F.gx.estim {Rdistance}

F.gx.estim - Estimate g(0) or g(x)

Description

Estimate g(0) or g(x) for a specified distance function.

Usage

F.gx.estim(fit, x.scl = NULL, g.x.scl = NULL, observer = NULL)

Arguments

fit

An estimated dfunc object. See dfuncEstim.

x.scl

The x coordinate (a distance) at which to scale the sightability function to g.x.scl, or the string "max". When x.scl is specified (i.e., not 0 or "max"), it must have measurement units assigned using either library(units);units(x.scl) <- '<units>' or x.scl <- units::set_units(x.scl, <units>). See units::valid_udunits() for valid symbolic units. See Details for more on scaling the sightability function.

g.x.scl

Height of the distance function at coordinate x. The distance function will be scaled so that g(x.scl) = g.x.scl. If g.x.scl is not a data frame, it must be a numeric value (vector of length 1) between 0 and 1. See Details.

observer

A numeric scalar or text string specifying whether observer 1 or observer 2 or both were full-time observers. This parameter dictates which set of observations form the denominator of a double observer system. If, for example, observer 2 was a data recorder and part-time observer, or if observer 2 was the pilot, set observer = 1. If observer = 1, observations by observer 1 not seen by observer 2 are ignored. The estimate of detection in this case is the ratio of number of targets seen by both observers to the number seen by both plus the number seen by just observer 2. If observer = "both", the computation goes both directions.

Details

This routine scales sightability such that g(x.scl) = g.x.scl, where g() is the sightability function. Specification of x.scl and g.x.scl covers several estimation cases:

1. g(0) = 1 : (the default) Inputs are x.scl = 0, g.x.scl = 1. If w.lo > 0, x.scl will be set to w.lo so technically this case is g(w.low) = 1.

2. User supplied probability at specified distance: Inputs are x.scl = a number greater than or equal to w.lo, g.x.scl = a number between 0 and 1. This case covers situations where sightability on the transect (distance 0) is not perfect. This case assumes researchers have an independent estimate of sightability at distance x.scl off the transect. For example, researchers could be using multiple observers to estimate that sightability at distance x.scl is g.x.scl.

3. Maximum sightability specified: Inputs are x.scl="max", g.x.scl = a number between 0 and 1. In this case, g() is scaled such that its maximum value is g.x.scl. This routine computes the distance at which g() is maximum, sets g()'s height there to g.x.scl, and returns x.max where x.max is the distance at which g is maximized. This case covers the common aerial survey situation where maximum sightability is slightly off the transect, but the distance at which the maximum occurs is unknown. This case is the default, with g.x.scl = 1, when gamma distance functions are estimated.

4. Double observer system: Inputs are x.scl="max", g.x.scl = <a data frame>. In this case, g(x) = h, where x is the distance that maximizes g and h is the height of g() at x computed from the double observer data frame (see below for structure of the double observer data frame).

5. Distance of independence specified, height computed from double observer system: Inputs are x.scl = a number greater than or equal to w.lo g.x.scl = a data frame. In this case, g(x.scl) = h, where h is computed from the double observer data frame (see below for structure of the double observer data frame).

When x.scl, g.x.scl, or observer are NULL, the routine will look for and use $call.x.scl, or $call.g.x.scl, or $call.observer components of the fit object for whichever of these three parameters is missing. Later, different values can be specified in a direct call to F.gx.estim without having to re-estimate the distance function. Because of this feature, the default values in dfuncEstim are x.scl = 0 and g.x.scl = 1 and observer = "both".

Value

A list comprised of the following components:

x.scl

The value of x (distance) at which g() is evaluated.

comp2

The estimated value of g() when evaluated at x.scl.

Structure of the double observer data frame

When g.x.scl is a data frame, it is assumed to contain the components $obsby.1 and $obsby.2 (no flexibility on names). Each row in the data frame contains data from one sighted target. The $obsby.1 and $obsby.2 components are TRUE/FALSE (logical) vectors indicating whether observer 1 (obsby.1) or observer 2 (obsby.2) spotted the target.

See Also

dfuncEstim

Examples

  set.seed(555574)
  x <- rnorm(1000) * 100
  x <- x[ 0 < x & x < 100 ]
  x <- units::set_units(x, "m")
  un.dfunc <- dfuncEstim( x ~ 1
                       , likelihood = "logistic")    
  F.gx.estim(un.dfunc)
  
  x <- rgamma(1000, shape = 5)
  x <- units::set_units(x, "m")
  gam.dfunc <- dfuncEstim( x ~ 1
                         , likelihood="Gamma")    
  F.gx.estim(gam.dfunc)