fit.ns: Fitting a Neyman-Scott point process model

Description Usage Arguments Details Value References Examples

View source: R/fit-ns.r

Description

Estimates parameters for a Neyman-Scott point process by maximising the Palm likelihood. This approach was first proposed by Tanaka et al. (2008) for two-dimensional Thomas processes. Further generalisations were made by Stevenson, Borchers, and Fewster (in prep) and Jones-Todd (2017).

Usage

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fit.ns(points, lims, R, disp = "gaussian", child.dist = "pois",
  child.info = NULL, sibling.list = NULL, edge.correction = "pbc",
  start = NULL, bounds = NULL, trace = FALSE)

Arguments

points

A matrix containing locations of observed points, where each row corresponds to a point and each column corresponds to a dimension.

lims

A matrix with two columns, corresponding to the upper and lower limits of each dimension, respectively.

R

Truncation distance for the difference process.

disp

A character string indicating the distribution of children around their parents. Use "gaussian" for multivariate normal dispersion with standard deviation sigma, or "uniform" for uniform dispersion within distance tau of the parent.

child.dist

The distribution of the number of children generated by a randomly selected parent. For a Poisson distribution, use "pois"; for a binomial distribution, use "binomx", where "x" is replaced by the fixed value of the number of independent trials (e.g., "binom5" for a Binomial(5, p) distribution, and "binom50" for a Binomial(50, p) distribution); and "twoplane" for a child distribution appropriate for a two-plane aerial survey.

child.info

A list of further information that is required about the distribution for the number of children generated by parents. See ‘Details’.

sibling.list

An optional list that comprises (i) a component named sibling.mat, containing a matrix such that the jth entry in the ith row is TRUE if the ith and jth points are known siblings, FALSE if they are known nonsiblings, and NA if their sibling status is not known; (ii) alpha, providing the probability that a sibling is successfully identified as a sibling; and (iii) beta, providing the probability that a nonsibling is successfully identified as a nonsibling.

edge.correction

The method used for the correction of edge effects. Either "pbc" for periodic boundary conditions, or "buffer" for a buffer-zone correction.

start

A named vector of starting values for the model parameters.

bounds

A list with named components. Each component should be a vector of length two, giving the upper and lower bounds for the named parameter.

trace

Logical; if TRUE, parameter values are printed to the screen for each iteration of the optimisation procedure.

Details

The parameter D is the density of parent points, which is always estimated. Possible additional parameters are

The "child.info" argument is required when child.dist is set to "twoplane". It must be a list that comprises (i) a component named w, providing the halfwidth of the detection zone; (ii) a component named b, providing the halfwidth of the survey area; (iii) a component named l, providing the time lag between planes (in seconds); and (iv) a component named tau, providing the mean dive-cycle duration. See Stevenson, Borchers, and Fewster (in prep) for details.

Value

An R6 reference class object. Extraction of the information held within is best handled by functions coef.nspp, confint.nspp, summary.nspp, and plot.nspp.

References

Tanaka, U., Ogata, Y., and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal, 50: 43–57.

Stevenson, B. C., Borchers, D. L., and Fewster, R. M. (in prep) Trace-contrast methods to account for identification uncertainty on aerial surveys of cetacean populations.

Jones-Todd, C. M. (2017) Modelling complex dependencies inherent in spatial and spatio-temporal point pattern data. PhD thesis, University of St Andrews.

Examples

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## Fit model.
fit <- fit.ns(example.2D, lims = rbind(c(0, 1), c(0, 1)), R = 0.5)
## Print estimates.
coef(fit)
## Plot the estimated Palm intensity.
plot(fit)

b-steve/nspp documentation built on June 4, 2017, 12:10 a.m.