Various functions used to specify key and adjustment functions for detection functions.
Usage
detfct(distance, ddfobj, select=NULL, index=NULL, width=NULL,
standardize = TRUE, stdint=FALSE, left=0)
adjfct.cos(distance, scaling = 1, adj.order, adj.parm = NULL, adj.exp=FALSE)
adjfct.poly(distance, scaling = 1, adj.order, adj.parm = NULL, adj.exp=FALSE)
adjfct.herm(distance, scaling = 1, adj.order, adj.parm = NULL, adj.exp=FALSE)
scalevalue(key.scale, z)
keyfct.hn(distance, key.scale)
keyfct.hz(distance, key.scale, key.shape)
keyfct.gamma(distance, key.scale, key.shape)
fx(distance,ddfobj,select=NULL,index=NULL,width=NULL,
standardize=TRUE,stdint=FALSE, left=0)
fr(distance,ddfobj,select=NULL,index=NULL,width=NULL,
standardize=TRUE,stdint=FALSE)
distpdf(distance,ddfobj,select=NULL,index=NULL,width=NULL,standardize=TRUE,
stdint=FALSE,point=FALSE, left=0)Arguments
- distance
vector of distances
- ddfobj
distance sampling object (see
create.ddfobj)- select
logical vector for selection of data values
- index
specific data row index
- width
(right) truncation width
- standardize
logical used to decide whether to divide through by the function evaluated at 0
- stdint
logical used to decide whether integral is standardized
- point
if TRUE, point counts; otherwise line transects
- left
(left) truncation distance
- z
design matrix for scale function
- key.scale
vector of scale values
- key.shape
vector of shape values
- adj.order
vector of adjustment orders
- adj.parm
vector of adjustment parameters
- scaling
the scaling for the adjustment terms
- adj.exp
if TRUE uses exp(adj) for adjustment to keep f(x)>0
Value
For detfct, the value is a vector of detection probabilities
For keyfct.*, vector of key function evaluations
For adjfct.*, vector of adjustment series evaluations
For scalevalue, vector of the scale parameters.
Details
Multi-covariate detection functions (MCDS) are represented by a function \(g(x,w,\theta)\) where x is distance, z is a set of covariates and \(\theta\) is the parameter vector. The functions are defined such that \(g(0,w,\theta)=1\) and the covariates modify the scale \((x/\sigma)\) where a log link is used to relate \(\sigma\) to the covariates, \(\sigma=exp(\theta*w)\). A CDS function is obtained with a constant \(\sigma\) which is equivalent to an intercept design matrix, z.
detfct will call either a gamma, half-normal, hazard-rate or uniform
function only returning the probability of detection at that distance. In
addition to the simple model above, we may specify adjustment terms to fit
the data better. These adjustments are either Cosine, Hermite and simple
polynomials. These are specified as arguments to detfct, as detailed
below.
detfct function which calls the others and assembles the final result
using either key(x)[1+series(x)] or
(key(x)[1+series(x)])/(key(0)[1+series(0)]) (depending on the value of
standardize).
keyfct.* functions calculate key function values and adjfct.*
calculate adjustment term values.
scalevalue for either detection function it computes the scale with
the log link using the parameters and the covariate design matrix
fx, fr non-normalized probability density for line transects
and point counts respectively
References
Marques, F. F. C., & Buckland, S. T. (2003). Incorporating covariates into standard line transect analyses. Biometrics, 59(4), 924-935.
Buckland, S. T., Anderson, D. R., Burnham, K. P., Laake, J. L., Borchers, D. L., & Thomas, L. (2004). Advanced Distance Sampling. Oxford University Press, Oxford, UK.
Becker, E. F. and P. X. Quang. 2009. A gamma-shaped detection function for line transect surveys with mark-recapture and covariate data. Journal of Agricultural Biological and Environmental Statistics 14:207-223.