D(X)$ is the expected density at $X$, given the model. $D(X)$ is constant (i.e. density surface flat) if object$CL == TRUE or object$model$D == ~1, and for some other possible models. If the bycluster option is selected and detectors are not, in fact, assigned to clusters then each detector will be treated as a cluster, with a warning. By default, a full habitat mask is used for each cluster. This is the more robust option. Alternatively, the mask may be split into subregions defined by the cells closest to each cluster. The calculation takes account of any fitted continuous model for spatial variation in density (note Warning).

Examples

Run this code

expected.n(secrdemo.0)

expected.n(secrdemo.0, bycluster = TRUE)
expected.n(ovenbird.model.D)

## Clustered design
mini <- make.grid(nx = 3, ny = 3, spacing = 50, detector =
    "proximity")
tempgrids <- trap.builder (cluster = mini , method = "all",
    frame = expand.grid(x = seq(1000, 9000, 2000),
    y = seq(1000, 9000, 2000)), plt = TRUE)
capt <- sim.capthist(tempgrids, popn = list(D = 2))
tempmask <- make.mask(tempgrids, buffer = 100,
    type = "clusterbuffer")
fit <- secr.fit(capt, mask = tempmask, trace = FALSE)
En <- expected.n(fit, bycluster = TRUE)

## GoF or overdispersion statistic
p <- length(fit$fit$par)
y <- cluster.counts(capt)
## scaled by n-p
sum((y - En)^2 / En) / (length(En)-p)
sum((y - En)^2 / En) / sum(y/En)

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