Calculate Area of Intersection inside Circle and Square with Common Center

Description

Calculate Area of Intersection inside Circle and Square with Common Center

Usage

Acins(r, s)

Arguments

Value

vector of intersections of interiors of circles with squaure

Examples

 # calculate area in annulus intersecting square
s <- 10 # radius or half-width of square
r <- c(11, 12) # inner and outer radii of circle
diff(Acins(r, s)) # intersection of square and annulus
# figure to illustrate the calculated area:
theta <- seq(0, 2 * pi, length = 1500)
plot(0, xlim = max(r) * c(-1, 1), ylim = max(r) * c(-1, 1),
  xlab = "x", ylab = "y", asp = 1, bty = "n", type = "n")
xi <- r[1] * cos(theta)
yi <- r[1] * sin(theta)
xo <- r[2] * cos(theta)
yo <- r[2] * sin(theta)
i1 <- which(abs(xi) <= s & abs(yi) <= s)
i2 <- which(abs(xo) <= s & abs(yo) <= s)
i2 <- sort(i2, decreasing = TRUE)
xi <- xi[i1]
yi <- yi[i1]
xo <- xo[i2]
yo <- yo[i2]
polygon(col = 8, border = NA,
  x = c(xi[xi >= 0 & yi >= 0], xo[xo >= 0 & yo >= 0]), 
  y = c(yi[xi >= 0 & yi >= 0], yo[xo >= 0 & yo >= 0]))
polygon(col = 8, border = NA, 
  x = c(xi[xi <= 0 & yi >= 0], xo[xo <= 0 & yo >= 0]), 
  y = c(yi[xi <= 0 & yi >= 0], yo[xo <= 0 & yo >= 0]))
polygon(col = 8, border = NA,
  x = c(xi[xi <= 0 & yi <= 0], xo[xo <= 0 & yo <= 0]), 
 y = c(yi[xi <= 0 & yi <= 0], yo[xo <= 0 & yo <= 0]))
polygon(col = 8, border = NA,
 x = c(xi[xi >= 0 & yi <= 0], xo[xo >= 0 & yo <= 0]), 
 y = c(yi[xi >= 0 & yi <= 0], yo[xo >= 0 & yo <= 0]))
lines(r[1] * cos(theta), r[1]* sin(theta))
lines(r[2]* cos(theta), r[2] * sin(theta))
rect(-s, -s, s, s)
 # calculate areas in series of 1 m annuli extending to corner of square
 s <- 10.5 # radius of square (center to side)
 diff(Acins(r = 0:ceiling(sqrt(2) * s), s))

Probability Distributions for Carcasses Versus Distance from Turbine

Description

PDFs and CDFs that are required by ddd, pdd and qdd but are not included among the standard R distributions. Relying on custom code and included here are the Maxwell-Boltzmann (pmb and dmb), xep0 (Pareto), xep1, xepi0 (inverse gamma), xep2 (Rayleigh), xep02, xep12, xep012, xep123, and xep0123. Not included here are the distributions that can be calculated using standard probability functions from base R, namely the exponential, truncated normal, lognormal, gamma (xep01), and chisquared distributions and the inverse gaussian, which is calculated using statmod::dinvgauss and statmod::dinvgauss. The functions are designed for vector x or q and scalar parameters.

Usage

dmb(x, a)

pmb(q, a)

dxep1(x, b1)

pxep1(q, b1)

pxep02(q, b0, b2)

dxep02(x, b0, b2)

dxep12(x, b1, b2)

pxep12(x, b1, b2)

dxep123(x, b1, b2, b3, const = NULL)

pxep123(x, b1, b2, b3, const = NULL)

dxepi0(x, shape, scale)

pxepi0(x, shape, scale)

dxep0123(x, b0, b1, b2, b3, const = NULL)

pxep0123(x, b0, b1, b2, b3, const = NULL)

dxep012(x, b0, b1, b2, const = NULL)

pxep012(x, b0, b1, b2, const = NULL)

dxep2(x, s2)

pxep2(x, s2)

dxep0(x, a)

pxep0(x, a)

Arguments

Details

An xep distribution is calculated by dividing its kernel (for the densities) or the integral of its kernel (for the cumulative distributions) by the normalizing constant, which is the integral of the kernel from 0 to Inf. The kernel of an xep distribution is defined as x e^{P(x)}, where P(x) is a polynomial with terms defined by the suffix on xep. For example, the kernel of xep12 would be x e^{b_1*x + b_2*x^2}. A 0 in the suffix indicates a log(X) term and an i indicates a 1/x term. The parameters of the xep distributions are some combination of b_0, b_1, b_2, b_3. The parameterizations of the inverse gamma (xepi0), Rayleigh (xep2), and Pareto (xep0) follow the standard conventions of shape and scale for the inverse gamma, s2 = s^2 for the Rayleigh, and a = a for the Pareto (with a scale or location parameter of 1 and PDF = a/x^(x + 1) with support (1, Inf).

The Maxwell-Boltzmann is a one-parameter family with parameter a and PDF f(a) = \sqrt{2/\pi}\frac{x^2 e^{-x^2/(2a^2)}}{a^3}. The kernel is f(a) = x^2 e^{-x^2}, which has a simple closed-form integral that involves the error function (pracma::erf).

Value

vector of probability densities or cumulative probabilities

Check validity of format of custom prior for M

Description

Check validity of format of custom prior for M

Usage

MpriorOK(prior)

Arguments

Value

boolean. Is the prior formatted properly?

Plot dd and ddArray Objects

Description

Plot CDF, PDF, or rcd (relative carcass density) for a single carcass dispersion glm model (dd object) or a list of models (ddArray object).

Usage

## S3 method for class 'ddArray'
plot(
  x,
  type = "CDF",
  extent = "full",
  distr = "all",
  xmax = NULL,
  resolution = 250,
  mod_highlight = NULL,
  ...
)

## S3 method for class 'dd'
plot(
  x,
  type = "CDF",
  extent = "full",
  xmax = NULL,
  resolution = 250,
  nsim = 1000,
  CL = 0.9,
  ...
)

## S3 method for class 'fmod'
plot(x, ...)

## S3 method for class 'polygonLayout'
plot(x, ...)

## S3 method for class 'layoutSimple'
plot(x, ...)

## S3 method for class 'psiHat'
plot(x, ...)

## S3 method for class 'dwphat'
plot(x, ...)

Arguments

Details

ddArray objects are plotted with lines in order of decreasing AICc, so that the "better" models are closer to the top and more prominent. The model with the lowest AICc ("best" model) is plotted last with a heavier line than the others.

For dd objects, the curve for the MLE of the parameters is plotted, along with a 100CL% confidence bounds determined for nsim simulation reps

The legend follows the ordering given by modelFilter with the default sieve or, if extent = "win" by (1) delta AICc < 10, (2) the absence of high-influence points, and (2) AICc. The best model according to the filter is listed first, with a heavier line than the others; the remaining distributions are listed in descending order, with the best models in the leftmost column.

Value

Plot displayed; no return value.

Subset a Set of Fitted Dispersion Models (ddArray)

Description

Subset a Set of Fitted Dispersion Models (ddArray)

Usage

## S3 method for class 'ddArray'
x[distr]

Arguments

Details

Subset the ddArray object as if it were a simple vector

Value

list of selected models with crucial statistics

Subset Simulated Dispersion Parameters while Preserving Attributes

Description

Subset Simulated Dispersion Parameters while Preserving Attributes

Usage

## S3 method for class 'ddSim'
x[i, j, ...]

Arguments

Details

Subset the ddSim object as if it were a simple matrix or array

Value

array with simulated beta parameters from the glm model, their conversion to distribution parameters. NOTE: subsetting to a column or a row returns a matrix rather than a vector. This simplifies the coding and makes it easier to maintain integrity of data structures, but behavior differs from what is done when subsetting standard R matrices and arrays to a single column or row. Also unlike with standard R arrays and matrices, the class structure and attributes are preserved upon subsetting.

Add Carcasses to a Site Layout

Description

After the site layout is analyzed and structured by rings for analysis, carcass data may still need to be added to the site data. addCarcass grabs carcass location data from a shape file or data frame and formats it into ring data, with carcass tallies in every 1m ring from the turbine to the maximum search distance away from any turbine.

Usage

addCarcass(x, ...)

## S3 method for class 'shapeCarcass'
addCarcass(
  x,
  data_ring,
  plotLayout = NULL,
  ncarcReset = TRUE,
  ccCol = NULL,
  ...
)

## S3 method for class 'data.frame'
addCarcass(
  x,
  data_ring,
  ccCol = NULL,
  ncarcReset = TRUE,
  unitCol = "turbine",
  rCol = "r",
  ...
)

Arguments

Value

an object of class rings with a tally of the number of of carcasses discovered in each concentric 1m ring from the turbine to the most distant point searched.

Examples

 data(layout_simple)
 data(carcass_simple)
 sitedata <- initLayout(layout_simple)
 ringdata <- prepRing(sitedata)
 ringsWithCarcasses <- addCarcass(carcass_simple, data_ring = ringdata)

Calculate Akaike Information Criterion (AICc) for Distance Distributions

Description

functions for calculating AICc for carcass dispersion models.

Usage

aic(x, ...)

## S3 method for class 'ddArray'
aic(x, extent = "full", ...)

## S3 method for class 'ddArraycc'
aic(x, extent = "full", ...)

## S3 method for class 'dd'
aic(x, ...)

Arguments

Value

Data frame with AICc and deltaAICc for all models in x

Names of the Named Distributions

Description

Names of the Named Distributions

Usage

alt_names

Format

An object of class character of length 10.

Example Carcass Distances to Accompany the Polygon Layout Data Set

Description

Example Carcass Distances to Accompany the Polygon Layout Data Set

Usage

carcass_polygon

Format

A data frame illustrating an import format for carcass distances. There are columns with turbine IDs (turbine) and carcass distances from turbine (r). Distances (r) are in meters from the nearest turbine. The data set is used in the "polygon" example in the User Guide.

Carcass Data to Accompany the Simple Geometry Data Format

Description

Carcass Data to Accompany the Simple Geometry Data Format

Usage

carcass_simple

Format

An object of class data.frame with 55 rows and 2 columns.

Full, Simulated carcass_simple Data Set (Including Locations and Missed Carcasses)

Description

Full, Simulated carcass_simple Data Set (Including Locations and Missed Carcasses)

Usage

carcass_simple0

Format

An object of class data.frame with 100 rows and 6 columns.

Convert GLM Coefficients into Named Distribution Parameters

Description

Convert GLM Coefficients into Named Distribution Parameters

Usage

cof2parms(x, ...)

## S3 method for class 'matrix'
cof2parms(x, distr, ...)

## S3 method for class 'numeric'
cof2parms(x, distr, ...)

## S3 method for class 'dd'
cof2parms(x, ...)

## S3 method for class 'matrix'
parms2cof(x, distr, ...)

Arguments

Value

matrix of parameters

Check Whether GLM Coefficients Give Proper Distribution

Description

In order for a fitted GLM to convert to a proper distance distribution, its integral from 0 to Inf must be finite. As a rule, when the leading coefficient is positive, the integral diverges as the upper bound of integration approaches infinity, and cofOK would return FALSE. Likewise, in some cases, the GLM coefficients yield an integral that diverges as the lower bound approaches 0, in which case cofOK returns FALSE as well. cofOK0 and cofOKInf check the left and right tails of the candidate distribution, repectively, for convergence.

Usage

cofOK(cof, distr)

cofOK0(cof, distr)

cofOKInf(cof, distr)

Arguments

Value

boolean vector (or scalar)

Names of the GLM Coefficients for Each Distribution

Description

Names of the GLM Coefficients for Each Distribution

Usage

cof_name

Format

A list with the names of the coefficients (vector of character strings) as they appear in the $coefficients value returned from glm for each model.

Constraints on GLM Coefficients for Extensibility to a Distribution

Description

Constraints on GLM Coefficients for Extensibility to a Distribution

Usage

constraints

Format

A list of matrices giving the upper and lower bounds that each model's coefficients must meet for the model to be extensible to a distribution. The parscale column may be used in optim for fitting a truncated weighted likelihood model.

Constraints on Parameters to Assure Extensibility

Description

Constraints on Parameters to Assure Extensibility

Usage

constraints_par

Format

An object of class list of length 17.

Extract Parameters from a Distance Model (dd) and Format as ddSim Object

Description

This is a utility function called internally by dwp functions to extract parameters from a fitted dd model and formats them for analysis and calculation.

Usage

dd2ddSim(dd)

Arguments

Value

ddSim object with 1 row

Calculate CI for CDF, PDF, or quantile

Description

Calculate a confidence interval for the CDF, PDF, or quantile of a carcass distance distribution.

Usage

ddCI(
  mod,
  x,
  type = "CDF",
  CL = 0.9,
  nsim = 1000,
  extent = "full",
  zrad = 200,
  na.tol = 0.1
)

Arguments

Value

array (ddCI class) with columns for distance and the CI bounds

Fit Distance Distribution Model(s)

Description

Fit generalized linear models (glm) for distance distribution models corresponding to standard forms [xep1, xep01 (gamma), xep2 (Rayleigh), xep02, xep12, xep012, xep123, xep0123 (normal-gamma with x = tau), lognormal, truncated normal, Maxwell Boltzmann, and constant] and supplentary forms [exponential, chi-squared, inverse gamma, and inverse Gaussian].

The glm is converted to a probability distribution by dividing by a normalizing constant, namely the integral of the glm evaluated from 0 to infinity. In some cases (most notably when the leading coefficient of the glm is positive so the fitted curve does not converge to zero as x increases), converted to a probability distribution. In these cases, the distribution parameters are given as NA, but the fitted model itself is saved.

Usage

ddFit(x, ...)

## S3 method for class 'data.frame'
ddFit(
  x,
  distr = "standard",
  scVar = NULL,
  rCol = "r",
  expoCol = "exposure",
  ncarcCol = "ncarc",
  silent = FALSE,
  ...
)

## S3 method for class 'rings'
ddFit(
  x,
  distr = "standard",
  scVar = NULL,
  rCol = "r",
  expoCol = "exposure",
  ncarcCol = "ncarc",
  silent = FALSE,
  ...
)

## S3 method for class 'list'
ddFit(
  x,
  distr = "standard",
  scVar = NULL,
  rCol = "r",
  expoCol = "exposure",
  ncarcCol = "ncarc",
  silent = FALSE,
  ...
)

## S3 method for class 'xyLayout'
ddFit(
  x,
  distr = "standard",
  scVar = NULL,
  notSearched = NULL,
  rCol = "r",
  ncarcCol = "ncarc",
  unitCol = "turbine",
  silent = FALSE,
  ...
)

## S3 method for class 'ringscc'
ddFit(
  x,
  distr = "standard",
  scVar = NULL,
  rCol = "r",
  expoCol = "exposure",
  ncarcCol = "ncarc",
  silent = FALSE,
  ...
)

Arguments

Value

A list of fitted glm models as dd objects in a ddArray object if a vector of distributions is fit, or a single dd object if a single model is fit. The dd objects are lists that include the following elements:

glm

the fitted model

$distr

name of the distribution ("xep01", etc.)

$parms

vector of distribution parameter estimates (or NA if the model based on the MLE is not extensible)

$varbeta

the variance-covariance matrix of the glm parameter estimates. NOTE: This is identical to the covariance matrix from the glm, which can be extracted via summary(x)$cov.unscaled

$scVar

name of the (optional) search class variable (or NULL)

$ncarc

number of carcasses

$aicc

the AICc value of the fit

$n

number of rings

$k

number of parameters

$srad

search radius

When a dd object is printed, only a small subset of the elements are shown. To see a full list of the objects, use names(x). The elements can be extracted in the usual R way via $ or [[x]].

Examples

 data(layout_simple) 
 data(carcass_simple)
 sitedata <- initLayout(layout_simple) # initialize
 ringdata <- prepRing(sitedata) # format site layout data for modeling
 ringsWithCarcasses <- addCarcass(carcass_simple, data_ring = ringdata) # add carcasses to site
 distanceModels <- ddFit(ringsWithCarcasses) # fit distance models

Print S3 Objects in dwp Package

Description

dd, ddArray, and fmod objects are lists consisting of a great amount of data. Only a few of the elements are printed automatically. Other elements of object x can be viewed and extracted as with other lists in R, namely, by using the x$element or x[[element]] operator, where element is the name of one of the elements of x, all of which can be viewed via names(x).

Usage

## S3 method for class 'dd'
print(x, ...)

## S3 method for class 'ddArray'
print(x, ...)

## S3 method for class 'fmod'
print(x, ...)

Arguments

Value

no return value; output printed to the console

Simulation of Dispersion Parameters

Description

Simulation of Dispersion Parameters

Usage

ddSim(x, ...)

## S3 method for class 'dd'
ddSim(x, nsim = 1000, extent = "full", ...)

Arguments

Value

array with simulated beta parameters from the glm model, and their conversion to distribution parameters

Calculate Probability Functions for Distance Distributions

Description

Calculate the standard d/p/q/r family of R probability functions for distance distributions (dd) as well as the relative carcass density (rcd). Usage broadly parallels that of the d/p/q/r probability functions like dnorm, pnorm, qnorm, and rnorm.

Usage

ddd(x, model, parms = NULL, extent = "full", zrad = 200)

pdd(q, model, parms = NULL, extent = "full", zrad = 200, silent = FALSE)

qdd(p, model, parms = NULL, extent = "full", zrad = 200, subdiv = 1000)

rdd(n, model, parms = NULL, extent = "full", zrad = 200, subdiv = 1000)

rcd(x, model, parms = NULL, extent = "full", zrad = 200)

Arguments

Details

The probability density function (PDF(x) = f(x) = ddd(x, ...)) gives the probability that a carcass falls in a 1 meter ring centered at the turbine and with an outer radius of x meters. The cumulative distribution function [CDF(x) = F(x) = pdd(x, ...)] gives the probability that a carcass falls within x meters from the turbine. For a given probability, p, the inverse CDF [qdd(p,...)] gives the p quantile of carcass distances. For example, qdd(0.5,...) gives the median carcass distance, and qdd(0.9, ...) gives the radius that 90% of the carcasses are expected to fall in. Random carcass distances can be generated using rdd.

The relative carcass density function(rcd) gives relative carcass densities at a point x meters from a turbine. In general, rcd is proportional to PDF(x)/x, normalized so that the surface of rotation of rcd(x) has total volume of 1. There are more stringent contstraints on the allowable parameters in the fitted (or simulated) glm's because the integral of PDF(x)/x must converge.

Distributions may be extrapolated beyond the search radius to account for all carcasses, including those that land beyond the search radius (extent = "full"), or may be restricted to carcasses falling within the searched area (extent = "win"). Typically, in estimating dwp for a fatality estimator like eoa or GenEst, the full distributions would be used.

The probability functions have a number of purposes. A few of the more commonly used are listed below.

PDF and CDF (ddd and pdd):

• to calculate the probability that carcass lands at a distance x meters from the turbine (or, more precisely, within 0.5 meters of x) or within x meters from the turbine, use a scalar value of x and a single model (dd or ddSim) with ddd or pdd, repspectively;

• to account for uncertainty in the probabilities at x, use ddd or pdd for with scalar x and a simulated set of parameters from the fitted model (ddSim object). This would be useful for calculating confidence intervals for the probabilities;

• to calculate probabilities for a range of x values according to a single model, use a vector x with a dd object or a ddSim object with one row. This would be useful for drawing graphs of PDFs or CDFs;

• to calculate simulated probabilites for a range of x values, use a vector x and a ddSim object of simulated parameter sets. This would be useful for drawing confidence regions around a fitted PDF or CDF.

Inverse CDF (qdd):

• to calculate the distance that 100p% of the carcasses are expected to fall, use a scalar p in the interval (0, 1) and a single model (dd) or parameter set (ddSim with one row);

• to calculate account for the uncertainty in estimating the inverse CDF for a given p, use a scalar p and a ddSim object. This would be useful for calculating a confidence interval for, say, the median or the expected 90th percentile of carcass distances;

• to calculate the inverse CDF for a range of probabilities for a single model, use a vector p and a single model (dd or ddSim object with one row.

Random Carcasses Distances (rdd):

• to generate n random carcass distances for a given (fixed) model, use a dd object or a ddSim object with a single row;

• to generate n random carcass distances for a model and account for the uncertainty in estimating the model, use a ddSim object with n rows, where n is also used as the n argument in the call to rdd.

Relative Carcass Density (per m^2):

• to calculate the relative carcass density at a number of distances, use a vector x. This would be useful in generating maps of carcass density at a site.

Value

vector or matrix of values; a vector is returned unless model is a ddSim object with more than one row and is to be calculated for more than one value (x, q, p), in which case an array with dimensions length(x) by nrow(model) is returned (where "x" is x, q, or p, depending on whether ddd, pdd, or qdd is called).

Examples

data(layout_simple)
data(carcass_simple)
sitedata <- initLayout(layout_simple)
ringdata <- prepRing(sitedata)
ringsWithCarcasses <- addCarcass(carcass_simple, data_ring = ringdata)
distanceModels <- ddFit(ringsWithCarcasses)
modelEvaluations <- modelFilter(distanceModels)
bestModel <- modelEvaluations$filtered
pdd(100, model = bestModel) # estimated fraction of carcasses within 100m
ddd(1:150, model = bestModel) # estimated PDF of the carcass distances
qdd(0.9, model = bestModel) # estimated 0.9 quantile of carcass distances
rdd(1000, model = bestModel) # 1000 random draws from estimated carcass distribution

An Ordering of the Models by Degree of the Polynomial

Description

An Ordering of the Models by Degree of the Polynomial

Usage

degOrder

Format

An object of class character of length 17.

Full List of Names of Distributions

Description

Full List of Names of Distributions

Usage

distr_names

Format

An object of class character of length 17.

Density-Weighted Proportion

Description

This package is designed to analyze carcass dispersion data and fit models of carcass density as function of distance from turbine.

Data sets

carcass_polygon
carcass_simple
layout_eagle
layout_polygon
layout_simple
layout_xy
xyr
sieve_default

Main Command-Line Functions

initLayout, prepRing, readCarcass, addCarcass

import and format data

ddFit

fit carcass distribution models

estpsi, estdwp

estimate probability that carcass will lie in the searched area (psi) and the fraction of carcasses lying in the searched area ('dwp')

formatGenEst, exportGenEst

format and export 'dwphat' objects for use with GenEst

aic, modelFilter, stats, ddCI

statistics for fitted models

plot

S3 function for ddArray, dd, fmod, polygonLayout, psiHat, dwpHat objects.

ddd, pdd, qdd, rdd, rcd

probability functions for distance distributions

Potentially Useful Calculation and Editing Functions

ddSim, dd2ddSim

functions for simulating dd models

,

getncarc

extract the number of carcasses per turbine from a data set; method for many types of objects

,

cof2parms, cofOK, cofOK0, cofOKInf, constraints

functions for manipulating and checking model coefficients

Acins

calculate the area of the intersection of a circle and square sharing a common center

rmat, off

functions for constructing functions out of distribution information

exclude

simple function for excluding items from a superset

Estimate DWP

Description

Estimate the density-weighted proportion (DWP) of carcasses lying in the searched area at each turbine at a site. The calculation requires prior estimation of the expected proportion (psi) and the number of carcasses found (ncarc). NOTE: The carcass counts affect the uncertainty in the estimate of the fraction of carcasses in the searched area (DWP), and ncarc is required for accounting for uncertainty in estimates of DWP.

Usage

estdwp(x, ...)

## S3 method for class 'psiHat'
estdwp(x, ncarc, nboot = NULL, forGenEst = FALSE, silent = TRUE, ...)

## S3 method for class 'psiHatcc'
estdwp(x, ncarc, nboot = NULL, forGenEst = FALSE, silent = TRUE, ...)

Arguments

Value

list

Estimate Probability Carcass lands in Searched Area

Description

Estimated probability that carcass lands in searched area. This is an intermediate step in estimating dwp but is also interesting in its own right. The estimation involves integrating the modeled carcass distribution (model) over the search plots at the turbines. Data for the search plots is stored in the generic argument, x, which can take any of a number of different forms, as described in the Arguments section (below).

Usage

estpsi(x, ...)

## S3 method for class 'rings'
estpsi(x, model, extent = "full", nsim = 1000, zrad = 200, ...)

## S3 method for class 'ringscc'
estpsi(
  x,
  model,
  modnames = NULL,
  extent = "full",
  nsim = 1000,
  zrad = 200,
  ...
)

## S3 method for class 'xyLayout'
estpsi(x, model, extent = "full", nsim = 1000, zrad = 200, ...)

## S3 method for class 'rpA'
estpsi(x, model, extent = "full", nsim = 1000, zrad = 200, ...)

## S3 method for class 'rdat'
estpsi(x, model, extent = "full", nsim = 1000, zrad = 200, ...)

## S3 method for class 'data.frame'
estpsi(x, model, extent = "full", nsim = 1000, zrad = 200, ...)

Arguments

Value

A psiHat object, which is either 1) an array giving the expected fraction of carcasses lying in the searched area at each turbine with nsim rows and one column for each turbine + one row for the total; or 2) a list of such arrays, one for each carcass class if x is a ringscc object. The uncertainty in the expected fractions is characterized by simulation and reflected in the variation in psi values within each column.

Remove Particular Names from a Longer List

Description

Removes specific values (what) from a longer vector of values (from). By default, from = mod_standard, and the intent is to simplify the subsetting of ddArray objects created with the default standard models. For example, dmod2 <- dmod[exclude("lognormal")] would subset the list of models in mod_standard to exclude "lognomal". The default can be overridden by providing a specific vector for from (for example, dmod[exclude("lognormal", from = names(dmod)])).

Usage

exclude(what, from = mod_standard)

Arguments

Value

vector of names from "from" after excluding "what"

Export Estimated Density-Weighted Proportion to File in Proper GenEst Format

Description

GenEst imports DWP from files with comma-separated values (.csv), with a column giving turbine ID and a column of DWP values for each carcass class. Column lengths are equal to the number of turbines times the number of simulation reps (typically, nsim = 1000), giving nsim copies of DWP values for each turbine in a single column.

Usage

exportGenEst(dwp, file)

Arguments

Details

NOTE: The .csv file uses the English convention (used in USA, UK, Mexico, China, India, Australia, Japan, Korea, and others) with the comma ( , ) and not the semi-colon ( ; ) to separate values among different columns and uses the period ( . ) as the decimal mark. Although GenEst can seamlessly accommodate either format, users in countries where the comma or other character is used as a decimal mark may need to adjust their software settings or edit the data to be able to view it in a spreadsheet program (such as Excel).

Value

The function writes the formatted data to a .csv file and returns NULL.

Find suitable mmax for clipping improper priors for M

Description

Improper priors need to be clipped in order to be usable. fmmax and fmmax.ab find values of m that are large enough that the probability of exceeding is less than 0.0001 (depends on g and X).

Usage

fmmax(x, g)

fmmax.ab(x, pBa, pBb)

Arguments

Value

integer m such that Pr(M >= m) < 0.0001

Format DWP Estimate for Use in GenEst

Description

GenEst requires dwp data to be formatted as a data frame with columns for turbine ID and for estimated dwp for each carcass class. To incorporate uncertainty in the estimates, nsim simulated copies of the basic format are appended to the columns in the data set.

Usage

formatGenEst(dwphat)

Arguments

Value

an nsim*nturbine by nclass + 1 data frame, with columns for the turbine ID and for estimated dwp for each carcass class (e.g., large, medium, small, bat).

Simple Function to Extract Carcass Counts

Description

Carcass counts are easy to extract from any of the data structures, but it may be difficult to remember where to retrieve the data from for any particular structure. getncarc simplifies the task by having the same usage for all data types.

Usage

getncarc(x, ...)

## S3 method for class 'ringscc'
getncarc(x, ...)

## S3 method for class 'rings'
getncarc(x, ...)

## S3 method for class 'xyLayout'
getncarc(x, ...)

## S3 method for class 'ddArray'
getncarc(x, ...)

## S3 method for class 'ddArraycc'
getncarc(x, ...)

## S3 method for class 'dd'
getncarc(x, ...)

Arguments

Value

• scalar number of carcasses used in the fitted model (dd and ddArray objects

• vector of numbers of carcasses of each size used in the fitted models (ddArraycc objects)

• vector of carcass counts at each turbine and total at the site (xyLayout and rings objects

• list of vectors of carcass counts at each turbine for each carcass class

Incomplete Gamma Function

Description

Incomplete Gamma Function

Usage

incGamma(a, x, lower = FALSE)

Arguments

Details

The upper incomplete gamma function, following Wolfram Alpha, namely, incGamma(a, x) = \int_x^\infty e^{-t} * t^{a - 1}dt, calculated using pgamma. Within the dwp package, incGamma is used in the calculation of the cumulative distribution function (CDF) of the xep02 distribution (pxep02). NOTE: The function pracma::incgam also calculates incomplete gamma with pracma::incgam(x, a) = incGamma(a, x), but pracma::incgam is not vectorized and not used here.

Value

scalar or vector of length = max(length(x), length(a)), with values of the shorter recycled to match the length of the longer a la pnorm etc.

Create a Data Structure or Map for the Site Layout

Description

Read plot layout data and perform premliminary error-checking and formatting. Search plot layout data can come in any of several different formats, including shape files for search area polygons and turbine locations, R polygons, (x, y) coordinates, or simple description of search plot type for each turbine (square, circular, road & pad). A vector of distances along with a search radius is also accommodated by dwp, but these can be directly processed in prepRing without preprocessing in initLayout.

Usage

initLayout(
  data_layout,
  dataType = "simple",
  unitCol = "turbine",
  file_turbine = NULL,
  radCol = "radius",
  shapeCol = "shape",
  padCol = "padrad",
  roadwidCol = "roadwidth",
  nRoadCol = "n_road",
  xCol = "x",
  yCol = "y",
  ncarcCol = "ncarc",
  scCol = NULL,
  notSearched = NULL,
  quiet = FALSE
)

Arguments

Details

All the layout types (except for vector, which is addressed elsewhere) can accommodate patterns of seached and not searched areas. If the searched areas are subdivided into different search classes with different detection probabilities, then search plot layout data must be input either from shape files with non-intersecting polgons delineating the search classes or from x-y grid data. If there is more than one search class variable (for example, ground cover and search schedule), then the covariates may be entered in separate columns if the layout files give grid coordinates or may be combined into one column in the shape files. For example, ground visibility may be easy or difficult and search schedule may be 1-day or 14-day. These can be combined into a single column with values of, say, easy1, easy14, difficult1, and difficult14.

There must be a turbine ID column (unitCol) in each of the files. The individual turbine ID's must be syntactically valid R names, i.e., contain combinations of letters, numbers, dot ( . ), and underscores ( _ ) only and not begin with a number or a dot followed by a number. Other characters are not allowed: no spaces, hyphens, parentheses, etc.

If shape files are to be imported, both shape files (search area polygons and turbine locations) must have their three standard, mandatory component files (.shp, .shx, .dbf) stored in the same folder. Only the name of the .shp should be entered in the function call. Other components are automatically searched for and processed if available.

Value

A list or data frame with components appropriate to the type of data imported. The data structure is returned as an S3 class object, which other functions in dwp can recognize and properly process. There is minimal processing on the data after importing, but the structures are lightly error-checked and formatted for more thorough processing, depending on data type and analysis objectives. Typically, the layout data will be later processed by a call to prepRing to create a characterization of the searched area at the site by "rings", with tallies of searched area, search classes, and fraction of area searched in concentric, 1 meter rings around each turbine. The format of the output depends on the format of the input. There are several possibilities, including, each of which is an S3 object with characteristics specific to the imported data:

shapeLayout

List with elements:

• $layout = turbine search area configurations (polygons and multipolygons) from data_layout shape file as an sf object.

• $layoutAdj = polygons from $layout but recentered at (0, 0)

• $turbines = turbine data (as sf object)

• $unitCol = name of the column with turbine IDs (character string)

• $tset = turbine names (vector of character strings)

• $tcenter = locations of turbine centers (nturb by 2 array) with UTMs of turbine locations, extracted and simplified from $turbines. Column names are X and Y, measuring meters from a reference point. Row names are the names of the turbines.

simpleLayout

Data frame with columns:

• turbine = turbine IDs (syntactically valid R names)

• radius = search radius. If shape = "square", then radius is 1/2 the width of the square.

• shape = general descriptor of the shape of the search plot as "square", "circular", or "RP" (for roads and pads search).

• padrad = radius of the turbine pad (assumed circular)

• roadwidth = width of the access road(s)

• n_road = number of access roads

polygonLayout

List of polygons, one for each turbine. The maximum search radius at any turbine is assigned as an attribute (attr(, "rad")).

xyLayout

List with elements:

• xydat = data frame with columns for turbine names, x and y coordinates of 1m grid centers spanning the searched area, number of carcasses found in each grid cell, and optional covariates.

• tcenter = matrix giving turbine locations (x, y), with row names = turbine names.

• ncarc = vector giving the number of carcasses found at each turbine.

• unitCol = name of the column where turbine IDs are stored in xydat.

• tset = names of the searched turbines

Examples

data(layout_simple)
# converts properly formatted dataframe to 'simpleLayout' object
initLayout(layout_simple) 

data(layout_xy)
initLayout(layout_xy, dataType = "xy")

data(layout_polygon)
initLayout(layout_polygon, dataType = "polygon", unitCol = "turbine")

Example Bare Vector Format for Eagle Data

Description

Example Bare Vector Format for Eagle Data

Usage

layout_eagle

Format

An object of class data.frame with 60 rows and 3 columns.

Example Polygon Data for Site Layout

Description

Example Polygon Data for Site Layout

Usage

layout_polygon

Format

A data frame illustrating the required raw data format for using standard R polygons to characterize a site layout. There must be three columns: one giving turbine IDs (turbine) and columns for the x and y coordinates that delineate the plot layouts. Turbine IDs must be syntactitally valid R names, that is, combinations of letters, numbers, underscores ( _ ) and periods ( . ) and no spaces, hyphens, or other special characters. Names must not begin with a number, so 1, 2, 3, ..., 3B1, and .72S are NOT valid names. Coordinates shoud be in meters relative to a turbine at (0, 0).

Example Simple Geometry Data Format for Site Layout

Description

Example Simple Geometry Data Format for Site Layout

Usage

layout_simple

Format

A data frame illustrating an import format for a simple description of a site layout by turbine. Each turbine (turbine) is classed according to the shape of its search plot, either circular, square, or RP (search on the roads and turbine pad only). For circular plots, all ground within radius meters of the turbine is searched. For square plots, the radius is half the width of the square along the x-axis, NOT the distance to the corner. For RP plots, the radius is the maximum distance searched on the roads. The geometry of the RP also includes a circular turbine pad with radius padrad, a road width of roadwidth meters, and the number of roads (n_road) searched out to radius meters from the turbine.

Example Data for Site Layout on an (x, y) Grid

Description

Example Data for Site Layout on an (x, y) Grid

Usage

layout_xy

Format

A data frame illustrating the required raw data format for using a grid format to characterize a site layout. There are five columns: one giving turbine IDs (turbine), columns for the x and y coordinates on 1 m. grids that overlay the search plot, a column giving the carcass count in each grid cell, and a column giving the distance of each cell from the turbine. There is only one turbine, searched on road and pad out. Coordinates are in meters relative to the turbine at (0, 0).

Names of All the Available Models

Description

Names of All the Available Models

Usage

mod_all

Format

An object of class character of length 17.

Vector of Colors Used in Graphs of Fitted Models

Description

Vector of Colors Used in Graphs of Fitted Models

Usage

mod_color

Format

An object of class character of length 17.

Vector of Line Types Used in Graphs of Fitted Models

Description

Vector of Line Types Used in Graphs of Fitted Models

Usage

mod_lty

Format

An object of class numeric of length 17.

Vector of GLM Offsets for Available Models

Description

Vector of GLM Offsets for Available Models

Usage

mod_offset

Format

An object of class character of length 17.

Vector of Names of Standard Models

Description

Vector of Names of Standard Models

Usage

mod_standard

Format

An object of class character of length 12.

Vector of Names of Models Available for Grid Layout

Description

Vector of Names of Models Available for Grid Layout

Usage

mod_xy

Format

An object of class character of length 8.

Run Models through a Sieve to Filter out Dubious Fits

Description

A set of fitted models (ddArray) is filtered according to a set of criteria that test for high AIC, high-influence points, and plausibility of the tail probabilities of each fitted distribution. modelFilter will either auto-select the best model according to a set of pre-defined, objective criteria or will will return all models that meet a set of user-defined, or default criteria. A table of how the models score according to each criterion is printed to the console.

Usage

modelFilter(dmod, sieve = "default", quiet = FALSE)

Arguments

Details

The criteria to test are entered in a list (sieve) with components:

1. $rtail = vector of probabilities that define a checkpoints on distributions to avoid situations where a model that may fit well within the range of data is nonetheless implausible because it predicts a significant or substantial probability of carcasses falling great distances from the nearest turbine. The default is to check whether or not a distribution predicts that less than 50% of carcasses fall within 80 meters, 90% within 120 meters, 95% within 150 meters, or 99% within 200 meters. Distributions that fall below any of these points (for example predicting only 42% within 80 meters or only 74% within 120 meters) fail the default rtail test. The format of the default for the test is $rtail = c(p80 = 0.5, p120 = 0.90, p150 = 0.95, p200 = 0.99). Users may override the default by using, for example, sieve = list(rtail = c(p80 = 0.8, p120 = 0.99, p150 = 0.99, p200 = 0.999)) in the argument list for a more stringent test or for a situation where turbines are small or winds are light. Alternatively, users may forego the test altogether by entering sieve = list(rtail = FALSE). If specific probabilities are provided, they must be in a vector of length 4 with names "p80" etc. as in the examples above.

2. $ltail = vector of probabilities that define checkpoints on distributions to avoid situations where the search radius is short and a distribution that fits the limited data set well but crashes to zero just outside the search radius. The default is to check whether or not a distribution predicts that greater than 50% of carcasses fall with 20 meters or 90% within 50 meters. Distributions that pass above either of these checkpoints (for example predicting 61% of carcasses within 20 meters or 93% within 50 meters) are eliminated by the default ltail test. The format of the default for the test is $ltail = c(p20 = 0.5, p50 = 0.90). Users may override the default by using, for example, sieve = list(rtail = c(p20 = 0.6, p50 = 0.8)) in the argument list for a situation where it is known that carcasses beyond 50 meters are common.

3. $aic = a numeric scalar cutoff value for model's delta AICc scores. Models with AICc scores exceeding the minimum AICc among all the fitted models by sieve$aic or more fail the test. The default value is 10. Users may override the default by using, for example, sieve = list(aic = 7) in the argument list to use a delta AIC score of 7 as the cutoff or may forego the test altogether by setting sieve = list(aic = FALSE)

4. $hin = TRUE or FALSE to test for high influence points, the presence of which cast doubt on the reliability of the model. The function defines "high influence" as models with high leverage points, namely, points with \frac{h}{1 - h} > \frac{2p}{n - 2p} (where h is leverage, p is the number of parameters in the model, and n is the search radius) with Cook's distance > 8/(n - 2*p). The criteria for high influence points were adapted from Brian Ripley's GLM diagnostics package boot (glm.diag). The test is perhaps most valuable in identifying distributions with high probability of carcasses landing well beyond what could reasonably be expected.

Several choices of pre-defined sieves are available (or, as described above, users may define their own criteria):

sieve = "default"

The models are ordered by the following criteria:

1. extensibility

2. weight of right tail (discounting models that predict implausibly high proportions of carcasses beyond the search radius)

3. weight of the left tail (discounting models that predict implausibly high proportions of carcasses near the turbines)

4. AICc test (discounting models with delta AICc > 10)

5. high influence points (discounting models in which one or more of the data points exert a high influence on the fitted model, according to Ripley's GLM diagnostics package boot (glm.diag))

6. ranking by AICc

Precise definitions of the default sieve parameters are given in sieve_default.

sieve = NULL

Returns a list of the extensible models without scoring them by other model selection criteria.

sieve = "win"

Sorts models by high-influence points and AICc

sieve = list(<custom>)

User provides a custom sieve, which may be a modification of the default sieve or de novo. To modify the default, use, for example, sieve = list(hin = FALSE) to disable the hin test but keep the other default tests, or sieve = list(aic = 7) to use 7 rather than 10 as the AIC cutoff, or sieve = list(ltail = c(p20 = 0.3, p50 = 0.8)) to use a more stringent left tail test that requires CDF graphs to pass below the points (20, 0.3) and (50, 0.8). Custom ltail and rtail parameters must match the formats of the default tests, but their probabilities may vary. To turn off the aic filter, use sieve = list(aic = Inf). To turn off the ltail filter, use sieve = list(ltail = c(p20 = 1, p50 = 1)). To turn off the rtail filter, use sieve = list(rtail = c(p80 = 0, p120 = 0, p150 = 0, p200 = 0)). These custom components may be mixed and matched as desired.

Value

An fmod object, which is an unordered list of extensible models if sieve = NULL; otherwise, a list of class fmod with following components:

$filtered

the selected dd object or a ddArray list of models that passed the tests

$scores

a matrix with all models tested (rownames = model names) and the results of each test (columns aic_test, rtail, ltail, hin, aic)

$sieve

the test criteria, stored in a list with

• $aic_test = cutoff for AIC

• $hin = boolean to indicate whether high influence points were considered

• $rtail = numeric vector giving the probabilities that the right tail of the distribution must exceed at distances of 80, 120, 150, and 200 meters in order to pass

• $ltail = numeric vector giving the probabilities that the left tail of the distribution must NOT exceed at distances of 20 and 50 meters in order to pass

models

a list (ddArray object) of all models tested

note

notes on the tests

When a fmod object is printed, only a small subset of the elements are shown. To see a full list of the objects, use names(x), where x is the name of the fmod return value. The elements can be extracted in the usual R way via, for example, x$sieve or x[["sieve"]].

Examples

 data(layout_simple)
 data(carcass_simple)
 sitedata <- initLayout(layout_simple)
 ringdata <- prepRing(sitedata)
 ringsWithCarcasses <- addCarcass(carcass_simple, data_ring = ringdata)
 distanceModels <- ddFit(ringsWithCarcasses)
 stats(distanceModels)
 stats(distanceModels[["tnormal"]])
 stats(distanceModels[["lognormal"]])
 

Convert Distribution Name + Parameters to ddSim Object

Description

Utility function to format a distribution name and a vector of its parameter values to a ddSim object for use in the p/d/r/q family of functions

Usage

mpp2ddSim(distr, parms)

Arguments

Value

a ddSim object with srad = NA

Vector of Names of Models with Natural Offset

Description

The natural offset is the area (m^2) searched at a given distance. Models that use the natural offset are referred to as "natural". Other models may use different offsets which alter the shape of the curve with distance in an a priori way that is unaffected by the data.

Usage

natural

Format

An object of class logical of length 17.

Utility Function for Constructing Offsets for GLMs

Description

This is a simple utility function for calculating offsets when exposure is assumed to be 100 calculating fitted distributions (PDF and CDF) but cannot be used in the fitting of the distributions themselves because it does not account for incomplete search coverages at given distances.

Usage

off(r, distr)

Arguments

Value

A vector of offset values to use with distances r when fitting the distr model.

Check Parameter Value Validity the Distribution

Description

Performs a ouick check on whether the parameters given in parms are valid for the distr.

Usage

parOK(parms, distr)

Arguments

Value

vector (or scalar) of 0s, 1s, and 2s to indicate whether the parameters are non-extensible (i.e., flat-out bogus), valid for the distribution, or valid for the distribution and give finite point densities.

Default Graphics Parameters

Description

Default Graphics Parameters

Usage

par_default

Format

An object of class list of length 65.

List of Names of the Distribution Parameters Associated with Respective Models

Description

List of Names of the Distribution Parameters Associated with Respective Models

Usage

parm_name

Format

An object of class list of length 17.

Calculate posterior distribution of M and extract statistics (M* and CI)

Description

Calculation of the posterior distribution of total mortality (M) given the carcass count, overall detection probability (g), and prior distribtion; calculation of summary statistics from the posterior distribution of M, including M* and credibility intervals.

Usage

postM(x, g, prior = "IbinRef", mmax = NA)

postM.ab(x, Ba, Bb, prior = "IbinRef", mmax = NULL)

calcMstar(pMgX, alpha)

MCI(pMgX, crlev = 0.95)

Arguments

Details

The functions postM and postM.ab return the posterior distributions of M|(X, g) and M|(X, Ba, Bb), respectively, where Ba and Bb are beta distribution parameters for the estimated detection probability. postM and postM.ab include options to to specify a prior distribution for M and a limit for truncating the prior to disregard implausibly large values of M and make the calculations tractable in certain cases where they otherwise might not be. Use postM when g is fixed and known; otherwise, use postM.ab when uncertainty in g is characterized in a beta distribution with parameters Ba and Bb. The non-informative, integrated reference prior for binomial random variables is the default (prior = "IbinRef"). Other options include "binRef", "IbetabinRef", and "betabinRef", which are the non-integrated and integrated forms of the binomial and betabinomial reference priors (Berger et al., 2012). For X > 2, the integrated and non-integrated reference priors give virtually identical posteriors. However, the non-integrated priors assign infinite weight to m = 0 and return a posterior of Pr(M = 0| X = 0, \hat{g}) = 1, implying absolute certainty that the total number of fatalities was 0 if no carcasses were observed. In addition, a uniform prior may be specified by prior = "uniform". Alternatively, a custom prior may be given as a 2-dimensional array with columns for m and Pr(M = m), respectively. The first column (m) must be sequential integers starting at m = 0. The second column gives the probabilities associated with m, which must be non-negative and sum to 1. The named priors ("IbinRef", "binRef", "IbetabinRef", and "betabinRef") are functions of m and defined on m=0,1,2,... without upper bound. However, the posteriors can only be calculated for a finite number of m's up to a maximum of mmax, which is set by default to the smallest value of m such that Pr(X \leq x | m, \hat{g}) < 0.0001, where x is the observed carcass count, or, alternatively, mmax may be specified by the user.

Value

The functions postM and postM.ab return the posterior distributions of M | (X, g) and M | (X, Ba, Bb), respectively. The functions calcMstar and MCI return M^* value and credibility interval for the given posterior distribution, pMgX (which may be the return value of postM or postM.ab) and \alpha value or credibility level.

Format a Search Layout into Rings for Analysis

Description

A function for creating a characterization of the search plot at each turbine by rings. The ground around each turbine is divided into 1 meter concentric rings out to the limit of the search plot. The amount of area searched in each ring and search class (if a search class column is present in the data) at each turbine is calculated, along with the fraction of area searched in each ring. In addition, sum totals of the area in each ring and the average fraction of the area searched in each ring across all turbines at the site are tallied as well. This is a convenient structure for the Poisson regressions that are used to estimate the carcass distributions with respect to distance from the turbines, the probabilities of carcasses landing in the searched areas, and the fraction of carcasses in the searched area.

Usage

prepRing(x, ...)

## S3 method for class 'shapeLayout'
prepRing(x, scVar = NULL, notSearched = NULL, silent = FALSE, ...)

## S3 method for class 'simpleLayout'
prepRing(x, ...)

## S3 method for class 'numeric'
prepRing(x, srad, ...)

## S3 method for class 'polygonLayout'
prepRing(x, ...)

Arguments

Value

an object of class rings, which is a list with components

$rdat

list of data frames giving the area searched ("exposure"), in a 1 meter ring with outer radius "r" and the number of carcasses found "ncarc" in each ring, with search class scVar optional. There is also a summary data frame $rdat[["total"]] that sums the exposures and carcass counts for all turbines across the site. The $rdat[["total"]] is the data frame used in fitting the GLMs.

$rpA

list of data frames giving the proportion of area included in the searches ("pinc") in each ring ("r"). and the number of carcasses found "ncarc" in each ring, with search class scVar optional. There is also a summary data frame that sums the exposures and carcass counts for all turbines across the site. The $rpA data frames are used in estimating the probability of carcasses falling in the searched area at each turbine, which, in turn is used for calculating dwp

$srad

the maximum search radius at any of the turbines

$ncarc

vector of the number of carcasses at each turbine with names equal to the turbine names.

$scVar

name of the search class variable(s) or NULL

$tcenter

locations of turbine centers (nturb x 2 matrix) with UTMs of turbine locations. Column names are X and Y. Row names are the names of the turbines.

Internal Utility Function to Parse and Format Model for Calculating Psihat

Description

Internal Utility Function to Parse and Format Model for Calculating Psihat

Usage

prepmod(model, nsim)

Arguments

Value

ddSim object of simulated distribution model parameters

Simple Extension of a dd Model beyond the Search Radius

Description

Extend a distance model beyond the search radius via multiplication by a fixed, assumed constant rather than the default normalization used for extensible models. psi_extend should not be used with psiHat objects that were calculated with extent = "full".

Usage

psi_extend(psi, fwin)

Arguments

Value

psiHat object extended beyond the search radius

Import Carcass Observations Locations from Shape Files

Description

Carcass coordiates (x, y) and turbine IDs are read using st_read and formatted for adding to rings data structures for analysis.

Usage

readCarcass(file_cod, unitCol = "turbine", quiet = FALSE)

Arguments

Value

a shapeCarcass object, which is a list with $carcasses, which is a sf representation of the shape file file_cod data; $unitCol, which is the name of the unit column; and $ncarc, which is a vector of carcass counts at the turbines listed in unitCol. The elements of the $ncarc are named by turbines at which they were found.

Simple Utility Function Used in Optimizing the GLM

Description

A simple utility function that is used in fitting a GLM, creating a matrix of "x" values for use in the polynomial part of a xep-type model.

Usage

rmat(r, distr)

Arguments

Value

array with length(r) rows and p columns, where p is the number of parameters in the glm (including the intercept). The first column is all 1s, and the remaining columns are functions of r, specifically, log(r), r, r^2, r^3, or 1/r, depending on what the distribution requires.

Test Criteria for Model Selection

Description

Test Criteria for Model Selection

Usage

sieve_default

Format

A list containing the parameters used for test criteria in model selection an ddArray objects. The sieve_default values are used as a default in modelFilter. If desired, users may create their own tests, using sieve_default as a template. The same list elements must all be present and have the same structure as the defaults, namely:

$aic

the cutoff for DeltaAIC scores; models with higher scores are removed from further consideration. Default is $aic = 10

$hin

a boolean to indicate whether or not to use high leverage points as a criterion for model selection. Default is $hin = TRUE

$rtail

a vector of probabilities that the fitted model must exceed at 80, 120, 150, and 200 meters. Default is rtail = c(p80 = 0.50, p120 = 0.90, p150 = 0.95, p200 = 0.99). Custom test parameters must be a vector probabilities with "p80", "p120", "p150", and "p200" in the names.

ltail

a vector of probabilities that a fitted model must not exceed at 20 and 50 meters. Default is ltail = c(p20 = 0.50, p50 = 0.90). Custom test parameters must be a vector of probabilities with "p20" and "p50" in names.

Test Criteria for Model Selection within Search Area

Description

Test Criteria for Model Selection within Search Area

Usage

sieve_win

Format

A list containing the parameters used for test criteria in model selection in ddArray objects. The sieve_win values are used when either sieve = "win" or extent = "win" in arg list of modelFilter. The sieve parameters are:

$aic = 10

the cutoff for DeltaAIC scores; models with higher scores are removed from further consideration.

$hin = T

a boolean to indicate whether or not to use high leverage points as a criterion for model selection.

$rtail

Appropriate only for extrapolating beyond the search radius. Automatically disabled viartail = sieve_default$rtail * 0.

ltail

Appropriate only for extrapolating beyond the search radius. Automaticall disabled via ltail = sieve_default$ltail * 0 + 1

Display a Tables of Summary Statistics for Distance Distributions

Description

Calculate summary statistics for a single distance distribution (dd object), an array of distance distributions all fit to the same data set (ddArray), or a list of arrays of distance distributions fit for different carcass classes but the same site layout (ddArraycc).

Usage

stats(x, ...)

## S3 method for class 'dd'
stats(x, extent = "full", zrad = 200, ...)

## S3 method for class 'ddArray'
stats(x, extent = "full", zrad = 200, ...)

## S3 method for class 'ddArraycc'
stats(x, extent = "full", zrad = 200, ...)

Arguments

Value

list (or list of lists if x is ddArray) with $model giving the model parameters and $stats giving the median, and 75th, 90th, and 95th quantiles of carcass distances and the estimated probability a carcass falls within the search area according to each model

Subset Data from an Imported and Formatted Shape File

Description

Subset Data from an Imported and Formatted Shape File

Usage

## S3 method for class 'shapeCarcass'
subset(x, subset, select, ...)

## S3 method for class 'shapeLayout'
subset(x, subset, select, ...)

Arguments

Value

object of the same class as x, subsetted to values of select equal to some element in subset.

Locations of All Carcasses in Grid Data

Description

Locations of All Carcasses in Grid Data

Usage

xyr

Format

matrix with columns x, y, r for all 100 carcasses in the simulation to generate the carcass data for the xy grid that was searched on road and pad.