gxEstim function

gxEstim - Estimate g(0) or g(x)

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

gxEstim(fit)

Arguments

• fit: An estimated dfunc object. See dfuncEstim.

Returns

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.

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.

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 doubleobserver 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".

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.

Examples

data(sparrowDf)
fit <- dfuncEstim(sparrowDf, dist ~ groupsize(groupsize))
gxEstim(fit)
  
fit <- dfuncEstim(sparrowDf, dist ~ groupsize(groupsize)
                , x.scl = units::set_units(50,"m")
                , g.x.scl = 0.75)
gxEstim(fit)
plot(fit)
abline(h=0.75)
abline(v=units::set_units(50,"m"))

See Also

dfuncEstim