fit.ns: Fitting a Neyman-Scott point process model
In b-steve/nspp: Fitting point process models via the Palm likelihood

Description Usage Arguments Details Value References Examples

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).

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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)

`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.

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

lambda, the expected number of children generated per parent (when child.dist = "pois").
p, the proportion of the x possible children are generated (when child.dist = "binomx").
kappa, the average length of the surface phase of a diving cetacean (when child.dist = "twoplane"; see Stevenson, Borchers, and Fewster, in prep).
sigma, the standard deviation of dispersion along each dimension (when disp = "gaussian").
tau, the maximum distance a child can be from its parent (when disp = "uniform")

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.

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.

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.

## 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)